Results of Elliptic Integrals II: Difference between revisions

Latest revision as of 07:16, 25 May 2021

DLMF	Formula	Constraints	Maple	Mathematica	Symbolic Maple	Symbolic Mathematica	Numeric Maple	Numeric Mathematica
19.22.E1	${\displaystyle{\displaystyle R_{F}\left(0,x^{2},y^{2}\right)=R_{F}\left(0,xy,a% ^{2}\right)}}$ `\CarlsonsymellintRF@{0}{x^{2}}{y^{2}} = \CarlsonsymellintRF@{0}{xy}{a^{2}}`		0.5int(1/(sqrt(t+0)sqrt(t+(x)^(2))sqrt(t+(y)^(2))), t = 0..infinity) = 0.5int(1/(sqrt(t+0)sqrt(t+xy)*sqrt(t+(a)^(2))), t = 0..infinity)	EllipticF[ArcCos[Sqrt[0/(y)^(2)]],((y)^(2)-(x)^(2))/((y)^(2)-0)]/Sqrt[(y)^(2)-0] == EllipticF[ArcCos[Sqrt[0/(a)^(2)]],((a)^(2)-x*y)/((a)^(2)-0)]/Sqrt[(a)^(2)-0]	Aborted	Failure	Skipped - Because timed out	Failed [102 / 108] Result: Complex[0.1731783664325578, 0.8740191847640398] Test Values: {Rule[a, -1.5], Rule[x, 1.5], Rule[y, -1.5]} Result: Complex[0.4406854652170371, 0.9732684211375591] Test Values: {Rule[a, -1.5], Rule[x, 1.5], Rule[y, -0.5]} ... skip entries to safe data
19.22.E2	${\displaystyle{\displaystyle 2R_{G}\left(0,x^{2},y^{2}\right)=4R_{G}\left(0,xy% ,a^{2}\right)-xyR_{F}\left(0,xy,a^{2}\right)}}$ `2\CarlsonsymellintRG@{0}{x^{2}}{y^{2}} = 4\CarlsonsymellintRG@{0}{xy}{a^{2}}-xy\CarlsonsymellintRF@{0}{xy}{a^{2}}`		Error	2Sqrt[(y)^(2)-0](EllipticE[ArcCos[Sqrt[0/(y)^(2)]],((y)^(2)-(x)^(2))/((y)^(2)-0)]+(Cot[ArcCos[Sqrt[0/(y)^(2)]]])^2EllipticF[ArcCos[Sqrt[0/(y)^(2)]],((y)^(2)-(x)^(2))/((y)^(2)-0)]+Cot[ArcCos[Sqrt[0/(y)^(2)]]]Sqrt[1-k^2Sin[ArcCos[Sqrt[0/(y)^(2)]]]^2]) == 4Sqrt[(a)^(2)-0](EllipticE[ArcCos[Sqrt[0/(a)^(2)]],((a)^(2)-xy)/((a)^(2)-0)]+(Cot[ArcCos[Sqrt[0/(a)^(2)]]])^2EllipticF[ArcCos[Sqrt[0/(a)^(2)]],((a)^(2)-xy)/((a)^(2)-0)]+Cot[ArcCos[Sqrt[0/(a)^(2)]]]Sqrt[1-k^2Sin[ArcCos[Sqrt[0/(a)^(2)]]]^2])- xyEllipticF[ArcCos[Sqrt[0/(a)^(2)]],((a)^(2)-x*y)/((a)^(2)-0)]/Sqrt[(a)^(2)-0]	Missing Macro Error	Failure	-	Failed [108 / 108] Result: Complex[-0.848574889541176, -1.6278775384876862] Test Values: {Rule[a, -1.5], Rule[x, 1.5], Rule[y, -1.5]} Result: -2.356194490192345 Test Values: {Rule[a, -1.5], Rule[x, 1.5], Rule[y, 1.5]} ... skip entries to safe data
19.22.E3	${\displaystyle{\displaystyle 2y^{2}R_{D}\left(0,x^{2},y^{2}\right)=\tfrac{1}{4% }(y^{2}-x^{2})R_{D}\left(0,xy,a^{2}\right)+3R_{F}\left(0,xy,a^{2}\right)}}$ `2y^{2}\CarlsonsymellintRD@{0}{x^{2}}{y^{2}} = \tfrac{1}{4}(y^{2}-x^{2})\CarlsonsymellintRD@{0}{xy}{a^{2}}+3\CarlsonsymellintRF@{0}{xy}{a^{2}}`		Error	2(y)^(2) 3(EllipticF[ArcCos[Sqrt[0/(y)^(2)]],((y)^(2)-(x)^(2))/((y)^(2)-0)]-EllipticE[ArcCos[Sqrt[0/(y)^(2)]],((y)^(2)-(x)^(2))/((y)^(2)-0)])/(((y)^(2)-(x)^(2))((y)^(2)-0)^(1/2)) == Divide[1,4]((y)^(2)- (x)^(2))3(EllipticF[ArcCos[Sqrt[0/(a)^(2)]],((a)^(2)-xy)/((a)^(2)-0)]-EllipticE[ArcCos[Sqrt[0/(a)^(2)]],((a)^(2)-xy)/((a)^(2)-0)])/(((a)^(2)-xy)((a)^(2)-0)^(1/2))+ 3EllipticF[ArcCos[Sqrt[0/(a)^(2)]],((a)^(2)-x*y)/((a)^(2)-0)]/Sqrt[(a)^(2)-0]	Missing Macro Error	Failure	-	Failed [108 / 108] Result: Indeterminate Test Values: {Rule[a, -1.5], Rule[x, 1.5], Rule[y, -1.5]} Result: Indeterminate Test Values: {Rule[a, -1.5], Rule[x, 1.5], Rule[y, 1.5]} ... skip entries to safe data
19.22.E4	${\displaystyle{\displaystyle(p_{+}^{2}-p_{-}^{2})R_{J}\left(0,x^{2},y^{2},p^{2% }\right)=2(p_{+}^{2}-a^{2})R_{J}\left(0,xy,a^{2},p_{+}^{2}\right)-3R_{F}\left(% 0,xy,a^{2}\right)+3\pi/(2p)}}$ `(p_{+}^{2}-p_{-}^{2})\CarlsonsymellintRJ@{0}{x^{2}}{y^{2}}{p^{2}} = 2(p_{+}^{2}-a^{2})\CarlsonsymellintRJ@{0}{xy}{a^{2}}{p_{+}^{2}}-3\CarlsonsymellintRF@{0}{xy}{a^{2}}+3\pi/(2p)`		Error	((Subscript[p, +])^(2)- (Subscript[p, -])^(2))3((y)^(2)-0)/((y)^(2)-(p)^(2))(EllipticPi[((y)^(2)-(p)^(2))/((y)^(2)-0),ArcCos[Sqrt[0/(y)^(2)]],((y)^(2)-(x)^(2))/((y)^(2)-0)]-EllipticF[ArcCos[Sqrt[0/(y)^(2)]],((y)^(2)-(x)^(2))/((y)^(2)-0)])/Sqrt[(y)^(2)-0] == 2((Subscript[p, +])^(2)- (a)^(2))3((a)^(2)-0)/((a)^(2)-(Subscript[p, +])^(2))(EllipticPi[((a)^(2)-(Subscript[p, +])^(2))/((a)^(2)-0),ArcCos[Sqrt[0/(a)^(2)]],((a)^(2)-xy)/((a)^(2)-0)]-EllipticF[ArcCos[Sqrt[0/(a)^(2)]],((a)^(2)-xy)/((a)^(2)-0)])/Sqrt[(a)^(2)-0]- 3EllipticF[ArcCos[Sqrt[0/(a)^(2)]],((a)^(2)-xy)/((a)^(2)-0)]/Sqrt[(a)^(2)-0]+ 3Pi/(2*p)	Missing Macro Error	Failure	-	Error
19.22.E4	${\displaystyle{\displaystyle(p_{-}^{2}-p_{+}^{2})R_{J}\left(0,x^{2},y^{2},p^{2% }\right)=2(p_{-}^{2}-a^{2})R_{J}\left(0,xy,a^{2},p_{-}^{2}\right)-3R_{F}\left(% 0,xy,a^{2}\right)+3\pi/(2p)}}$ `(p_{-}^{2}-p_{+}^{2})\CarlsonsymellintRJ@{0}{x^{2}}{y^{2}}{p^{2}} = 2(p_{-}^{2}-a^{2})\CarlsonsymellintRJ@{0}{xy}{a^{2}}{p_{-}^{2}}-3\CarlsonsymellintRF@{0}{xy}{a^{2}}+3\pi/(2p)`		Error	((Subscript[p, -])^(2)- (Subscript[p, +])^(2))3((y)^(2)-0)/((y)^(2)-(p)^(2))(EllipticPi[((y)^(2)-(p)^(2))/((y)^(2)-0),ArcCos[Sqrt[0/(y)^(2)]],((y)^(2)-(x)^(2))/((y)^(2)-0)]-EllipticF[ArcCos[Sqrt[0/(y)^(2)]],((y)^(2)-(x)^(2))/((y)^(2)-0)])/Sqrt[(y)^(2)-0] == 2((Subscript[p, -])^(2)- (a)^(2))3((a)^(2)-0)/((a)^(2)-(Subscript[p, -])^(2))(EllipticPi[((a)^(2)-(Subscript[p, -])^(2))/((a)^(2)-0),ArcCos[Sqrt[0/(a)^(2)]],((a)^(2)-xy)/((a)^(2)-0)]-EllipticF[ArcCos[Sqrt[0/(a)^(2)]],((a)^(2)-xy)/((a)^(2)-0)])/Sqrt[(a)^(2)-0]- 3EllipticF[ArcCos[Sqrt[0/(a)^(2)]],((a)^(2)-xy)/((a)^(2)-0)]/Sqrt[(a)^(2)-0]+ 3Pi/(2*p)	Missing Macro Error	Failure	-	Error
19.22#Ex1	${\displaystyle{\displaystyle p_{+}p_{-}=pa}}$ `p_{+}p_{-} = pa`		p[+]p[-] = pa	Subscript[p, +]Subscript[p, -] == pa	Skipped - no semantic math	Skipped - no semantic math	-	-
19.22#Ex2	${\displaystyle{\displaystyle p_{+}^{2}+p_{-}^{2}=p^{2}+xy}}$ `p_{+}^{2}+p_{-}^{2} = p^{2}+xy`		(p[+])^(2)+ (p[-])^(2) = (p)^(2)+ x*y	(Subscript[p, +])^(2)+ (Subscript[p, -])^(2) == (p)^(2)+ x*y	Skipped - no semantic math	Skipped - no semantic math	-	-
19.22#Ex3	${\displaystyle{\displaystyle p_{+}^{2}-p_{-}^{2}=\sqrt{(p^{2}-x^{2})(p^{2}-y^{% 2})}}}$ `p_{+}^{2}-p_{-}^{2} = \sqrt{(p^{2}-x^{2})(p^{2}-y^{2})}`		(p[+])^(2)- (p[-])^(2) = sqrt(((p)^(2)- (x)^(2))*((p)^(2)- (y)^(2)))	(Subscript[p, +])^(2)- (Subscript[p, -])^(2) == Sqrt[((p)^(2)- (x)^(2))*((p)^(2)- (y)^(2))]	Skipped - no semantic math	Skipped - no semantic math	-	-
19.22#Ex4	${\displaystyle{\displaystyle 4(p_{+}^{2}-a^{2})=(\sqrt{p^{2}-x^{2}}+\sqrt{p^{2% }-y^{2}})^{2}}}$ `4(p_{+}^{2}-a^{2}) = (\sqrt{p^{2}-x^{2}}+\sqrt{p^{2}-y^{2}})^{2}`		4*((p[+])^(2)- (a)^(2)) = (sqrt((p)^(2)- (x)^(2))+sqrt((p)^(2)- (y)^(2)))^(2)	4*((Subscript[p, +])^(2)- (a)^(2)) == (Sqrt[(p)^(2)- (x)^(2)]+Sqrt[(p)^(2)- (y)^(2)])^(2)	Skipped - no semantic math	Skipped - no semantic math	-	-
19.22.E7	${\displaystyle{\displaystyle 2p^{2}R_{J}\left(0,x^{2},y^{2},p^{2}\right)=v_{+}% v_{-}R_{J}\left(0,xy,a^{2},v^{2}_{+}\right)+3R_{F}\left(0,xy,a^{2}\right)}}$ `2p^{2}\CarlsonsymellintRJ@{0}{x^{2}}{y^{2}}{p^{2}} = v_{+}v_{-}\CarlsonsymellintRJ@{0}{xy}{a^{2}}{v^{2}_{+}}+3\CarlsonsymellintRF@{0}{xy}{a^{2}}`	${\displaystyle{\displaystyle v_{+}=(p^{2}+xy)/(2p),v_{-}=(p^{2}-xy)/(2p)}}$	Error	2(p)^(2) 3((y)^(2)-0)/((y)^(2)-(p)^(2))(EllipticPi[((y)^(2)-(p)^(2))/((y)^(2)-0),ArcCos[Sqrt[0/(y)^(2)]],((y)^(2)-(x)^(2))/((y)^(2)-0)]-EllipticF[ArcCos[Sqrt[0/(y)^(2)]],((y)^(2)-(x)^(2))/((y)^(2)-0)])/Sqrt[(y)^(2)-0] == Subscript[v, +]Subscript[v, -]3((a)^(2)-0)/((a)^(2)-(Subscript[v, +])^(2))(EllipticPi[((a)^(2)-(Subscript[v, +])^(2))/((a)^(2)-0),ArcCos[Sqrt[0/(a)^(2)]],((a)^(2)-xy)/((a)^(2)-0)]-EllipticF[ArcCos[Sqrt[0/(a)^(2)]],((a)^(2)-xy)/((a)^(2)-0)])/Sqrt[(a)^(2)-0]+ 3EllipticF[ArcCos[Sqrt[0/(a)^(2)]],((a)^(2)-xy)/((a)^(2)-0)]/Sqrt[(a)^(2)-0]	Missing Macro Error	Failure	-	Error
19.22.E8	${\displaystyle{\displaystyle\frac{2}{\pi}R_{F}\left(0,a_{0}^{2},g_{0}^{2}% \right)=\frac{1}{M\left(a_{0},g_{0}\right)}}}$ `\frac{2}{\pi}\CarlsonsymellintRF@{0}{a_{0}^{2}}{g_{0}^{2}} = \frac{1}{\AGM@{a_{0}}{g_{0}}}`		(2)/(Pi)0.5int(1/(sqrt(t+0)sqrt(t+(a[0])^(2))sqrt(t+(g[0])^(2))), t = 0..infinity) = (1)/(GaussAGM(a[0], g[0]))	Error	Aborted	Missing Macro Error	Skipped - Because timed out	-
19.22.E9	${\displaystyle{\displaystyle\frac{1}{M\left(a_{0},g_{0}\right)}\left(a_{0}^{2}% -\sum_{n=0}^{\infty}2^{n-1}c_{n}^{2}\right)=\frac{1}{M\left(a_{0},g_{0}\right)% }\left(a_{1}^{2}-\sum_{n=2}^{\infty}2^{n-1}c_{n}^{2}\right)}}$ `\frac{1}{\AGM@{a_{0}}{g_{0}}}\left(a_{0}^{2}-\sum_{n=0}^{\infty}2^{n-1}c_{n}^{2}\right) = \frac{1}{\AGM@{a_{0}}{g_{0}}}\left(a_{1}^{2}-\sum_{n=2}^{\infty}2^{n-1}c_{n}^{2}\right)`		(1)/(GaussAGM(a[0], g[0]))((a[0])^(2)- sum((2)^(n - 1) (c[n])^(2), n = 0..infinity)) = (1)/(GaussAGM(a[0], g[0]))((a[1])^(2)- sum((2)^(n - 1) (c[n])^(2), n = 2..infinity))	Error	Failure	Missing Macro Error	Error	-
19.22#Ex5	${\displaystyle{\displaystyle Q_{0}=1}}$ `Q_{0} = 1`		Q[0] = 1	Subscript[Q, 0] == 1	Skipped - no semantic math	Skipped - no semantic math	-	-
19.22#Ex6	${\displaystyle{\displaystyle Q_{n+1}=\tfrac{1}{2}Q_{n}\frac{a_{n}-g_{n}}{a_{n}% +g_{n}}}}$ `Q_{n+1} = \tfrac{1}{2}Q_{n}\frac{a_{n}-g_{n}}{a_{n}+g_{n}}`		Q[n + 1] = (1)/(2)Q[n](a[n]- g[n])/(a[n]+ g[n])	Subscript[Q, n + 1] == Divide[1,2]Subscript[Q, n]Divide[Subscript[a, n]- Subscript[g, n],Subscript[a, n]+ Subscript[g, n]]	Skipped - no semantic math	Skipped - no semantic math	-	-
19.22#Ex7	${\displaystyle{\displaystyle p_{n+1}=\frac{p_{n}^{2}+a_{n}g_{n}}{2p_{n}}}}$ `p_{n+1} = \frac{p_{n}^{2}+a_{n}g_{n}}{2p_{n}}`		p[n + 1] = ((p[n])^(2)+ a[n]g[n])/(2p[n])	Subscript[p, n + 1] == Divide[(Subscript[p, n])^(2)+ Subscript[a, n]Subscript[g, n],2Subscript[p, n]]	Skipped - no semantic math	Skipped - no semantic math	-	-
19.22#Ex8	${\displaystyle{\displaystyle\varepsilon_{n}=\frac{p_{n}^{2}-a_{n}g_{n}}{p_{n}^% {2}+a_{n}g_{n}}}}$ `\varepsilon_{n} = \frac{p_{n}^{2}-a_{n}g_{n}}{p_{n}^{2}+a_{n}g_{n}}`		varepsilon[n] = ((p[n])^(2)- a[n]g[n])/((p[n])^(2)+ a[n]g[n])	Subscript[\[CurlyEpsilon], n] == Divide[(Subscript[p, n])^(2)- Subscript[a, n]Subscript[g, n],(Subscript[p, n])^(2)+ Subscript[a, n]Subscript[g, n]]	Skipped - no semantic math	Skipped - no semantic math	-	-
19.22#Ex9	${\displaystyle{\displaystyle Q_{0}=1}}$ `Q_{0} = 1`		Q[0] = 1	Subscript[Q, 0] == 1	Skipped - no semantic math	Skipped - no semantic math	-	-
19.22#Ex10	${\displaystyle{\displaystyle Q_{n+1}=\tfrac{1}{2}Q_{n}\varepsilon_{n}}}$ `Q_{n+1} = \tfrac{1}{2}Q_{n}\varepsilon_{n}`		Q[n + 1] = (1)/(2)Q[n]varepsilon[n]	Subscript[Q, n + 1] == Divide[1,2]Subscript[Q, n]Subscript[\[CurlyEpsilon], n]	Skipped - no semantic math	Skipped - no semantic math	-	-
19.22.E15	${\displaystyle{\displaystyle p_{0}^{2}=a_{0}^{2}(q_{0}^{2}+g_{0}^{2})/(q_{0}^{% 2}+a_{0}^{2})}}$ `p_{0}^{2} = a_{0}^{2}(q_{0}^{2}+g_{0}^{2})/(q_{0}^{2}+a_{0}^{2})`		(p[0])^(2) = (a[0])^(2)*((q[0])^(2)+ (g[0])^(2))/((q[0])^(2)+ (a[0])^(2))	(Subscript[p, 0])^(2) == (Subscript[a, 0])^(2)*((Subscript[q, 0])^(2)+ (Subscript[g, 0])^(2))/((Subscript[q, 0])^(2)+ (Subscript[a, 0])^(2))	Skipped - no semantic math	Skipped - no semantic math	-	-
19.22#Ex11	${\displaystyle{\displaystyle a=(x+y)/2}}$ `a = (x+y)/2`		a = (x + y)/2	a == (x + y)/2	Skipped - no semantic math	Skipped - no semantic math	-	-
19.22#Ex12	${\displaystyle{\displaystyle 2z_{+}=\sqrt{(z+x)(z+y)}+\sqrt{(z-x)(z-y)}}}$ `2z_{+} = \sqrt{(z+x)(z+y)}+\sqrt{(z-x)(z-y)}`		2x + yI[+] = sqrt(((x + yI)+ x)((x + yI)+ y))+sqrt(((x + yI)- x)((x + yI)- y))	2Subscript[x + yI, +] == Sqrt[((x + yI)+ x)((x + yI)+ y)]+Sqrt[((x + yI)- x)((x + yI)- y)]	Skipped - no semantic math	Skipped - no semantic math	-	-
19.22#Ex13	${\displaystyle{\displaystyle z_{+}z_{-}=za}}$ `z_{+}z_{-} = za`		z[+]z[-] = za	Subscript[z, +]Subscript[z, -] == za	Skipped - no semantic math	Skipped - no semantic math	-	-
19.22#Ex14	${\displaystyle{\displaystyle z_{+}^{2}+z_{-}^{2}=z^{2}+xy}}$ `z_{+}^{2}+z_{-}^{2} = z^{2}+xy`		(x + yI[+])^(2)+(x + yI[-])^(2) = (x + yI)^(2)+ xy	(Subscript[x + yI, +])^(2)+(Subscript[x + yI, -])^(2) == (x + yI)^(2)+ xy	Skipped - no semantic math	Skipped - no semantic math	-	-
19.22#Ex15	${\displaystyle{\displaystyle z_{+}^{2}-z_{-}^{2}=\sqrt{(z^{2}-x^{2})(z^{2}-y^{% 2})}}}$ `z_{+}^{2}-z_{-}^{2} = \sqrt{(z^{2}-x^{2})(z^{2}-y^{2})}`		(x + yI[+])^(2)-(x + yI[-])^(2) = sqrt(((x + yI)^(2)- (x)^(2))((x + y*I)^(2)- (y)^(2)))	(Subscript[x + yI, +])^(2)-(Subscript[x + yI, -])^(2) == Sqrt[((x + yI)^(2)- (x)^(2))((x + y*I)^(2)- (y)^(2))]	Skipped - no semantic math	Skipped - no semantic math	-	-
19.22#Ex16	${\displaystyle{\displaystyle 4(z_{+}^{2}-a^{2})=(\sqrt{z^{2}-x^{2}}+\sqrt{z^{2% }-y^{2}})^{2}}}$ `4(z_{+}^{2}-a^{2}) = (\sqrt{z^{2}-x^{2}}+\sqrt{z^{2}-y^{2}})^{2}`		4((x + yI[+])^(2)- (a)^(2)) = (sqrt((x + yI)^(2)- (x)^(2))+sqrt((x + yI)^(2)- (y)^(2)))^(2)	4((Subscript[x + yI, +])^(2)- (a)^(2)) == (Sqrt[(x + yI)^(2)- (x)^(2)]+Sqrt[(x + yI)^(2)- (y)^(2)])^(2)	Skipped - no semantic math	Skipped - no semantic math	-	-
19.22.E18	${\displaystyle{\displaystyle R_{F}\left(x^{2},y^{2},z^{2}\right)=R_{F}\left(a^% {2},z_{-}^{2},z_{+}^{2}\right)}}$ `\CarlsonsymellintRF@{x^{2}}{y^{2}}{z^{2}} = \CarlsonsymellintRF@{a^{2}}{z_{-}^{2}}{z_{+}^{2}}`		0.5int(1/(sqrt(t+(x)^(2))sqrt(t+(y)^(2))sqrt(t+(x + yI)^(2))), t = 0..infinity) = 0.5int(1/(sqrt(t+(a)^(2))sqrt(t+(x + yI[-])^(2))sqrt(t+(x + y*I[+])^(2))), t = 0..infinity)	EllipticF[ArcCos[Sqrt[(x)^(2)/(x + yI)^(2)]],((x + yI)^(2)-(y)^(2))/((x + yI)^(2)-(x)^(2))]/Sqrt[(x + yI)^(2)-(x)^(2)] == EllipticF[ArcCos[Sqrt[(a)^(2)/(Subscript[x + yI, +])^(2)]],((Subscript[x + yI, +])^(2)-(Subscript[x + yI, -])^(2))/((Subscript[x + yI, +])^(2)-(a)^(2))]/Sqrt[(Subscript[x + y*I, +])^(2)-(a)^(2)]	Error	Failure	-	Error
19.22.E19	${\displaystyle{\displaystyle(z_{+}^{2}-z_{-}^{2})R_{D}\left(x^{2},y^{2},z^{2}% \right)={2(z_{+}^{2}-a^{2})}R_{D}\left(a^{2},z_{-}^{2},z_{+}^{2}\right)-3R_{F}% \left(x^{2},y^{2},z^{2}\right)+(3/z)}}$ `(z_{+}^{2}-z_{-}^{2})\CarlsonsymellintRD@{x^{2}}{y^{2}}{z^{2}} = {2(z_{+}^{2}-a^{2})}\CarlsonsymellintRD@{a^{2}}{z_{-}^{2}}{z_{+}^{2}}-3\CarlsonsymellintRF@{x^{2}}{y^{2}}{z^{2}}+(3/z)`		Error	((Subscript[x + yI, +])^(2)-(Subscript[x + yI, -])^(2))3(EllipticF[ArcCos[Sqrt[(x)^(2)/(x + yI)^(2)]],((x + yI)^(2)-(y)^(2))/((x + yI)^(2)-(x)^(2))]-EllipticE[ArcCos[Sqrt[(x)^(2)/(x + yI)^(2)]],((x + yI)^(2)-(y)^(2))/((x + yI)^(2)-(x)^(2))])/(((x + yI)^(2)-(y)^(2))((x + yI)^(2)-(x)^(2))^(1/2)) == 2((Subscript[x + yI, +])^(2)- (a)^(2))3(EllipticF[ArcCos[Sqrt[(a)^(2)/(Subscript[x + yI, +])^(2)]],((Subscript[x + yI, +])^(2)-(Subscript[x + yI, -])^(2))/((Subscript[x + yI, +])^(2)-(a)^(2))]-EllipticE[ArcCos[Sqrt[(a)^(2)/(Subscript[x + yI, +])^(2)]],((Subscript[x + yI, +])^(2)-(Subscript[x + yI, -])^(2))/((Subscript[x + yI, +])^(2)-(a)^(2))])/(((Subscript[x + yI, +])^(2)-(Subscript[x + yI, -])^(2))((Subscript[x + yI, +])^(2)-(a)^(2))^(1/2))- 3EllipticF[ArcCos[Sqrt[(x)^(2)/(x + yI)^(2)]],((x + yI)^(2)-(y)^(2))/((x + yI)^(2)-(x)^(2))]/Sqrt[(x + yI)^(2)-(x)^(2)]+(3/(x + y*I))	Missing Macro Error	Failure	-	Error
19.22.E19	${\displaystyle{\displaystyle(z_{-}^{2}-z_{+}^{2})R_{D}\left(x^{2},y^{2},z^{2}% \right)={2(z_{-}^{2}-a^{2})}R_{D}\left(a^{2},z_{+}^{2},z_{-}^{2}\right)-3R_{F}% \left(x^{2},y^{2},z^{2}\right)+(3/z)}}$ `(z_{-}^{2}-z_{+}^{2})\CarlsonsymellintRD@{x^{2}}{y^{2}}{z^{2}} = {2(z_{-}^{2}-a^{2})}\CarlsonsymellintRD@{a^{2}}{z_{+}^{2}}{z_{-}^{2}}-3\CarlsonsymellintRF@{x^{2}}{y^{2}}{z^{2}}+(3/z)`		Error	((Subscript[x + yI, -])^(2)-(Subscript[x + yI, +])^(2))3(EllipticF[ArcCos[Sqrt[(x)^(2)/(x + yI)^(2)]],((x + yI)^(2)-(y)^(2))/((x + yI)^(2)-(x)^(2))]-EllipticE[ArcCos[Sqrt[(x)^(2)/(x + yI)^(2)]],((x + yI)^(2)-(y)^(2))/((x + yI)^(2)-(x)^(2))])/(((x + yI)^(2)-(y)^(2))((x + yI)^(2)-(x)^(2))^(1/2)) == 2((Subscript[x + yI, -])^(2)- (a)^(2))3(EllipticF[ArcCos[Sqrt[(a)^(2)/(Subscript[x + yI, -])^(2)]],((Subscript[x + yI, -])^(2)-(Subscript[x + yI, +])^(2))/((Subscript[x + yI, -])^(2)-(a)^(2))]-EllipticE[ArcCos[Sqrt[(a)^(2)/(Subscript[x + yI, -])^(2)]],((Subscript[x + yI, -])^(2)-(Subscript[x + yI, +])^(2))/((Subscript[x + yI, -])^(2)-(a)^(2))])/(((Subscript[x + yI, -])^(2)-(Subscript[x + yI, +])^(2))((Subscript[x + yI, -])^(2)-(a)^(2))^(1/2))- 3EllipticF[ArcCos[Sqrt[(x)^(2)/(x + yI)^(2)]],((x + yI)^(2)-(y)^(2))/((x + yI)^(2)-(x)^(2))]/Sqrt[(x + yI)^(2)-(x)^(2)]+(3/(x + y*I))	Missing Macro Error	Failure	-	Error
19.22.E20	${\displaystyle{\displaystyle(p_{+}^{2}-p_{-}^{2})R_{J}\left(x^{2},y^{2},z^{2},% p^{2}\right)=2(p_{+}^{2}-a^{2})R_{J}\left(a^{2},z_{+}^{2},z_{-}^{2},p_{+}^{2}% \right)-3R_{F}\left(x^{2},y^{2},z^{2}\right)+3R_{C}\left(z^{2},p^{2}\right)}}$ `(p_{+}^{2}-p_{-}^{2})\CarlsonsymellintRJ@{x^{2}}{y^{2}}{z^{2}}{p^{2}} = 2(p_{+}^{2}-a^{2})\CarlsonsymellintRJ@{a^{2}}{z_{+}^{2}}{z_{-}^{2}}{p_{+}^{2}}-3\CarlsonsymellintRF@{x^{2}}{y^{2}}{z^{2}}+3\CarlsonellintRC@{z^{2}}{p^{2}}`		Error	((Subscript[p, +])^(2)- (Subscript[p, -])^(2))3((x + yI)^(2)-(x)^(2))/((x + yI)^(2)-(p)^(2))(EllipticPi[((x + yI)^(2)-(p)^(2))/((x + yI)^(2)-(x)^(2)),ArcCos[Sqrt[(x)^(2)/(x + yI)^(2)]],((x + yI)^(2)-(y)^(2))/((x + yI)^(2)-(x)^(2))]-EllipticF[ArcCos[Sqrt[(x)^(2)/(x + yI)^(2)]],((x + yI)^(2)-(y)^(2))/((x + yI)^(2)-(x)^(2))])/Sqrt[(x + yI)^(2)-(x)^(2)] == 2((Subscript[p, +])^(2)- (a)^(2))3((Subscript[x + yI, -])^(2)-(a)^(2))/((Subscript[x + yI, -])^(2)-(Subscript[p, +])^(2))(EllipticPi[((Subscript[x + yI, -])^(2)-(Subscript[p, +])^(2))/((Subscript[x + yI, -])^(2)-(a)^(2)),ArcCos[Sqrt[(a)^(2)/(Subscript[x + yI, -])^(2)]],((Subscript[x + yI, -])^(2)-(Subscript[x + yI, +])^(2))/((Subscript[x + yI, -])^(2)-(a)^(2))]-EllipticF[ArcCos[Sqrt[(a)^(2)/(Subscript[x + yI, -])^(2)]],((Subscript[x + yI, -])^(2)-(Subscript[x + yI, +])^(2))/((Subscript[x + yI, -])^(2)-(a)^(2))])/Sqrt[(Subscript[x + yI, -])^(2)-(a)^(2)]- 3EllipticF[ArcCos[Sqrt[(x)^(2)/(x + yI)^(2)]],((x + yI)^(2)-(y)^(2))/((x + yI)^(2)-(x)^(2))]/Sqrt[(x + yI)^(2)-(x)^(2)]+ 31/Sqrt[(p)^(2)]Hypergeometric2F1[1/2,1/2,3/2,1-((x + y*I)^(2))/((p)^(2))]	Missing Macro Error	Failure	-	Error
19.22.E20	${\displaystyle{\displaystyle(p_{-}^{2}-p_{+}^{2})R_{J}\left(x^{2},y^{2},z^{2},% p^{2}\right)=2(p_{-}^{2}-a^{2})R_{J}\left(a^{2},z_{+}^{2},z_{-}^{2},p_{-}^{2}% \right)-3R_{F}\left(x^{2},y^{2},z^{2}\right)+3R_{C}\left(z^{2},p^{2}\right)}}$ `(p_{-}^{2}-p_{+}^{2})\CarlsonsymellintRJ@{x^{2}}{y^{2}}{z^{2}}{p^{2}} = 2(p_{-}^{2}-a^{2})\CarlsonsymellintRJ@{a^{2}}{z_{+}^{2}}{z_{-}^{2}}{p_{-}^{2}}-3\CarlsonsymellintRF@{x^{2}}{y^{2}}{z^{2}}+3\CarlsonellintRC@{z^{2}}{p^{2}}`		Error	((Subscript[p, -])^(2)- (Subscript[p, +])^(2))3((x + yI)^(2)-(x)^(2))/((x + yI)^(2)-(p)^(2))(EllipticPi[((x + yI)^(2)-(p)^(2))/((x + yI)^(2)-(x)^(2)),ArcCos[Sqrt[(x)^(2)/(x + yI)^(2)]],((x + yI)^(2)-(y)^(2))/((x + yI)^(2)-(x)^(2))]-EllipticF[ArcCos[Sqrt[(x)^(2)/(x + yI)^(2)]],((x + yI)^(2)-(y)^(2))/((x + yI)^(2)-(x)^(2))])/Sqrt[(x + yI)^(2)-(x)^(2)] == 2((Subscript[p, -])^(2)- (a)^(2))3((Subscript[x + yI, -])^(2)-(a)^(2))/((Subscript[x + yI, -])^(2)-(Subscript[p, -])^(2))(EllipticPi[((Subscript[x + yI, -])^(2)-(Subscript[p, -])^(2))/((Subscript[x + yI, -])^(2)-(a)^(2)),ArcCos[Sqrt[(a)^(2)/(Subscript[x + yI, -])^(2)]],((Subscript[x + yI, -])^(2)-(Subscript[x + yI, +])^(2))/((Subscript[x + yI, -])^(2)-(a)^(2))]-EllipticF[ArcCos[Sqrt[(a)^(2)/(Subscript[x + yI, -])^(2)]],((Subscript[x + yI, -])^(2)-(Subscript[x + yI, +])^(2))/((Subscript[x + yI, -])^(2)-(a)^(2))])/Sqrt[(Subscript[x + yI, -])^(2)-(a)^(2)]- 3EllipticF[ArcCos[Sqrt[(x)^(2)/(x + yI)^(2)]],((x + yI)^(2)-(y)^(2))/((x + yI)^(2)-(x)^(2))]/Sqrt[(x + yI)^(2)-(x)^(2)]+ 31/Sqrt[(p)^(2)]Hypergeometric2F1[1/2,1/2,3/2,1-((x + y*I)^(2))/((p)^(2))]	Missing Macro Error	Failure	-	Error
19.22.E21	${\displaystyle{\displaystyle 2R_{G}\left(x^{2},y^{2},z^{2}\right)=4R_{G}\left(% a^{2},z_{+}^{2},z_{-}^{2}\right)-xyR_{F}\left(x^{2},y^{2},z^{2}\right)-z}}$ `2\CarlsonsymellintRG@{x^{2}}{y^{2}}{z^{2}} = 4\CarlsonsymellintRG@{a^{2}}{z_{+}^{2}}{z_{-}^{2}}-xy\CarlsonsymellintRF@{x^{2}}{y^{2}}{z^{2}}-z`		Error	2Sqrt[(x + yI)^(2)-(x)^(2)](EllipticE[ArcCos[Sqrt[(x)^(2)/(x + yI)^(2)]],((x + yI)^(2)-(y)^(2))/((x + yI)^(2)-(x)^(2))]+(Cot[ArcCos[Sqrt[(x)^(2)/(x + yI)^(2)]]])^2EllipticF[ArcCos[Sqrt[(x)^(2)/(x + yI)^(2)]],((x + yI)^(2)-(y)^(2))/((x + yI)^(2)-(x)^(2))]+Cot[ArcCos[Sqrt[(x)^(2)/(x + yI)^(2)]]]Sqrt[1-k^2Sin[ArcCos[Sqrt[(x)^(2)/(x + yI)^(2)]]]^2]) == 4Sqrt[(Subscript[x + yI, -])^(2)-(a)^(2)](EllipticE[ArcCos[Sqrt[(a)^(2)/(Subscript[x + yI, -])^(2)]],((Subscript[x + yI, -])^(2)-(Subscript[x + yI, +])^(2))/((Subscript[x + yI, -])^(2)-(a)^(2))]+(Cot[ArcCos[Sqrt[(a)^(2)/(Subscript[x + yI, -])^(2)]]])^2EllipticF[ArcCos[Sqrt[(a)^(2)/(Subscript[x + yI, -])^(2)]],((Subscript[x + yI, -])^(2)-(Subscript[x + yI, +])^(2))/((Subscript[x + yI, -])^(2)-(a)^(2))]+Cot[ArcCos[Sqrt[(a)^(2)/(Subscript[x + yI, -])^(2)]]]Sqrt[1-k^2Sin[ArcCos[Sqrt[(a)^(2)/(Subscript[x + yI, -])^(2)]]]^2])- xyEllipticF[ArcCos[Sqrt[(x)^(2)/(x + yI)^(2)]],((x + yI)^(2)-(y)^(2))/((x + yI)^(2)-(x)^(2))]/Sqrt[(x + yI)^(2)-(x)^(2)]-(x + y*I)	Missing Macro Error	Failure	-	Error
19.22.E22	${\displaystyle{\displaystyle R_{C}\left(x^{2},y^{2}\right)=R_{C}\left(a^{2},ay% \right)}}$ `\CarlsonellintRC@{x^{2}}{y^{2}} = \CarlsonellintRC@{a^{2}}{ay}`		Error	1/Sqrt[(y)^(2)]Hypergeometric2F1[1/2,1/2,3/2,1-((x)^(2))/((y)^(2))] == 1/Sqrt[ay]Hypergeometric2F1[1/2,1/2,3/2,1-((a)^(2))/(ay)]	Missing Macro Error	Failure	-	Failed [108 / 108] Result: Indeterminate Test Values: {Rule[a, -1.5], Rule[x, 1.5], Rule[y, -1.5]} Result: Indeterminate Test Values: {Rule[a, -1.5], Rule[x, 1.5], Rule[y, 1.5]} ... skip entries to safe data
19.22#Ex17	${\displaystyle{\displaystyle x+y=2a}}$ `x+y = 2a`		x + y = 2*a	x + y == 2*a	Skipped - no semantic math	Skipped - no semantic math	-	-
19.22#Ex18	${\displaystyle{\displaystyle x-y=(\ifrac{2}{a})\sqrt{(a^{2}-z_{+}^{2})(a^{2}-z% _{-}^{2})}}}$ `x-y = (\ifrac{2}{a})\sqrt{(a^{2}-z_{+}^{2})(a^{2}-z_{-}^{2})}`		x - y = ((2)/(a))sqrt(((a)^(2)-(x + yI[+])^(2))((a)^(2)-(x + yI[-])^(2)))	x - y == (Divide[2,a])Sqrt[((a)^(2)-(Subscript[x + yI, +])^(2))((a)^(2)-(Subscript[x + yI, -])^(2))]	Skipped - no semantic math	Skipped - no semantic math	-	-
19.22#Ex19	${\displaystyle{\displaystyle z=\ifrac{z_{+}z_{-}}{a}}}$ `z = \ifrac{z_{+}z_{-}}{a}`		z = (z[+]*z[-])/(a)	z == Divide[Subscript[z, +]*Subscript[z, -],a]	Skipped - no semantic math	Skipped - no semantic math	-	-
19.23.E1	${\displaystyle{\displaystyle R_{F}\left(0,y,z\right)=\int_{0}^{\pi/2}(y{\cos^{% 2}}\theta+z{\sin^{2}}\theta)^{-1/2}\mathrm{d}\theta}}$ `\CarlsonsymellintRF@{0}{y}{z} = \int_{0}^{\pi/2}(y\cos^{2}@@{\theta}+z\sin^{2}@@{\theta})^{-1/2}\diff{\theta}`		0.5int(1/(sqrt(t+0)sqrt(t+y)sqrt(t+x + yI)), t = 0..infinity) = int((y(cos(theta))^(2)+(x + yI)*(sin(theta))^(2))^(- 1/2), theta = 0..Pi/2)	EllipticF[ArcCos[Sqrt[0/x + yI]],(x + yI-y)/(x + yI-0)]/Sqrt[x + yI-0] == Integrate[(y(Cos[\[Theta]])^(2)+(x + yI)*(Sin[\[Theta]])^(2))^(- 1/2), {\[Theta], 0, Pi/2}, GenerateConditions->None]	Aborted	Failure	Skipped - Because timed out	Failed [18 / 18] Result: Complex[0.8397393007192011, 1.792316631638506] Test Values: {Rule[x, 1.5], Rule[y, -1.5]} Result: Complex[-1.057179647328743, -0.8381019542468571] Test Values: {Rule[x, 1.5], Rule[y, 1.5]} ... skip entries to safe data
19.23.E2	${\displaystyle{\displaystyle R_{G}\left(0,y,z\right)=\frac{1}{2}\int_{0}^{\pi/% 2}(y{\cos^{2}}\theta+z{\sin^{2}}\theta)^{1/2}\mathrm{d}\theta}}$ `\CarlsonsymellintRG@{0}{y}{z} = \frac{1}{2}\int_{0}^{\pi/2}(y\cos^{2}@@{\theta}+z\sin^{2}@@{\theta})^{1/2}\diff{\theta}`		Error	Sqrt[x + yI-0](EllipticE[ArcCos[Sqrt[0/x + yI]],(x + yI-y)/(x + yI-0)]+(Cot[ArcCos[Sqrt[0/x + yI]]])^2EllipticF[ArcCos[Sqrt[0/x + yI]],(x + yI-y)/(x + yI-0)]+Cot[ArcCos[Sqrt[0/x + yI]]]Sqrt[1-k^2Sin[ArcCos[Sqrt[0/x + yI]]]^2]) == Divide[1,2]Integrate[(y(Cos[\[Theta]])^(2)+(x + yI)(Sin[\[Theta]])^(2))^(1/2), {\[Theta], 0, Pi/2}, GenerateConditions->None]	Missing Macro Error	Failure	-	Failed [18 / 18] Result: Plus[Complex[0.5014070071339144, -0.6068932953779227], Times[Complex[1.345607733249115, -0.5573689727459014], Plus[Complex[1.465481142300126, -0.24396122198922798], Times[Complex[0.2643318009908678, -0.8730286325904596], Power[Plus[1.0, Times[Complex[-1.0, -1.5], Power[k, 2]]], Rational[1, 2]]]]]] Test Values: {Rule[x, 1.5], Rule[y, -1.5]} Result: Plus[Complex[-0.9996439786591846, -0.22609983985234913], Times[Complex[1.345607733249115, 0.5573689727459014], Plus[Complex[1.0084590214609772, 0.7147093671486319], Times[Complex[0.2643318009908678, 0.8730286325904596], Power[Plus[1.0, Times[Complex[-1.0, 1.5], Power[k, 2]]], Rational[1, 2]]]]]] Test Values: {Rule[x, 1.5], Rule[y, 1.5]} ... skip entries to safe data
19.23.E3	${\displaystyle{\displaystyle R_{D}\left(0,y,z\right)=3\int_{0}^{\pi/2}(y{\cos^% {2}}\theta+z{\sin^{2}}\theta)^{-3/2}{\sin^{2}}\theta\mathrm{d}\theta}}$ `\CarlsonsymellintRD@{0}{y}{z} = 3\int_{0}^{\pi/2}(y\cos^{2}@@{\theta}+z\sin^{2}@@{\theta})^{-3/2}\sin^{2}@@{\theta}\diff{\theta}`		Error	3(EllipticF[ArcCos[Sqrt[0/x + yI]],(x + yI-y)/(x + yI-0)]-EllipticE[ArcCos[Sqrt[0/x + yI]],(x + yI-y)/(x + yI-0)])/((x + yI-y)(x + yI-0)^(1/2)) == 3Integrate[(y(Cos[\[Theta]])^(2)+(x + yI)(Sin[\[Theta]])^(2))^(- 3/2)* (Sin[\[Theta]])^(2), {\[Theta], 0, Pi/2}, GenerateConditions->None]	Missing Macro Error	Aborted	-	Skipped - Because timed out
19.23.E4	${\displaystyle{\displaystyle R_{F}\left(0,y,z\right)=\frac{2}{\pi}\int_{0}^{% \pi/2}R_{C}\left(y,z{\cos^{2}}\theta\right)\mathrm{d}\theta}}$ `\CarlsonsymellintRF@{0}{y}{z} = \frac{2}{\pi}\int_{0}^{\pi/2}\CarlsonellintRC@{y}{z\cos^{2}@@{\theta}}\diff{\theta}`		Error	EllipticF[ArcCos[Sqrt[0/x + yI]],(x + yI-y)/(x + yI-0)]/Sqrt[x + yI-0] == Divide[2,Pi]Integrate[1/Sqrt[(x + yI)(Cos[\[Theta]])^(2)]Hypergeometric2F1[1/2,1/2,3/2,1-(y)/((x + yI)(Cos[\[Theta]])^(2))], {\[Theta], 0, Pi/2}, GenerateConditions->None]	Missing Macro Error	Aborted	-	Skipped - Because timed out
19.23.E4	${\displaystyle{\displaystyle\frac{2}{\pi}\int_{0}^{\pi/2}R_{C}\left(y,z{\cos^{% 2}}\theta\right)\mathrm{d}\theta=\frac{2}{\pi}\int_{0}^{\infty}R_{C}\left(y{% \cosh^{2}}t,z\right)\mathrm{d}t}}$ `\frac{2}{\pi}\int_{0}^{\pi/2}\CarlsonellintRC@{y}{z\cos^{2}@@{\theta}}\diff{\theta} = \frac{2}{\pi}\int_{0}^{\infty}\CarlsonellintRC@{y\cosh^{2}@@{t}}{z}\diff{t}`		Error	Divide[2,Pi]Integrate[1/Sqrt[(x + yI)(Cos[\[Theta]])^(2)]Hypergeometric2F1[1/2,1/2,3/2,1-(y)/((x + yI)(Cos[\[Theta]])^(2))], {\[Theta], 0, Pi/2}, GenerateConditions->None] == Divide[2,Pi]Integrate[1/Sqrt[x + yI]Hypergeometric2F1[1/2,1/2,3/2,1-(y(Cosh[t])^(2))/(x + y*I)], {t, 0, Infinity}, GenerateConditions->None]	Missing Macro Error	Aborted	-	Skipped - Because timed out
19.23.E5	${\displaystyle{\displaystyle R_{F}\left(x,y,z\right)=\frac{2}{\pi}\int_{0}^{% \pi/2}R_{C}\left(x,y{\cos^{2}}\theta+z{\sin^{2}}\theta\right)\mathrm{d}\theta}}$ `\CarlsonsymellintRF@{x}{y}{z} = \frac{2}{\pi}\int_{0}^{\pi/2}\CarlsonellintRC@{x}{y\cos^{2}@@{\theta}+z\sin^{2}@@{\theta}}\diff{\theta}`	${\displaystyle{\displaystyle\Re y>0,\Re z>0}}$	Error	EllipticF[ArcCos[Sqrt[x/x + yI]],(x + yI-y)/(x + yI-x)]/Sqrt[x + yI-x] == Divide[2,Pi]Integrate[1/Sqrt[y(Cos[\[Theta]])^(2)+(x + yI)(Sin[\[Theta]])^(2)]Hypergeometric2F1[1/2,1/2,3/2,1-(x)/(y(Cos[\[Theta]])^(2)+(x + yI)(Sin[\[Theta]])^(2))], {\[Theta], 0, Pi/2}, GenerateConditions->None]	Missing Macro Error	Aborted	-	Skipped - Because timed out
19.23.E6	${\displaystyle{\displaystyle 4\pi R_{F}\left(x,y,z\right)=\int_{0}^{2\pi}\!\!% \!\!\int_{0}^{\pi}\frac{\sin\theta\mathrm{d}\theta\mathrm{d}\phi}{(x{\sin^{2}}% \theta{\cos^{2}}\phi+y{\sin^{2}}\theta{\sin^{2}}\phi+z{\cos^{2}}\theta)^{1/2}}}}$ `4\pi\CarlsonsymellintRF@{x}{y}{z} = \int_{0}^{2\pi}\!\!\!\!\int_{0}^{\pi}\frac{\sin@@{\theta}\diff{\theta}\diff{\phi}}{(x\sin^{2}@@{\theta}\cos^{2}@@{\phi}+y\sin^{2}@@{\theta}\sin^{2}@@{\phi}+z\cos^{2}@@{\theta})^{1/2}}`		4Pi0.5int(1/(sqrt(t+x)sqrt(t+y)sqrt(t+x + yI)), t = 0..infinity) = int(int((sin(theta))/((x(sin(theta))^(2) (cos(phi))^(2)+ y(sin(theta))^(2) (sin(phi))^(2)+(x + yI)(cos(theta))^(2))^(1/2)), theta = 0..Pi), phi = 0..2*Pi)	4PiEllipticF[ArcCos[Sqrt[x/x + yI]],(x + yI-y)/(x + yI-x)]/Sqrt[x + yI-x] == Integrate[Integrate[Divide[Sin[\[Theta]],(x(Sin[\[Theta]])^(2) (Cos[\[Phi]])^(2)+ y(Sin[\[Theta]])^(2) (Sin[\[Phi]])^(2)+(x + yI)(Cos[\[Theta]])^(2))^(1/2)], {\[Theta], 0, Pi}, GenerateConditions->None], {\[Phi], 0, 2*Pi}, GenerateConditions->None]	Aborted	Aborted	Skipped - Because timed out	Skipped - Because timed out
19.23.E7	${\displaystyle{\displaystyle R_{G}\left(x,y,z\right)=\frac{1}{4}\int_{0}^{% \infty}\frac{1}{\sqrt{t+x}\sqrt{t+y}\sqrt{t+z}}\\left(\frac{x}{t+x}+\frac{y}{% t+y}+\frac{z}{t+z}\right)t\mathrm{d}t}}$ `\CarlsonsymellintRG@{x}{y}{z} = \frac{1}{4}\int_{0}^{\infty}\frac{1}{\sqrt{t+x}\sqrt{t+y}\sqrt{t+z}}\\left(\frac{x}{t+x}+\frac{y}{t+y}+\frac{z}{t+z}\right)t\diff{t}`		Error	Sqrt[x + yI-x](EllipticE[ArcCos[Sqrt[x/x + yI]],(x + yI-y)/(x + yI-x)]+(Cot[ArcCos[Sqrt[x/x + yI]]])^2EllipticF[ArcCos[Sqrt[x/x + yI]],(x + yI-y)/(x + yI-x)]+Cot[ArcCos[Sqrt[x/x + yI]]]Sqrt[1-k^2Sin[ArcCos[Sqrt[x/x + yI]]]^2]) == Divide[1,4]Integrate[Divide[1,Sqrt[t + x]Sqrt[t + y]Sqrt[t +(x + yI)]](Divide[x,t + x]+Divide[y,t + y]+Divide[x + yI,t +(x + yI)])t, {t, 0, Infinity}, GenerateConditions->None]	Missing Macro Error	Aborted	-	Skipped - Because timed out
19.24.E1	${\displaystyle{\displaystyle\ln 4\leq\sqrt{z}R_{F}\left(0,y,z\right)+\ln\sqrt{% y/z}}}$ `\ln@@{4} \leq \sqrt{z}\CarlsonsymellintRF@{0}{y}{z}+\ln@@{\sqrt{y/z}}`	${\displaystyle{\displaystyle 0<y,y\leq z}}$	ln(4) <= sqrt(x + yI)0.5int(1/(sqrt(t+0)sqrt(t+y)sqrt(t+x + yI)), t = 0..infinity)+ ln(sqrt(y/(x + y*I)))	Log[4] <= Sqrt[x + yI]EllipticF[ArcCos[Sqrt[0/x + yI]],(x + yI-y)/(x + yI-0)]/Sqrt[x + yI-0]+ Log[Sqrt[y/(x + y*I)]]	Error	Failure	-	Failed [9 / 9] Result: LessEqual[1.3862943611198906, Complex[0.5672499697282593, -1.7874177081206242]] Test Values: {Rule[x, 1.5], Rule[y, 1.5]} Result: LessEqual[1.3862943611198906, Complex[0.6277320470267476, -0.9602476282953896]] Test Values: {Rule[x, 1.5], Rule[y, 0.5]} ... skip entries to safe data
19.24.E1	${\displaystyle{\displaystyle\sqrt{z}R_{F}\left(0,y,z\right)+\ln\sqrt{y/z}\leq% \tfrac{1}{2}\pi}}$ `\sqrt{z}\CarlsonsymellintRF@{0}{y}{z}+\ln@@{\sqrt{y/z}} \leq \tfrac{1}{2}\pi`	${\displaystyle{\displaystyle 0<y,y\leq z}}$	sqrt(x + yI)0.5int(1/(sqrt(t+0)sqrt(t+y)sqrt(t+x + yI)), t = 0..infinity)+ ln(sqrt(y/(x + yI))) <= (1)/(2)Pi	Sqrt[x + yI]EllipticF[ArcCos[Sqrt[0/x + yI]],(x + yI-y)/(x + yI-0)]/Sqrt[x + yI-0]+ Log[Sqrt[y/(x + yI)]] <= Divide[1,2]Pi	Error	Failure	-	Failed [9 / 9] Result: LessEqual[Complex[0.5672499697282593, -1.7874177081206242], 1.5707963267948966] Test Values: {Rule[x, 1.5], Rule[y, 1.5]} Result: LessEqual[Complex[0.6277320470267476, -0.9602476282953896], 1.5707963267948966] Test Values: {Rule[x, 1.5], Rule[y, 0.5]} ... skip entries to safe data
19.24.E2	${\displaystyle{\displaystyle\tfrac{1}{2}\leq z^{-1/2}R_{G}\left(0,y,z\right)}}$ `\tfrac{1}{2} \leq z^{-1/2}\CarlsonsymellintRG@{0}{y}{z}`	${\displaystyle{\displaystyle 0\leq y,y\leq z}}$	Error	Divide[1,2] <= (x + yI)^(- 1/2) Sqrt[x + yI-0](EllipticE[ArcCos[Sqrt[0/x + yI]],(x + yI-y)/(x + yI-0)]+(Cot[ArcCos[Sqrt[0/x + yI]]])^2EllipticF[ArcCos[Sqrt[0/x + yI]],(x + yI-y)/(x + yI-0)]+Cot[ArcCos[Sqrt[0/x + yI]]]Sqrt[1-k^2Sin[ArcCos[Sqrt[0/x + yI]]]^2])	Missing Macro Error	Failure	-	Failed [9 / 9] Result: LessEqual[0.5, Plus[Complex[1.0084590214609772, 0.7147093671486319], Times[Complex[0.2643318009908678, 0.8730286325904596], Power[Plus[1.0, Times[Complex[-1.0, 1.5], Power[k, 2]]], Rational[1, 2]]]]] Test Values: {Rule[x, 1.5], Rule[y, 1.5]} Result: LessEqual[0.5, Plus[Complex[1.0897585107701309, 0.2919625251300463], Times[Complex[0.3515775842541431, 0.5688644810057831], Power[Plus[1.0, Times[Complex[-1.0, 0.5], Power[k, 2]]], Rational[1, 2]]]]] Test Values: {Rule[x, 1.5], Rule[y, 0.5]} ... skip entries to safe data
19.24.E2	${\displaystyle{\displaystyle z^{-1/2}R_{G}\left(0,y,z\right)\leq\tfrac{1}{4}% \pi}}$ `z^{-1/2}\CarlsonsymellintRG@{0}{y}{z} \leq \tfrac{1}{4}\pi`	${\displaystyle{\displaystyle 0\leq y,y\leq z}}$	Error	(x + yI)^(- 1/2) Sqrt[x + yI-0](EllipticE[ArcCos[Sqrt[0/x + yI]],(x + yI-y)/(x + yI-0)]+(Cot[ArcCos[Sqrt[0/x + yI]]])^2EllipticF[ArcCos[Sqrt[0/x + yI]],(x + yI-y)/(x + yI-0)]+Cot[ArcCos[Sqrt[0/x + yI]]]Sqrt[1-k^2Sin[ArcCos[Sqrt[0/x + yI]]]^2]) <= Divide[1,4]*Pi	Missing Macro Error	Failure	-	Failed [9 / 9] Result: LessEqual[Plus[Complex[1.0084590214609772, 0.7147093671486319], Times[Complex[0.2643318009908678, 0.8730286325904596], Power[Plus[1.0, Times[Complex[-1.0, 1.5], Power[k, 2]]], Rational[1, 2]]]], 0.7853981633974483] Test Values: {Rule[x, 1.5], Rule[y, 1.5]} Result: LessEqual[Plus[Complex[1.0897585107701309, 0.2919625251300463], Times[Complex[0.3515775842541431, 0.5688644810057831], Power[Plus[1.0, Times[Complex[-1.0, 0.5], Power[k, 2]]], Rational[1, 2]]]], 0.7853981633974483] Test Values: {Rule[x, 1.5], Rule[y, 0.5]} ... skip entries to safe data
19.24.E3	${\displaystyle{\displaystyle\left(\frac{y^{3/2}+z^{3/2}}{2}\right)^{2/3}\leq% \frac{4}{\pi}R_{G}\left(0,y^{2},z^{2}\right)}}$ `\left(\frac{y^{3/2}+z^{3/2}}{2}\right)^{2/3} \leq \frac{4}{\pi}\CarlsonsymellintRG@{0}{y^{2}}{z^{2}}`	${\displaystyle{\displaystyle y>0,z>0}}$	Error	(Divide[(y)^(3/2)+(x + yI)^(3/2),2])^(2/3) <= Divide[4,Pi]Sqrt[(x + yI)^(2)-0](EllipticE[ArcCos[Sqrt[0/(x + yI)^(2)]],((x + yI)^(2)-(y)^(2))/((x + yI)^(2)-0)]+(Cot[ArcCos[Sqrt[0/(x + yI)^(2)]]])^2EllipticF[ArcCos[Sqrt[0/(x + yI)^(2)]],((x + yI)^(2)-(y)^(2))/((x + yI)^(2)-0)]+Cot[ArcCos[Sqrt[0/(x + yI)^(2)]]]Sqrt[1-k^2Sin[ArcCos[Sqrt[0/(x + yI)^(2)]]]^2])	Missing Macro Error	Failure	-	Failed [9 / 9] Result: LessEqual[Complex[1.4250443092558214, 0.7875512141675095], Complex[2.850438542245679, 1.5730146161508307]] Test Values: {Rule[x, 1.5], Rule[y, 1.5]} Result: LessEqual[Complex[1.0588191704631045, 0.29794136993360365], Complex[2.118851869395612, 0.5983245902184247]] Test Values: {Rule[x, 1.5], Rule[y, 0.5]} ... skip entries to safe data
19.24.E3	${\displaystyle{\displaystyle\frac{4}{\pi}R_{G}\left(0,y^{2},z^{2}\right)\leq% \left(\frac{y^{2}+z^{2}}{2}\right)^{1/2}}}$ `\frac{4}{\pi}\CarlsonsymellintRG@{0}{y^{2}}{z^{2}} \leq \left(\frac{y^{2}+z^{2}}{2}\right)^{1/2}`	${\displaystyle{\displaystyle y>0,z>0}}$	Error	Divide[4,Pi]Sqrt[(x + yI)^(2)-0](EllipticE[ArcCos[Sqrt[0/(x + yI)^(2)]],((x + yI)^(2)-(y)^(2))/((x + yI)^(2)-0)]+(Cot[ArcCos[Sqrt[0/(x + yI)^(2)]]])^2EllipticF[ArcCos[Sqrt[0/(x + yI)^(2)]],((x + yI)^(2)-(y)^(2))/((x + yI)^(2)-0)]+Cot[ArcCos[Sqrt[0/(x + yI)^(2)]]]Sqrt[1-k^2Sin[ArcCos[Sqrt[0/(x + yI)^(2)]]]^2]) <= (Divide[(y)^(2)+(x + yI)^(2),2])^(1/2)	Missing Macro Error	Failure	-	Failed [9 / 9] Result: LessEqual[Complex[2.850438542245679, 1.5730146161508307], Complex[1.3491805799609005, 0.8338394553771318]] Test Values: {Rule[x, 1.5], Rule[y, 1.5]} Result: LessEqual[Complex[2.118851869395612, 0.5983245902184247], Complex[1.112897508375995, 0.3369582528288897]] Test Values: {Rule[x, 1.5], Rule[y, 0.5]} ... skip entries to safe data
19.24.E4	${\displaystyle{\displaystyle\frac{2}{\sqrt{p}}(2yz+yp+zp)^{-1/2}\leq\frac{4}{3% \pi}R_{J}\left(0,y,z,p\right)}}$ `\frac{2}{\sqrt{p}}(2yz+yp+zp)^{-1/2} \leq \frac{4}{3\pi}\CarlsonsymellintRJ@{0}{y}{z}{p}`		Error	Divide[2,Sqrt[p]](2y(x + yI)+ yp +(x + yI)p)^(- 1/2) <= Divide[4,3Pi]3(x + yI-0)/(x + yI-p)(EllipticPi[(x + yI-p)/(x + yI-0),ArcCos[Sqrt[0/x + yI]],(x + yI-y)/(x + yI-0)]-EllipticF[ArcCos[Sqrt[0/x + yI]],(x + yI-y)/(x + yI-0)])/Sqrt[x + yI-0]	Missing Macro Error	Failure	-	Failed [180 / 180] Result: LessEqual[Complex[0.13508456755677706, -1.1829936015765863], Complex[-0.3213270063391195, -0.3051912044731223]] Test Values: {Rule[p, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[x, 1.5], Rule[y, -1.5]} Result: LessEqual[Complex[0.7797231369520263, -0.6247258696161743], Complex[-0.6706782382611747, 0.54526856836685]] Test Values: {Rule[p, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[x, 1.5], Rule[y, 1.5]} ... skip entries to safe data
19.24.E4	${\displaystyle{\displaystyle\frac{4}{3\pi}R_{J}\left(0,y,z,p\right)\leq(yzp^{2% })^{-3/8}}}$ `\frac{4}{3\pi}\CarlsonsymellintRJ@{0}{y}{z}{p} \leq (yzp^{2})^{-3/8}`		Error	Divide[4,3Pi]3(x + yI-0)/(x + yI-p)(EllipticPi[(x + yI-p)/(x + yI-0),ArcCos[Sqrt[0/x + yI]],(x + yI-y)/(x + yI-0)]-EllipticF[ArcCos[Sqrt[0/x + yI]],(x + yI-y)/(x + yI-0)])/Sqrt[x + yI-0] <= (y(x + yI)(p)^(2))^(- 3/8)	Missing Macro Error	Failure	-	Failed [180 / 180] Result: LessEqual[Complex[-0.3213270063391195, -0.3051912044731223], Complex[0.5136265917030035, 0.9609277658721954]] Test Values: {Rule[p, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[x, 1.5], Rule[y, -1.5]} Result: LessEqual[Complex[-0.6706782382611747, 0.54526856836685], Complex[0.8422602311268256, -0.6912251080442312]] Test Values: {Rule[p, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[x, 1.5], Rule[y, 1.5]} ... skip entries to safe data
19.24.E5	${\displaystyle{\displaystyle\frac{1}{a_{n}}\leq\frac{2}{\pi}R_{F}\left(0,a_{0}% ^{2},g_{0}^{2}\right)}}$ `\frac{1}{a_{n}} \leq \frac{2}{\pi}\CarlsonsymellintRF@{0}{a_{0}^{2}}{g_{0}^{2}}`		(1)/(a[n]) <= (2)/(Pi)0.5int(1/(sqrt(t+0)sqrt(t+(a[0])^(2))sqrt(t+(g[0])^(2))), t = 0..infinity)	Divide[1,Subscript[a, n]] <= Divide[2,Pi]*EllipticF[ArcCos[Sqrt[0/(Subscript[g, 0])^(2)]],((Subscript[g, 0])^(2)-(Subscript[a, 0])^(2))/((Subscript[g, 0])^(2)-0)]/Sqrt[(Subscript[g, 0])^(2)-0]	Aborted	Failure	Skipped - Because timed out	Failed [300 / 300] Result: LessEqual[Complex[1.7320508075688774, -0.9999999999999999], Times[2.0, Power[Times[Complex[0.5000000000000001, 0.8660254037844386], g], Rational[-1, 2]], EllipticK[Times[Complex[2.0000000000000004, -3.4641016151377544], Plus[Times[Complex[-0.12500000000000003, -0.21650635094610965], a], Times[Complex[0.12500000000000003, 0.21650635094610965], g]], Power[g, -1]]]]] Test Values: {Rule[n, 3], Rule[Subscript[a, 0], Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[Subscript[a, n], Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[Subscript[g, 0], Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]} Result: LessEqual[Complex[1.7320508075688774, -0.9999999999999999], Times[2.0, Power[Times[Complex[-0.4999999999999998, -0.8660254037844387], g], Rational[-1, 2]], EllipticK[Times[Complex[-1.9999999999999991, 3.464101615137755], Plus[Times[Complex[-0.12500000000000003, -0.21650635094610965], a], Times[Complex[-0.12499999999999994, -0.21650635094610968], g]], Power[g, -1]]]]] Test Values: {Rule[n, 3], Rule[Subscript[a, 0], Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[Subscript[a, n], Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[Subscript[g, 0], Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]]} ... skip entries to safe data
19.24.E5	${\displaystyle{\displaystyle\frac{2}{\pi}R_{F}\left(0,a_{0}^{2},g_{0}^{2}% \right)\leq\frac{1}{g_{n}}}}$ `\frac{2}{\pi}\CarlsonsymellintRF@{0}{a_{0}^{2}}{g_{0}^{2}} \leq \frac{1}{g_{n}}`		(2)/(Pi)0.5int(1/(sqrt(t+0)sqrt(t+(a[0])^(2))sqrt(t+(g[0])^(2))), t = 0..infinity) <= (1)/(g[n])	Divide[2,Pi]*EllipticF[ArcCos[Sqrt[0/(Subscript[g, 0])^(2)]],((Subscript[g, 0])^(2)-(Subscript[a, 0])^(2))/((Subscript[g, 0])^(2)-0)]/Sqrt[(Subscript[g, 0])^(2)-0] <= Divide[1,Subscript[g, n]]	Aborted	Failure	Skipped - Because timed out	Failed [300 / 300] Result: LessEqual[Times[2.0, Power[Times[Complex[0.5000000000000001, 0.8660254037844386], g], Rational[-1, 2]], EllipticK[Times[Complex[2.0000000000000004, -3.4641016151377544], Plus[Times[Complex[-0.12500000000000003, -0.21650635094610965], a], Times[Complex[0.12500000000000003, 0.21650635094610965], g]], Power[g, -1]]]], Complex[1.7320508075688774, -0.9999999999999999]] Test Values: {Rule[n, 3], Rule[Subscript[a, 0], Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[Subscript[g, 0], Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[Subscript[g, n], Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]} Result: LessEqual[Times[2.0, Power[Times[Complex[0.5000000000000001, 0.8660254037844386], g], Rational[-1, 2]], EllipticK[Times[Complex[2.0000000000000004, -3.4641016151377544], Plus[Times[Complex[-0.12500000000000003, -0.21650635094610965], a], Times[Complex[0.12500000000000003, 0.21650635094610965], g]], Power[g, -1]]]], Complex[-0.9999999999999996, -1.7320508075688774]] Test Values: {Rule[n, 3], Rule[Subscript[a, 0], Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[Subscript[g, 0], Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[Subscript[g, n], Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]]} ... skip entries to safe data
19.24#Ex1	${\displaystyle{\displaystyle a_{n+1}=(a_{n}+g_{n})/2}}$ `a_{n+1} = (a_{n}+g_{n})/2`		a[n + 1] = (a[n]+ g[n])/2	Subscript[a, n + 1] == (Subscript[a, n]+ Subscript[g, n])/2	Skipped - no semantic math	Skipped - no semantic math	-	-
19.24#Ex2	${\displaystyle{\displaystyle g_{n+1}=\sqrt{a_{n}g_{n}}}}$ `g_{n+1} = \sqrt{a_{n}g_{n}}`		g[n + 1] = sqrt(a[n]*g[n])	Subscript[g, n + 1] == Sqrt[Subscript[a, n]*Subscript[g, n]]	Skipped - no semantic math	Skipped - no semantic math	-	-
19.24.E7	${\displaystyle{\displaystyle L(a,b)=8R_{G}\left(0,a^{2},b^{2}\right)}}$ `L(a,b) = 8\CarlsonsymellintRG@{0}{a^{2}}{b^{2}}`		Error	L[a , b] == 8Sqrt[(b)^(2)-0](EllipticE[ArcCos[Sqrt[0/(b)^(2)]],((b)^(2)-(a)^(2))/((b)^(2)-0)]+(Cot[ArcCos[Sqrt[0/(b)^(2)]]])^2EllipticF[ArcCos[Sqrt[0/(b)^(2)]],((b)^(2)-(a)^(2))/((b)^(2)-0)]+Cot[ArcCos[Sqrt[0/(b)^(2)]]]Sqrt[1-k^2*Sin[ArcCos[Sqrt[0/(b)^(2)]]]^2])	Missing Macro Error	Failure	-	Error
19.24#Ex3	${\displaystyle{\displaystyle R_{F}\left(x,y,0\right)R_{G}\left(x,y,0\right)>% \tfrac{1}{8}\pi^{2}}}$ `\CarlsonsymellintRF@{x}{y}{0}\CarlsonsymellintRG@{x}{y}{0} > \tfrac{1}{8}\pi^{2}`		Error	EllipticF[ArcCos[Sqrt[x/0]],(0-y)/(0-x)]/Sqrt[0-x]Sqrt[0-x](EllipticE[ArcCos[Sqrt[x/0]],(0-y)/(0-x)]+(Cot[ArcCos[Sqrt[x/0]]])^2EllipticF[ArcCos[Sqrt[x/0]],(0-y)/(0-x)]+Cot[ArcCos[Sqrt[x/0]]]Sqrt[1-k^2Sin[ArcCos[Sqrt[x/0]]]^2]) > Divide[1,8](Pi)^(2)	Missing Macro Error	Failure	-	Failed [18 / 18] Result: Greater[Indeterminate, 1.2337005501361697] Test Values: {Rule[x, 1.5], Rule[y, -1.5]} Result: Greater[Indeterminate, 1.2337005501361697] Test Values: {Rule[x, 1.5], Rule[y, 1.5]} ... skip entries to safe data
19.24#Ex4	${\displaystyle{\displaystyle R_{F}\left(x,y,0\right)+2R_{G}\left(x,y,0\right)>% \pi}}$ `\CarlsonsymellintRF@{x}{y}{0}+2\CarlsonsymellintRG@{x}{y}{0} > \pi`		Error	EllipticF[ArcCos[Sqrt[x/0]],(0-y)/(0-x)]/Sqrt[0-x]+ 2Sqrt[0-x](EllipticE[ArcCos[Sqrt[x/0]],(0-y)/(0-x)]+(Cot[ArcCos[Sqrt[x/0]]])^2EllipticF[ArcCos[Sqrt[x/0]],(0-y)/(0-x)]+Cot[ArcCos[Sqrt[x/0]]]Sqrt[1-k^2*Sin[ArcCos[Sqrt[x/0]]]^2]) > Pi	Missing Macro Error	Failure	-	Failed [18 / 18] Result: Greater[Indeterminate, 3.141592653589793] Test Values: {Rule[x, 1.5], Rule[y, -1.5]} Result: Greater[Indeterminate, 3.141592653589793] Test Values: {Rule[x, 1.5], Rule[y, 1.5]} ... skip entries to safe data
19.24.E9	${\displaystyle{\displaystyle\frac{1}{2}\,g_{1}^{2}\leq\frac{R_{G}\left(a_{0}^{% 2},g_{0}^{2},0\right)}{R_{F}\left(a_{0}^{2},g_{0}^{2},0\right)}}}$ `\frac{1}{2}\,g_{1}^{2} \leq \frac{\CarlsonsymellintRG@{a_{0}^{2}}{g_{0}^{2}}{0}}{\CarlsonsymellintRF@{a_{0}^{2}}{g_{0}^{2}}{0}}`		Error	Divide[1,2](Subscript[g, 1])^(2) <= Divide[Sqrt[0-(Subscript[a, 0])^(2)](EllipticE[ArcCos[Sqrt[(Subscript[a, 0])^(2)/0]],(0-(Subscript[g, 0])^(2))/(0-(Subscript[a, 0])^(2))]+(Cot[ArcCos[Sqrt[(Subscript[a, 0])^(2)/0]]])^2EllipticF[ArcCos[Sqrt[(Subscript[a, 0])^(2)/0]],(0-(Subscript[g, 0])^(2))/(0-(Subscript[a, 0])^(2))]+Cot[ArcCos[Sqrt[(Subscript[a, 0])^(2)/0]]]Sqrt[1-k^2*Sin[ArcCos[Sqrt[(Subscript[a, 0])^(2)/0]]]^2]),EllipticF[ArcCos[Sqrt[(Subscript[a, 0])^(2)/0]],(0-(Subscript[g, 0])^(2))/(0-(Subscript[a, 0])^(2))]/Sqrt[0-(Subscript[a, 0])^(2)]]	Missing Macro Error	Failure	-	Failed [300 / 300] Result: LessEqual[Complex[0.06250000000000001, 0.10825317547305482], Indeterminate] Test Values: {Rule[Subscript[a, 0], Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[Subscript[g, 0], Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[Subscript[g, 1], Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]} Result: LessEqual[Complex[-0.06249999999999997, -0.10825317547305484], Indeterminate] Test Values: {Rule[Subscript[a, 0], Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[Subscript[g, 0], Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[Subscript[g, 1], Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]]} ... skip entries to safe data
19.24.E9	${\displaystyle{\displaystyle\frac{R_{G}\left(a_{0}^{2},g_{0}^{2},0\right)}{R_{% F}\left(a_{0}^{2},g_{0}^{2},0\right)}\leq\frac{1}{2}\,a_{1}^{2}}}$ `\frac{\CarlsonsymellintRG@{a_{0}^{2}}{g_{0}^{2}}{0}}{\CarlsonsymellintRF@{a_{0}^{2}}{g_{0}^{2}}{0}} \leq \frac{1}{2}\,a_{1}^{2}`		Error	Divide[Sqrt[0-(Subscript[a, 0])^(2)](EllipticE[ArcCos[Sqrt[(Subscript[a, 0])^(2)/0]],(0-(Subscript[g, 0])^(2))/(0-(Subscript[a, 0])^(2))]+(Cot[ArcCos[Sqrt[(Subscript[a, 0])^(2)/0]]])^2EllipticF[ArcCos[Sqrt[(Subscript[a, 0])^(2)/0]],(0-(Subscript[g, 0])^(2))/(0-(Subscript[a, 0])^(2))]+Cot[ArcCos[Sqrt[(Subscript[a, 0])^(2)/0]]]Sqrt[1-k^2Sin[ArcCos[Sqrt[(Subscript[a, 0])^(2)/0]]]^2]),EllipticF[ArcCos[Sqrt[(Subscript[a, 0])^(2)/0]],(0-(Subscript[g, 0])^(2))/(0-(Subscript[a, 0])^(2))]/Sqrt[0-(Subscript[a, 0])^(2)]] <= Divide[1,2]*(Subscript[a, 1])^(2)	Missing Macro Error	Failure	-	Failed [300 / 300] Result: LessEqual[Indeterminate, Complex[0.06250000000000001, 0.10825317547305482]] Test Values: {Rule[Subscript[a, 0], Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[Subscript[a, 1], Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[Subscript[g, 0], Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]} Result: LessEqual[Indeterminate, Complex[0.06250000000000001, 0.10825317547305482]] Test Values: {Rule[Subscript[a, 0], Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[Subscript[a, 1], Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[Subscript[g, 0], Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]]} ... skip entries to safe data
19.24.E10	${\displaystyle{\displaystyle\frac{3}{\sqrt{x}+\sqrt{y}+\sqrt{z}}\leq R_{F}% \left(x,y,z\right)}}$ `\frac{3}{\sqrt{x}+\sqrt{y}+\sqrt{z}} \leq \CarlsonsymellintRF@{x}{y}{z}`		(3)/(sqrt(x)+sqrt(y)+sqrt(x + yI)) <= 0.5int(1/(sqrt(t+x)sqrt(t+y)sqrt(t+x + y*I)), t = 0..infinity)	Divide[3,Sqrt[x]+Sqrt[y]+Sqrt[x + yI]] <= EllipticF[ArcCos[Sqrt[x/x + yI]],(x + yI-y)/(x + yI-x)]/Sqrt[x + y*I-x]	Aborted	Failure	Error	Failed [18 / 18] Result: LessEqual[Complex[1.0934408788539995, -0.2839050517129825], Complex[-0.16214470973156064, 0.6784437678906974]] Test Values: {Rule[x, 1.5], Rule[y, -1.5]} Result: LessEqual[Complex[0.7738030002696183, -0.11364498174072818], Complex[-0.28823404661462, -0.7809212115368181]] Test Values: {Rule[x, 1.5], Rule[y, 1.5]} ... skip entries to safe data
19.24.E10	${\displaystyle{\displaystyle R_{F}\left(x,y,z\right)\leq\frac{1}{(xyz)^{1/6}}}}$ `\CarlsonsymellintRF@{x}{y}{z} \leq \frac{1}{(xyz)^{1/6}}`		0.5int(1/(sqrt(t+x)sqrt(t+y)sqrt(t+x + yI)), t = 0..infinity) <= (1)/((xy(x + y*I))^(1/6))	EllipticF[ArcCos[Sqrt[x/x + yI]],(x + yI-y)/(x + yI-x)]/Sqrt[x + yI-x] <= Divide[1,(xy(x + y*I))^(1/6)]	Aborted	Failure	Error	Failed [18 / 18] Result: LessEqual[Complex[-0.16214470973156064, 0.6784437678906974], Complex[0.7120063770987297, -0.29492269789042613]] Test Values: {Rule[x, 1.5], Rule[y, -1.5]} Result: LessEqual[Complex[-0.28823404661462, -0.7809212115368181], Complex[0.7640769591692358, -0.10059264002361257]] Test Values: {Rule[x, 1.5], Rule[y, 1.5]} ... skip entries to safe data
19.24.E11	${\displaystyle{\displaystyle\left(\frac{5}{\sqrt{x}+\sqrt{y}+\sqrt{z}+2\sqrt{p% }}\right)^{3}\leq R_{J}\left(x,y,z,p\right)}}$ `\left(\frac{5}{\sqrt{x}+\sqrt{y}+\sqrt{z}+2\sqrt{p}}\right)^{3} \leq \CarlsonsymellintRJ@{x}{y}{z}{p}`		Error	(Divide[5,Sqrt[x]+Sqrt[y]+Sqrt[x + yI]+ 2Sqrt[p]])^(3) <= 3(x + yI-x)/(x + yI-p)(EllipticPi[(x + yI-p)/(x + yI-x),ArcCos[Sqrt[x/x + yI]],(x + yI-y)/(x + yI-x)]-EllipticF[ArcCos[Sqrt[x/x + yI]],(x + yI-y)/(x + yI-x)])/Sqrt[x + y*I-x]	Missing Macro Error	Failure	-	Failed [180 / 180] Result: LessEqual[Complex[1.3310335634294785, -1.2911719373315522], Complex[-0.2876927312707393, -0.327259429717868]] Test Values: {Rule[p, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[x, 1.5], Rule[y, -1.5]} Result: LessEqual[Complex[0.7477899794343462, -0.4392695700678081], Complex[-0.36602768453446033, 0.5058947820270108]] Test Values: {Rule[p, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[x, 1.5], Rule[y, 1.5]} ... skip entries to safe data
19.24.E11	${\displaystyle{\displaystyle R_{J}\left(x,y,z,p\right)\leq(xyzp^{2})^{-3/10}}}$ `\CarlsonsymellintRJ@{x}{y}{z}{p} \leq (xyzp^{2})^{-3/10}`		Error	3(x + yI-x)/(x + yI-p)(EllipticPi[(x + yI-p)/(x + yI-x),ArcCos[Sqrt[x/x + yI]],(x + yI-y)/(x + yI-x)]-EllipticF[ArcCos[Sqrt[x/x + yI]],(x + yI-y)/(x + yI-x)])/Sqrt[x + yI-x] <= (xy(x + yI)*(p)^(2))^(- 3/10)	Missing Macro Error	Failure	-	Failed [180 / 180] Result: LessEqual[Complex[-0.2876927312707393, -0.327259429717868], Complex[0.6159220908806466, 0.7211521128667333]] Test Values: {Rule[p, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[x, 1.5], Rule[y, -1.5]} Result: LessEqual[Complex[-0.36602768453446033, 0.5058947820270108], Complex[0.8086249764673956, -0.49552602288885395]] Test Values: {Rule[p, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[x, 1.5], Rule[y, 1.5]} ... skip entries to safe data
19.24.E12	${\displaystyle{\displaystyle\tfrac{1}{3}(\sqrt{x}+\sqrt{y}+\sqrt{z})\leq R_{G}% \left(x,y,z\right)}}$ `\tfrac{1}{3}(\sqrt{x}+\sqrt{y}+\sqrt{z}) \leq \CarlsonsymellintRG@{x}{y}{z}`		Error	Divide[1,3](Sqrt[x]+Sqrt[y]+Sqrt[x + yI]) <= Sqrt[x + yI-x](EllipticE[ArcCos[Sqrt[x/x + yI]],(x + yI-y)/(x + yI-x)]+(Cot[ArcCos[Sqrt[x/x + yI]]])^2EllipticF[ArcCos[Sqrt[x/x + yI]],(x + yI-y)/(x + yI-x)]+Cot[ArcCos[Sqrt[x/x + yI]]]Sqrt[1-k^2Sin[ArcCos[Sqrt[x/x + yI]]]^2])	Missing Macro Error	Failure	-	Failed [18 / 18] Result: LessEqual[Complex[0.8567842015469013, 0.22245863288189585], Times[Complex[0.8660254037844386, -0.8660254037844385], Plus[Complex[0.9985512968581824, 0.2012315241723115], Times[Complex[0.3176872874027722, -1.049249833251038], Power[Plus[1.0, Times[Complex[0.0, -1.5], Power[k, 2]]], Rational[1, 2]]]]]] Test Values: {Rule[x, 1.5], Rule[y, -1.5]} Result: LessEqual[Complex[1.2650324920107643, 0.1857896575819671], Times[Complex[0.8660254037844386, 0.8660254037844385], Plus[Complex[1.0566228789425183, 0.3443432776585209], Times[Complex[0.3176872874027722, 1.049249833251038], Power[Plus[1.0, Times[Complex[0.0, 1.5], Power[k, 2]]], Rational[1, 2]]]]]] Test Values: {Rule[x, 1.5], Rule[y, 1.5]} ... skip entries to safe data
19.24#Ex7	${\displaystyle{\displaystyle R_{F}\left(x,y,z\right)R_{G}\left(x,y,z\right)>1}}$ `\CarlsonsymellintRF@{x}{y}{z}\CarlsonsymellintRG@{x}{y}{z} > 1`		Error	EllipticF[ArcCos[Sqrt[x/x + yI]],(x + yI-y)/(x + yI-x)]/Sqrt[x + yI-x]Sqrt[x + yI-x](EllipticE[ArcCos[Sqrt[x/x + yI]],(x + yI-y)/(x + yI-x)]+(Cot[ArcCos[Sqrt[x/x + yI]]])^2EllipticF[ArcCos[Sqrt[x/x + yI]],(x + yI-y)/(x + yI-x)]+Cot[ArcCos[Sqrt[x/x + yI]]]Sqrt[1-k^2Sin[ArcCos[Sqrt[x/x + y*I]]]^2]) > 1	Missing Macro Error	Failure	-	Failed [18 / 18] Result: Greater[Times[Complex[0.44712810031579164, 0.7279709757493625], Plus[Complex[0.9985512968581824, 0.2012315241723115], Times[Complex[0.3176872874027722, -1.049249833251038], Power[Plus[1.0, Times[Complex[0.0, -1.5], Power[k, 2]]], Rational[1, 2]]]]], 1.0] Test Values: {Rule[x, 1.5], Rule[y, -1.5]} Result: Greater[Times[Complex[0.42667960094115687, -0.925915614148855], Plus[Complex[1.0566228789425183, 0.3443432776585209], Times[Complex[0.3176872874027722, 1.049249833251038], Power[Plus[1.0, Times[Complex[0.0, 1.5], Power[k, 2]]], Rational[1, 2]]]]], 1.0] Test Values: {Rule[x, 1.5], Rule[y, 1.5]} ... skip entries to safe data
19.24#Ex8	${\displaystyle{\displaystyle R_{F}\left(x,y,z\right)+R_{G}\left(x,y,z\right)>2}}$ `\CarlsonsymellintRF@{x}{y}{z}+\CarlsonsymellintRG@{x}{y}{z} > 2`		Error	EllipticF[ArcCos[Sqrt[x/x + yI]],(x + yI-y)/(x + yI-x)]/Sqrt[x + yI-x]+ Sqrt[x + yI-x](EllipticE[ArcCos[Sqrt[x/x + yI]],(x + yI-y)/(x + yI-x)]+(Cot[ArcCos[Sqrt[x/x + yI]]])^2EllipticF[ArcCos[Sqrt[x/x + yI]],(x + yI-y)/(x + yI-x)]+Cot[ArcCos[Sqrt[x/x + yI]]]Sqrt[1-k^2Sin[ArcCos[Sqrt[x/x + yI]]]^2]) > 2	Missing Macro Error	Failure	-	Failed [18 / 18] Result: Greater[Plus[Complex[-0.16214470973156064, 0.6784437678906974], Times[Complex[0.8660254037844386, -0.8660254037844385], Plus[Complex[0.9985512968581824, 0.2012315241723115], Times[Complex[0.3176872874027722, -1.049249833251038], Power[Plus[1.0, Times[Complex[0.0, -1.5], Power[k, 2]]], Rational[1, 2]]]]]], 2.0] Test Values: {Rule[x, 1.5], Rule[y, -1.5]} Result: Greater[Plus[Complex[-0.28823404661462, -0.7809212115368181], Times[Complex[0.8660254037844386, 0.8660254037844385], Plus[Complex[1.0566228789425183, 0.3443432776585209], Times[Complex[0.3176872874027722, 1.049249833251038], Power[Plus[1.0, Times[Complex[0.0, 1.5], Power[k, 2]]], Rational[1, 2]]]]]], 2.0] Test Values: {Rule[x, 1.5], Rule[y, 1.5]} ... skip entries to safe data
19.24.E15	${\displaystyle{\displaystyle R_{C}\left(x,\tfrac{1}{2}(y+z)\right)\leq R_{F}% \left(x,y,z\right)}}$ `\CarlsonellintRC@{x}{\tfrac{1}{2}(y+z)} \leq \CarlsonsymellintRF@{x}{y}{z}`	${\displaystyle{\displaystyle x\geq 0}}$	Error	1/Sqrt[Divide[1,2](y +(x + yI))]Hypergeometric2F1[1/2,1/2,3/2,1-(x)/(Divide[1,2](y +(x + yI)))] <= EllipticF[ArcCos[Sqrt[x/x + yI]],(x + yI-y)/(x + yI-x)]/Sqrt[x + y*I-x]	Missing Macro Error	Failure	-	Failed [18 / 18] Result: LessEqual[Complex[0.9580693887321644, 0.49152363500125495], Complex[-0.16214470973156064, 0.6784437678906974]] Test Values: {Rule[x, 1.5], Rule[y, -1.5]} Result: LessEqual[Complex[0.7805167095081702, -0.12346643314922054], Complex[-0.28823404661462, -0.7809212115368181]] Test Values: {Rule[x, 1.5], Rule[y, 1.5]} ... skip entries to safe data
19.24.E15	${\displaystyle{\displaystyle R_{F}\left(x,y,z\right)\leq R_{C}\left(x,\sqrt{yz% }\right)}}$ `\CarlsonsymellintRF@{x}{y}{z} \leq \CarlsonellintRC@{x}{\sqrt{yz}}`	${\displaystyle{\displaystyle x\geq 0}}$	Error	EllipticF[ArcCos[Sqrt[x/x + yI]],(x + yI-y)/(x + yI-x)]/Sqrt[x + yI-x] <= 1/Sqrt[Sqrt[y(x + yI)]]Hypergeometric2F1[1/2,1/2,3/2,1-(x)/(Sqrt[y(x + y*I)])]	Missing Macro Error	Failure	-	Failed [18 / 18] Result: LessEqual[Complex[-0.16214470973156064, 0.6784437678906974], Complex[0.7308447207533646, -0.31118718328917466]] Test Values: {Rule[x, 1.5], Rule[y, -1.5]} Result: LessEqual[Complex[-0.28823404661462, -0.7809212115368181], Complex[0.765857524311696, -0.1031964554328576]] Test Values: {Rule[x, 1.5], Rule[y, 1.5]} ... skip entries to safe data
19.25#Ex1	${\displaystyle{\displaystyle K\left(k\right)=R_{F}\left(0,{k^{\prime}}^{2},1% \right)}}$ `\compellintKk@{k} = \CarlsonsymellintRF@{0}{{k^{\prime}}^{2}}{1}`		EllipticK(k) = 0.5int(1/(sqrt(t+0)sqrt(t+1 - (k)^(2))*sqrt(t+1)), t = 0..infinity)	EllipticK[(k)^2] == EllipticF[ArcCos[Sqrt[0/1]],(1-1 - (k)^(2))/(1-0)]/Sqrt[1-0]	Failure	Failure	Error	Failed [3 / 3] Result: DirectedInfinity[] Test Values: {Rule[k, 1]} Result: Complex[-0.16657773258291342, -1.0782578237498217] Test Values: {Rule[k, 2]} ... skip entries to safe data
19.25#Ex2	${\displaystyle{\displaystyle E\left(k\right)=2R_{G}\left(0,{k^{\prime}}^{2},1% \right)}}$ `\compellintEk@{k} = 2\CarlsonsymellintRG@{0}{{k^{\prime}}^{2}}{1}`		Error	EllipticE[(k)^2] == 2Sqrt[1-0](EllipticE[ArcCos[Sqrt[0/1]],(1-1 - (k)^(2))/(1-0)]+(Cot[ArcCos[Sqrt[0/1]]])^2EllipticF[ArcCos[Sqrt[0/1]],(1-1 - (k)^(2))/(1-0)]+Cot[ArcCos[Sqrt[0/1]]]Sqrt[1-k^2*Sin[ArcCos[Sqrt[0/1]]]^2])	Missing Macro Error	Failure	-	Failed [3 / 3] Result: -2.820197789027711 Test Values: {Rule[k, 1]} Result: Complex[-4.864068276731299, 1.343854231387098] Test Values: {Rule[k, 2]} ... skip entries to safe data
19.25#Ex3	${\displaystyle{\displaystyle E\left(k\right)=\tfrac{1}{3}{k^{\prime}}^{2}\left% (R_{D}\left(0,{k^{\prime}}^{2},1\right)+R_{D}\left(0,1,{k^{\prime}}^{2}\right)% \right)}}$ `\compellintEk@{k} = \tfrac{1}{3}{k^{\prime}}^{2}\left(\CarlsonsymellintRD@{0}{{k^{\prime}}^{2}}{1}+\CarlsonsymellintRD@{0}{1}{{k^{\prime}}^{2}}\right)`		Error	EllipticE[(k)^2] == Divide[1,3]1 - (k)^(2)(3(EllipticF[ArcCos[Sqrt[0/1]],(1-1 - (k)^(2))/(1-0)]-EllipticE[ArcCos[Sqrt[0/1]],(1-1 - (k)^(2))/(1-0)])/((1-1 - (k)^(2))(1-0)^(1/2))+ 3(EllipticF[ArcCos[Sqrt[0/1 - (k)^(2)]],(1 - (k)^(2)-1)/(1 - (k)^(2)-0)]-EllipticE[ArcCos[Sqrt[0/1 - (k)^(2)]],(1 - (k)^(2)-1)/(1 - (k)^(2)-0)])/((1 - (k)^(2)-1)(1 - (k)^(2)-0)^(1/2)))	Missing Macro Error	Failure	-	Failed [3 / 3] Result: DirectedInfinity[] Test Values: {Rule[k, 1]} Result: Complex[7.885081986624734, -2.293856789051463] Test Values: {Rule[k, 2]} ... skip entries to safe data
19.25#Ex4	${\displaystyle{\displaystyle K\left(k\right)-E\left(k\right)=k^{2}D\left(k% \right)}}$ `\compellintKk@{k}-\compellintEk@{k} = k^{2}\compellintDk@{k}`		EllipticK(k)- EllipticE(k) = (k)^(2)* (EllipticK(k) - EllipticE(k))/(k)^2	EllipticK[(k)^2]- EllipticE[(k)^2] == (k)^(2)* Divide[EllipticK[(k)^2] - EllipticE[(k)^2], (k)^4]	Successful	Failure	-	Failed [3 / 3] Result: Indeterminate Test Values: {Rule[k, 1]} Result: Complex[0.3274322182097533, -1.81658404135269] Test Values: {Rule[k, 2]} ... skip entries to safe data
19.25#Ex4	${\displaystyle{\displaystyle k^{2}D\left(k\right)=\tfrac{1}{3}k^{2}R_{D}\left(% 0,{k^{\prime}}^{2},1\right)}}$ `k^{2}\compellintDk@{k} = \tfrac{1}{3}k^{2}\CarlsonsymellintRD@{0}{{k^{\prime}}^{2}}{1}`		Error	(k)^(2)* Divide[EllipticK[(k)^2] - EllipticE[(k)^2], (k)^4] == Divide[1,3](k)^(2) 3(EllipticF[ArcCos[Sqrt[0/1]],(1-1 - (k)^(2))/(1-0)]-EllipticE[ArcCos[Sqrt[0/1]],(1-1 - (k)^(2))/(1-0)])/((1-1 - (k)^(2))(1-0)^(1/2))	Missing Macro Error	Failure	-	Failed [3 / 3] Result: DirectedInfinity[] Test Values: {Rule[k, 1]} Result: Complex[-1.5165865988698335, -0.6055280137842299] Test Values: {Rule[k, 2]} ... skip entries to safe data
19.25#Ex5	${\displaystyle{\displaystyle E\left(k\right)-{k^{\prime}}^{2}K\left(k\right)=% \tfrac{1}{3}k^{2}{k^{\prime}}^{2}R_{D}\left(0,1,{k^{\prime}}^{2}\right)}}$ `\compellintEk@{k}-{k^{\prime}}^{2}\compellintKk@{k} = \tfrac{1}{3}k^{2}{k^{\prime}}^{2}\CarlsonsymellintRD@{0}{1}{{k^{\prime}}^{2}}`		Error	EllipticE[(k)^2]-1 - (k)^(2)EllipticK[(k)^2] == Divide[1,3](k)^(2)1 - (k)^(2)3(EllipticF[ArcCos[Sqrt[0/1 - (k)^(2)]],(1 - (k)^(2)-1)/(1 - (k)^(2)-0)]-EllipticE[ArcCos[Sqrt[0/1 - (k)^(2)]],(1 - (k)^(2)-1)/(1 - (k)^(2)-0)])/((1 - (k)^(2)-1)(1 - (k)^(2)-0)^(1/2))	Missing Macro Error	Failure	-	Failed [3 / 3] Result: Indeterminate Test Values: {Rule[k, 1]} Result: Complex[-2.3636107378197124, 2.0191745059478237] Test Values: {Rule[k, 2]} ... skip entries to safe data
19.25.E2	${\displaystyle{\displaystyle\Pi\left(\alpha^{2},k\right)-K\left(k\right)=% \tfrac{1}{3}\alpha^{2}R_{J}\left(0,{k^{\prime}}^{2},1,1-\alpha^{2}\right)}}$ `\compellintPik@{\alpha^{2}}{k}-\compellintKk@{k} = \tfrac{1}{3}\alpha^{2}\CarlsonsymellintRJ@{0}{{k^{\prime}}^{2}}{1}{1-\alpha^{2}}`		Error	EllipticPi[\[Alpha]^(2), (k)^2]- EllipticK[(k)^2] == Divide[1,3]\[Alpha]^(2) 3(1-0)/(1-1 - \[Alpha]^(2))(EllipticPi[(1-1 - \[Alpha]^(2))/(1-0),ArcCos[Sqrt[0/1]],(1-1 - (k)^(2))/(1-0)]-EllipticF[ArcCos[Sqrt[0/1]],(1-1 - (k)^(2))/(1-0)])/Sqrt[1-0]	Missing Macro Error	Failure	-	Failed [9 / 9] Result: Indeterminate Test Values: {Rule[k, 1], Rule[α, 1.5]} Result: Complex[-1.5241433161083033, 0.5547659663605348] Test Values: {Rule[k, 2], Rule[α, 1.5]} ... skip entries to safe data
19.25.E4	${\displaystyle{\displaystyle\Pi\left(\alpha^{2},k\right)=-\tfrac{1}{3}(k^{2}/% \alpha^{2})R_{J}\left(0,1-k^{2},1,1-(k^{2}/\alpha^{2})\right)}}$ `\compellintPik@{\alpha^{2}}{k} = -\tfrac{1}{3}(k^{2}/\alpha^{2})\CarlsonsymellintRJ@{0}{1-k^{2}}{1}{1-(k^{2}/\alpha^{2})}`	${\displaystyle{\displaystyle-\infty<k^{2},k^{2}<1,1<\alpha^{2}}}$	Error	EllipticPi[\[Alpha]^(2), (k)^2] == -Divide[1,3]((k)^(2)/\[Alpha]^(2))3(1-0)/(1-1 -((k)^(2)/\[Alpha]^(2)))(EllipticPi[(1-1 -((k)^(2)/\[Alpha]^(2)))/(1-0),ArcCos[Sqrt[0/1]],(1-1 - (k)^(2))/(1-0)]-EllipticF[ArcCos[Sqrt[0/1]],(1-1 - (k)^(2))/(1-0)])/Sqrt[1-0]	Missing Macro Error	Failure	-	Skip - No test values generated
19.25.E5	${\displaystyle{\displaystyle F\left(\phi,k\right)=R_{F}\left(c-1,c-k^{2},c% \right)}}$ `\incellintFk@{\phi}{k} = \CarlsonsymellintRF@{c-1}{c-k^{2}}{c}`		EllipticF(sin(phi), k) = 0.5int(1/(sqrt(t+c - 1)sqrt(t+c - (k)^(2))*sqrt(t+c)), t = 0..infinity)	EllipticF[\[Phi], (k)^2] == EllipticF[ArcCos[Sqrt[c - 1/c]],(c-c - (k)^(2))/(c-c - 1)]/Sqrt[c-c - 1]	Failure	Failure	Failed [180 / 180] Result: Float(undefined)+Float(undefined)I Test Values: {c = -3/2, phi = 1/23^(1/2)+1/2I, k = 1} Result: 3.854689052+3.461698034I Test Values: {c = -3/2, phi = 1/23^(1/2)+1/2I, k = 2} ... skip entries to safe data	Failed [180 / 180] Result: Complex[2.0026000841930385, 1.2187088711714384] Test Values: {Rule[c, -1.5], Rule[k, 1], Rule[ϕ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]} Result: Complex[1.4748265293714395, 0.7583435972865697] Test Values: {Rule[c, -1.5], Rule[k, 2], Rule[ϕ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]} ... skip entries to safe data
19.25.E6	${\displaystyle{\displaystyle\frac{\partial F\left(\phi,k\right)}{\partial k}=% \tfrac{1}{3}kR_{D}\left(c-1,c,c-k^{2}\right)}}$ `\pderiv{\incellintFk@{\phi}{k}}{k} = \tfrac{1}{3}k\CarlsonsymellintRD@{c-1}{c}{c-k^{2}}`		Error	D[EllipticF[\[Phi], (k)^2], k] == Divide[1,3]k3(EllipticF[ArcCos[Sqrt[c - 1/c - (k)^(2)]],(c - (k)^(2)-c)/(c - (k)^(2)-c - 1)]-EllipticE[ArcCos[Sqrt[c - 1/c - (k)^(2)]],(c - (k)^(2)-c)/(c - (k)^(2)-c - 1)])/((c - (k)^(2)-c)(c - (k)^(2)-c - 1)^(1/2))	Missing Macro Error	Failure	-	Failed [180 / 180] Result: Indeterminate Test Values: {Rule[c, -1.5], Rule[k, 1], Rule[ϕ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]} Result: Complex[-0.4045300788217367, 0.4404710702025501] Test Values: {Rule[c, -1.5], Rule[k, 2], Rule[ϕ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]} ... skip entries to safe data
19.25.E7	${\displaystyle{\displaystyle E\left(\phi,k\right)=2R_{G}\left(c-1,c-k^{2},c% \right)-(c-1)R_{F}\left(c-1,c-k^{2},c\right)-\sqrt{(c-1)(c-k^{2})/c}}}$ `\incellintEk@{\phi}{k} = 2\CarlsonsymellintRG@{c-1}{c-k^{2}}{c}-(c-1)\CarlsonsymellintRF@{c-1}{c-k^{2}}{c}-\sqrt{(c-1)(c-k^{2})/c}`		Error	EllipticE[\[Phi], (k)^2] == 2Sqrt[c-c - 1](EllipticE[ArcCos[Sqrt[c - 1/c]],(c-c - (k)^(2))/(c-c - 1)]+(Cot[ArcCos[Sqrt[c - 1/c]]])^2EllipticF[ArcCos[Sqrt[c - 1/c]],(c-c - (k)^(2))/(c-c - 1)]+Cot[ArcCos[Sqrt[c - 1/c]]]Sqrt[1-k^2Sin[ArcCos[Sqrt[c - 1/c]]]^2])-(c - 1)EllipticF[ArcCos[Sqrt[c - 1/c]],(c-c - (k)^(2))/(c-c - 1)]/Sqrt[c-c - 1]-Sqrt[(c - 1)*(c - (k)^(2))/c]	Missing Macro Error	Failure	-	Failed [180 / 180] Result: Complex[5.787775994567906, 4.022803158659452] Test Values: {Rule[c, -1.5], Rule[k, 1], Rule[ϕ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]} Result: Complex[6.805668366738806, 3.968311704298834] Test Values: {Rule[c, -1.5], Rule[k, 2], Rule[ϕ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]} ... skip entries to safe data
19.25.E9	${\displaystyle{\displaystyle E\left(\phi,k\right)=R_{F}\left(c-1,c-k^{2},c% \right)-\tfrac{1}{3}k^{2}R_{D}\left(c-1,c-k^{2},c\right)}}$ `\incellintEk@{\phi}{k} = \CarlsonsymellintRF@{c-1}{c-k^{2}}{c}-\tfrac{1}{3}k^{2}\CarlsonsymellintRD@{c-1}{c-k^{2}}{c}`		Error	EllipticE[\[Phi], (k)^2] == EllipticF[ArcCos[Sqrt[c - 1/c]],(c-c - (k)^(2))/(c-c - 1)]/Sqrt[c-c - 1]-Divide[1,3](k)^(2) 3(EllipticF[ArcCos[Sqrt[c - 1/c]],(c-c - (k)^(2))/(c-c - 1)]-EllipticE[ArcCos[Sqrt[c - 1/c]],(c-c - (k)^(2))/(c-c - 1)])/((c-c - (k)^(2))(c-c - 1)^(1/2))	Missing Macro Error	Failure	-	Failed [180 / 180] Result: Complex[3.5743811704478246, 0.7698502565730785] Test Values: {Rule[c, -1.5], Rule[k, 1], Rule[ϕ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]} Result: Complex[3.9424508382496875, -1.017653751864599] Test Values: {Rule[c, -1.5], Rule[k, 2], Rule[ϕ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]} ... skip entries to safe data
19.25.E10	${\displaystyle{\displaystyle E\left(\phi,k\right)={k^{\prime}}^{2}R_{F}\left(c% -1,c-k^{2},c\right)+\tfrac{1}{3}k^{2}{k^{\prime}}^{2}R_{D}\left(c-1,c,c-k^{2}% \right)+k^{2}\sqrt{(c-1)/(c(c-k^{2}))}}}$ `\incellintEk@{\phi}{k} = {k^{\prime}}^{2}\CarlsonsymellintRF@{c-1}{c-k^{2}}{c}+\tfrac{1}{3}k^{2}{k^{\prime}}^{2}\CarlsonsymellintRD@{c-1}{c}{c-k^{2}}+k^{2}\sqrt{(c-1)/(c(c-k^{2}))}`	${\displaystyle{\displaystyle c>k^{2}}}$	Error	EllipticE[\[Phi], (k)^2] == 1 - (k)^(2)EllipticF[ArcCos[Sqrt[c - 1/c]],(c-c - (k)^(2))/(c-c - 1)]/Sqrt[c-c - 1]+Divide[1,3](k)^(2)1 - (k)^(2)3(EllipticF[ArcCos[Sqrt[c - 1/c - (k)^(2)]],(c - (k)^(2)-c)/(c - (k)^(2)-c - 1)]-EllipticE[ArcCos[Sqrt[c - 1/c - (k)^(2)]],(c - (k)^(2)-c)/(c - (k)^(2)-c - 1)])/((c - (k)^(2)-c)(c - (k)^(2)-c - 1)^(1/2))+ (k)^(2)Sqrt[(c - 1)/(c(c - (k)^(2)))]	Missing Macro Error	Failure	-	Failed [20 / 20] Result: Complex[-1.0687219916023158, 0.8637282710955538] Test Values: {Rule[c, 1.5], Rule[k, 1], Rule[ϕ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]} Result: Complex[-1.7724732696890155, 1.0672164584507502] Test Values: {Rule[c, 1.5], Rule[k, 1], Rule[ϕ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]]} ... skip entries to safe data
19.25.E11	${\displaystyle{\displaystyle E\left(\phi,k\right)=-\tfrac{1}{3}{k^{\prime}}^{2% }R_{D}\left(c-k^{2},c,c-1\right)+\sqrt{(c-k^{2})/(c(c-1))}}}$ `\incellintEk@{\phi}{k} = -\tfrac{1}{3}{k^{\prime}}^{2}\CarlsonsymellintRD@{c-k^{2}}{c}{c-1}+\sqrt{(c-k^{2})/(c(c-1))}`	${\displaystyle{\displaystyle\phi\neq\tfrac{1}{2}\pi}}$	Error	EllipticE[\[Phi], (k)^2] == -Divide[1,3]1 - (k)^(2)3(EllipticF[ArcCos[Sqrt[c - (k)^(2)/c - 1]],(c - 1-c)/(c - 1-c - (k)^(2))]-EllipticE[ArcCos[Sqrt[c - (k)^(2)/c - 1]],(c - 1-c)/(c - 1-c - (k)^(2))])/((c - 1-c)(c - 1-c - (k)^(2))^(1/2))+Sqrt[(c - (k)^(2))/(c*(c - 1))]	Missing Macro Error	Failure	-	Failed [180 / 180] Result: Complex[3.6312701919621486, -1.3602272606820804] Test Values: {Rule[c, -1.5], Rule[k, 1], Rule[ϕ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]} Result: Complex[0.7754142926962797, -0.6029933704091625] Test Values: {Rule[c, -1.5], Rule[k, 2], Rule[ϕ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]} ... skip entries to safe data
19.25.E12	${\displaystyle{\displaystyle\frac{\partial E\left(\phi,k\right)}{\partial k}=-% \tfrac{1}{3}kR_{D}\left(c-1,c-k^{2},c\right)}}$ `\pderiv{\incellintEk@{\phi}{k}}{k} = -\tfrac{1}{3}k\CarlsonsymellintRD@{c-1}{c-k^{2}}{c}`		Error	D[EllipticE[\[Phi], (k)^2], k] == -Divide[1,3]k3(EllipticF[ArcCos[Sqrt[c - 1/c]],(c-c - (k)^(2))/(c-c - 1)]-EllipticE[ArcCos[Sqrt[c - 1/c]],(c-c - (k)^(2))/(c-c - 1)])/((c-c - (k)^(2))(c-c - 1)^(1/2))	Missing Macro Error	Failure	-	Failed [180 / 180] Result: Complex[1.571781086254786, -0.44885861459835996] Test Values: {Rule[c, -1.5], Rule[k, 1], Rule[ϕ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]} Result: Complex[1.233812154439124, -0.8879986745755843] Test Values: {Rule[c, -1.5], Rule[k, 2], Rule[ϕ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]} ... skip entries to safe data
19.25.E13	${\displaystyle{\displaystyle D\left(\phi,k\right)=\tfrac{1}{3}R_{D}\left(c-1,c% -k^{2},c\right)}}$ `\incellintDk@{\phi}{k} = \tfrac{1}{3}\CarlsonsymellintRD@{c-1}{c-k^{2}}{c}`		Error	Divide[EllipticF[\[Phi], (k)^2] - EllipticE[\[Phi], (k)^2], (k)^4] == Divide[1,3]3(EllipticF[ArcCos[Sqrt[c - 1/c]],(c-c - (k)^(2))/(c-c - 1)]-EllipticE[ArcCos[Sqrt[c - 1/c]],(c-c - (k)^(2))/(c-c - 1)])/((c-c - (k)^(2))*(c-c - 1)^(1/2))	Missing Macro Error	Failure	-	Failed [180 / 180] Result: Complex[-1.571781086254786, 0.44885861459835996] Test Values: {Rule[c, -1.5], Rule[k, 1], Rule[ϕ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]} Result: Complex[-0.6083725296430629, 0.41279951787826946] Test Values: {Rule[c, -1.5], Rule[k, 2], Rule[ϕ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]} ... skip entries to safe data
19.25.E14	${\displaystyle{\displaystyle\Pi\left(\phi,\alpha^{2},k\right)-F\left(\phi,k% \right)=\tfrac{1}{3}\alpha^{2}R_{J}\left(c-1,c-k^{2},c,c-\alpha^{2}\right)}}$ `\incellintPik@{\phi}{\alpha^{2}}{k}-\incellintFk@{\phi}{k} = \tfrac{1}{3}\alpha^{2}\CarlsonsymellintRJ@{c-1}{c-k^{2}}{c}{c-\alpha^{2}}`		Error	EllipticPi[\[Alpha]^(2), \[Phi],(k)^2]- EllipticF[\[Phi], (k)^2] == Divide[1,3]\[Alpha]^(2) 3(c-c - 1)/(c-c - \[Alpha]^(2))(EllipticPi[(c-c - \[Alpha]^(2))/(c-c - 1),ArcCos[Sqrt[c - 1/c]],(c-c - (k)^(2))/(c-c - 1)]-EllipticF[ArcCos[Sqrt[c - 1/c]],(c-c - (k)^(2))/(c-c - 1)])/Sqrt[c-c - 1]	Missing Macro Error	Failure	-	Failed [300 / 300] Result: Complex[-0.9803588804354156, -0.9579910370435353] Test Values: {Rule[c, -1.5], Rule[k, 1], Rule[α, 1.5], Rule[ϕ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]} Result: Complex[-0.6164275583611891, -0.384238714210872] Test Values: {Rule[c, -1.5], Rule[k, 2], Rule[α, 1.5], Rule[ϕ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]} ... skip entries to safe data
19.25.E16	${\displaystyle{\displaystyle\Pi\left(\phi,\alpha^{2},k\right)=-\tfrac{1}{3}% \omega^{2}R_{J}\left(c-1,c-k^{2},c,c-\omega^{2}\right)+\sqrt{\frac{(c-1)(c-k^{% 2})}{(\alpha^{2}-1)(1-\omega^{2})}}\R_{C}\left(c(\alpha^{2}-1)(1-\omega^{2}),% (\alpha^{2}-c)(c-\omega^{2})\right)}}$ `\incellintPik@{\phi}{\alpha^{2}}{k} = -\tfrac{1}{3}\omega^{2}\CarlsonsymellintRJ@{c-1}{c-k^{2}}{c}{c-\omega^{2}}+\sqrt{\frac{(c-1)(c-k^{2})}{(\alpha^{2}-1)(1-\omega^{2})}}\\CarlsonellintRC@{c(\alpha^{2}-1)(1-\omega^{2})}{(\alpha^{2}-c)(c-\omega^{2})}`	${\displaystyle{\displaystyle\omega^{2}=k^{2}/\alpha^{2}}}$	Error	EllipticPi[\[Alpha]^(2), \[Phi],(k)^2] == -Divide[1,3]\[Omega]^(2) 3(c-c - 1)/(c-c - \[Omega]^(2))(EllipticPi[(c-c - \[Omega]^(2))/(c-c - 1),ArcCos[Sqrt[c - 1/c]],(c-c - (k)^(2))/(c-c - 1)]-EllipticF[ArcCos[Sqrt[c - 1/c]],(c-c - (k)^(2))/(c-c - 1)])/Sqrt[c-c - 1]+Sqrt[Divide[(c - 1)(c - (k)^(2)),(\[Alpha]^(2)- 1)(1 - \[Omega]^(2))]]* 1/Sqrt[(\[Alpha]^(2)- c)(c - \[Omega]^(2))]Hypergeometric2F1[1/2,1/2,3/2,1-(c(\[Alpha]^(2)- 1)(1 - \[Omega]^(2)))/((\[Alpha]^(2)- c)*(c - \[Omega]^(2)))]	Missing Macro Error	Aborted	-	Failed [300 / 300] Result: Complex[-0.11631142199526823, 0.9703799109463437] Test Values: {Rule[c, -1.5], Rule[k, 3], Rule[α, 1.5], Rule[ϕ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[ω, -2]} Result: Complex[-0.11631142199526823, 0.9703799109463437] Test Values: {Rule[c, -1.5], Rule[k, 3], Rule[α, 1.5], Rule[ϕ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[ω, 2]} ... skip entries to safe data
19.25.E17	${\displaystyle{\displaystyle F\left(\phi,k\right)=R_{F}\left(x,y,z\right)}}$ `\incellintFk@{\phi}{k} = \CarlsonsymellintRF@{x}{y}{z}`		EllipticF(sin(phi), k) = 0.5int(1/(sqrt(t+x)sqrt(t+y)sqrt(t+x + yI)), t = 0..infinity)	EllipticF[\[Phi], (k)^2] == EllipticF[ArcCos[Sqrt[x/x + yI]],(x + yI-y)/(x + yI-x)]/Sqrt[x + yI-x]	Aborted	Failure	Failed [300 / 300] Result: 2.547570015-.6488873983I Test Values: {phi = 1/23^(1/2)+1/2I, x = 3/2, y = -3/2, k = 1} Result: 2.209888328-.6080126261I Test Values: {phi = 1/23^(1/2)+1/2I, x = 3/2, y = -3/2, k = 2} ... skip entries to safe data	Failed [300 / 300] Result: Complex[0.5939484671297026, -0.40701440305540804] Test Values: {Rule[k, 1], Rule[x, 1.5], Rule[y, -1.5], Rule[ϕ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]} Result: Complex[0.5587134153531784, -0.34669285510288844] Test Values: {Rule[k, 2], Rule[x, 1.5], Rule[y, -1.5], Rule[ϕ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]} ... skip entries to safe data
19.25.E18	${\displaystyle{\displaystyle(x,y,z)=(c-1,c-k^{2},c)}}$ `(x,y,z) = (c-1,c-k^{2},c)`		(x , y ,(x + y*I)) = (c - 1 , c - (k)^(2), c)	(x , y ,(x + y*I)) == (c - 1 , c - (k)^(2), c)	Skipped - no semantic math	Skipped - no semantic math	-	-
19.25#Ex6	${\displaystyle{\displaystyle\phi=\operatorname{arccos}\sqrt{\ifrac{x}{z}}}}$ `\phi = \acos@@{\sqrt{\ifrac{x}{z}}}`		phi = arccos(sqrt((x)/(x + y*I)))	\[Phi] == ArcCos[Sqrt[Divide[x,x + y*I]]]	Failure	Failure	Failed [180 / 180] Result: .806272406e-1+.9406867936I Test Values: {phi = 1/23^(1/2)+1/2I, x = 3/2, y = -3/2} Result: .806272406e-1+.593132064e-1I Test Values: {phi = 1/23^(1/2)+1/2I, x = 3/2, y = 3/2} ... skip entries to safe data	Failed [180 / 180] Result: Complex[-0.35238546150522904, 0.6906867935097715] Test Values: {Rule[x, 1.5], Rule[y, -1.5], Rule[ϕ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]} Result: Complex[-1.0353981633974483, 0.8736994954019909] Test Values: {Rule[x, 1.5], Rule[y, -1.5], Rule[ϕ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]]} ... skip entries to safe data
19.25#Ex6	${\displaystyle{\displaystyle\operatorname{arccos}\sqrt{\ifrac{x}{z}}=% \operatorname{arcsin}\sqrt{\ifrac{(z-x)}{z}}}}$ `\acos@@{\sqrt{\ifrac{x}{z}}} = \asin@@{\sqrt{\ifrac{(z-x)}{z}}}`		arccos(sqrt((x)/(x + yI))) = arcsin(sqrt(((x + yI)- x)/(x + y*I)))	ArcCos[Sqrt[Divide[x,x + yI]]] == ArcSin[Sqrt[Divide[(x + yI)- x,x + y*I]]]	Failure	Failure	Successful [Tested: 18]	Successful [Tested: 18]
19.25#Ex7	${\displaystyle{\displaystyle k=\sqrt{\frac{z-y}{z-x}}}}$ `k = \sqrt{\frac{z-y}{z-x}}`		k = sqrt(((x + yI)- y)/((x + yI)- x))	k == Sqrt[Divide[(x + yI)- y,(x + yI)- x]]	Skipped - no semantic math	Skipped - no semantic math	-	-
19.25#Ex8	${\displaystyle{\displaystyle\alpha^{2}=\frac{z-p}{z-x}}}$ `\alpha^{2} = \frac{z-p}{z-x}`		(alpha)^(2) = ((x + yI)- p)/((x + yI)- x)	\[Alpha]^(2) == Divide[(x + yI)- p,(x + yI)- x]	Skipped - no semantic math	Skipped - no semantic math	-	-
19.25.E24	${\displaystyle{\displaystyle(z-x)^{1/2}R_{F}\left(x,y,z\right)=F\left(\phi,k% \right)}}$ `(z-x)^{1/2}\CarlsonsymellintRF@{x}{y}{z} = \incellintFk@{\phi}{k}`		((x + yI)- x)^(1/2) 0.5int(1/(sqrt(t+x)sqrt(t+y)sqrt(t+x + yI)), t = 0..infinity) = EllipticF(sin(phi), k)	((x + yI)- x)^(1/2) EllipticF[ArcCos[Sqrt[x/x + yI]],(x + yI-y)/(x + yI-x)]/Sqrt[x + yI-x] == EllipticF[\[Phi], (k)^2]	Aborted	Failure	Failed [300 / 300] Result: -1.167656510+1.966567574I Test Values: {phi = 1/23^(1/2)+1/2I, x = 3/2, y = -3/2, k = 1} Result: -.8299748231+1.925692802I Test Values: {phi = 1/23^(1/2)+1/2I, x = 3/2, y = -3/2, k = 2} ... skip entries to safe data	Failed [300 / 300] Result: Complex[0.015324342917649614, 0.4565416109140732] Test Values: {Rule[k, 1], Rule[x, 1.5], Rule[y, -1.5], Rule[ϕ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]} Result: Complex[0.050559394694173865, 0.3962200629615536] Test Values: {Rule[k, 2], Rule[x, 1.5], Rule[y, -1.5], Rule[ϕ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]} ... skip entries to safe data
19.25.E25	${\displaystyle{\displaystyle(z-x)^{3/2}R_{D}\left(x,y,z\right)=(3/k^{2})(F% \left(\phi,k\right)-E\left(\phi,k\right))}}$ `(z-x)^{3/2}\CarlsonsymellintRD@{x}{y}{z} = (3/k^{2})(\incellintFk@{\phi}{k}-\incellintEk@{\phi}{k})`		Error	((x + yI)- x)^(3/2) 3(EllipticF[ArcCos[Sqrt[x/x + yI]],(x + yI-y)/(x + yI-x)]-EllipticE[ArcCos[Sqrt[x/x + yI]],(x + yI-y)/(x + yI-x)])/((x + yI-y)(x + yI-x)^(1/2)) == (3/(k)^(2))*(EllipticF[\[Phi], (k)^2]- EllipticE[\[Phi], (k)^2])	Missing Macro Error	Failure	-	Failed [300 / 300] Result: Complex[-0.9041684186949032, 0.18989946051507803] Test Values: {Rule[k, 1], Rule[x, 1.5], Rule[y, -1.5], Rule[ϕ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]} Result: Complex[-0.8729885067685752, 0.19149534336253457] Test Values: {Rule[k, 2], Rule[x, 1.5], Rule[y, -1.5], Rule[ϕ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]} ... skip entries to safe data
19.25.E26	${\displaystyle{\displaystyle(z-x)^{3/2}R_{J}\left(x,y,z,p\right)=(3/\alpha^{2}% ){(\Pi\left(\phi,\alpha^{2},k\right)-F\left(\phi,k\right))}}}$ `(z-x)^{3/2}\CarlsonsymellintRJ@{x}{y}{z}{p} = (3/\alpha^{2}){(\incellintPik@{\phi}{\alpha^{2}}{k}-\incellintFk@{\phi}{k})}`		Error	((x + yI)- x)^(3/2) 3(x + yI-x)/(x + yI-p)(EllipticPi[(x + yI-p)/(x + yI-x),ArcCos[Sqrt[x/x + yI]],(x + yI-y)/(x + yI-x)]-EllipticF[ArcCos[Sqrt[x/x + yI]],(x + yI-y)/(x + yI-x)])/Sqrt[x + yI-x] == (3/\[Alpha]^(2))(EllipticPi[\[Alpha]^(2), \[Phi],(k)^2]- EllipticF[\[Phi], (k)^2])	Missing Macro Error	Failure	-	Failed [300 / 300] Result: Complex[-8.905365206673954*^-4, 0.6653826564189609] Test Values: {Rule[k, 1], Rule[p, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[x, 1.5], Rule[y, -1.5], Rule[α, 1.5], Rule[ϕ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]} Result: Complex[0.030816807002235325, 0.6810951786851601] Test Values: {Rule[k, 2], Rule[p, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[x, 1.5], Rule[y, -1.5], Rule[α, 1.5], Rule[ϕ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]} ... skip entries to safe data
19.25.E27	${\displaystyle{\displaystyle 2(z-x)^{-1/2}R_{G}\left(x,y,z\right)=E\left(\phi,% k\right)+(\cot\phi)^{2}F\left(\phi,k\right)+(\cot\phi)\sqrt{1-k^{2}{\sin^{2}}% \phi}}}$ `2(z-x)^{-1/2}\CarlsonsymellintRG@{x}{y}{z} = \incellintEk@{\phi}{k}+(\cot@@{\phi})^{2}\incellintFk@{\phi}{k}+(\cot@@{\phi})\sqrt{1-k^{2}\sin^{2}@@{\phi}}`		Error	2((x + yI)- x)^(- 1/2)* Sqrt[x + yI-x](EllipticE[ArcCos[Sqrt[x/x + yI]],(x + yI-y)/(x + yI-x)]+(Cot[ArcCos[Sqrt[x/x + yI]]])^2EllipticF[ArcCos[Sqrt[x/x + yI]],(x + yI-y)/(x + yI-x)]+Cot[ArcCos[Sqrt[x/x + yI]]]Sqrt[1-k^2Sin[ArcCos[Sqrt[x/x + yI]]]^2]) == EllipticE[\[Phi], (k)^2]+(Cot[\[Phi]])^(2)* EllipticF[\[Phi], (k)^2]+(Cot[\[Phi]])Sqrt[1 - (k)^(2) (Sin[\[Phi]])^(2)]	Missing Macro Error	Failure	-	Failed [300 / 300] Result: Complex[-1.8997799949200251, -0.4031557744461449] Test Values: {Rule[k, 1], Rule[x, 1.5], Rule[y, -1.5], Rule[ϕ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]} Result: Complex[-3.0701379688219372, -2.1411109504853227] Test Values: {Rule[k, 2], Rule[x, 1.5], Rule[y, -1.5], Rule[ϕ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]} ... skip entries to safe data
19.25#Ex9	${\displaystyle{\displaystyle\Delta(\mathrm{n,d})=k^{2}}}$ `\Delta(\mathrm{n,d}) = k^{2}`		Delta(n , d) = (k)^(2)	\[CapitalDelta][n , d] == (k)^(2)	Skipped - no semantic math	Skipped - no semantic math	-	-
19.25#Ex10	${\displaystyle{\displaystyle\Delta(\mathrm{d,c})={k^{\prime}}^{2}}}$ `\Delta(\mathrm{d,c}) = {k^{\prime}}^{2}`		Delta(d , c) = 1 - (k)^(2)	\[CapitalDelta][d , c] == 1 - (k)^(2)	Skipped - no semantic math	Skipped - no semantic math	-	-
19.25#Ex11	${\displaystyle{\displaystyle\Delta(\mathrm{n,c})=1}}$ `\Delta(\mathrm{n,c}) = 1`		Delta(n , c) = 1	\[CapitalDelta][n , c] == 1	Skipped - no semantic math	Skipped - no semantic math	-	-
19.25.E30	${\displaystyle{\displaystyle\operatorname{am}\left(u,k\right)=R_{C}\left({% \operatorname{cs}^{2}}\left(u,k\right),{\operatorname{ns}^{2}}\left(u,k\right)% \right)}}$ `\Jacobiamk@{u}{k} = \CarlsonellintRC@{\Jacobiellcsk^{2}@{u}{k}}{\Jacobiellnsk^{2}@{u}{k}}`		Error	JacobiAmplitude[u, Power[k, 2]] == 1/Sqrt[(JacobiNS[u, (k)^2])^(2)]*Hypergeometric2F1[1/2,1/2,3/2,1-((JacobiCS[u, (k)^2])^(2))/((JacobiNS[u, (k)^2])^(2))]	Missing Macro Error	Aborted	-	Failed [18 / 30] Result: Complex[-0.5428587296705786, 0.8636075147962846] Test Values: {Rule[k, 1], Rule[u, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]]} Result: Complex[-0.6732377468613371, 0.8494366739388763] Test Values: {Rule[k, 2], Rule[u, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]]} ... skip entries to safe data
19.25.E31	${\displaystyle{\displaystyle u=R_{F}\left({\operatorname{ps}^{2}}\left(u,k% \right),{\operatorname{qs}^{2}}\left(u,k\right),{\operatorname{rs}^{2}}\left(u% ,k\right)\right)}}$ `u = \CarlsonsymellintRF@{\genJacobiellk{p}{s}^{2}@{u}{k}}{\genJacobiellk{q}{s}^{2}@{u}{k}}{\genJacobiellk{r}{s}^{2}@{u}{k}}`		u = 0.5int(1/(sqrt(t+genJacobiellk(p)(s)^(2)* uk)sqrt(t+genJacobiellk(q)(s)^(2) uk)sqrt(t+genJacobiellk(r)(s)^(2) u*k)), t = 0..infinity)	u == EllipticF[ArcCos[Sqrt[genJacobiellk[p](s)^(2) uk/genJacobiellk[r](s)^(2)* uk]],(genJacobiellk[r](s)^(2)* uk-genJacobiellk[q](s)^(2)* uk)/(genJacobiellk[r](s)^(2)* uk-genJacobiellk[p](s)^(2)* uk)]/Sqrt[genJacobiellk[r](s)^(2)* uk-genJacobiellk[p](s)^(2)* u*k]	Aborted	Failure	Error	Failed [300 / 300] Result: Plus[Complex[0.43301270189221935, 0.24999999999999997], Times[Complex[-0.78471422644353, -0.9906313764027224], Power[Times[Complex[-1.7426678688862403, -1.3308892896287465], genJacobiellk], Rational[-1, 2]]]] Test Values: {Rule[k, 1], Rule[p, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[q, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[r, -1.5], Rule[s, -1.5], Rule[u, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]} Result: Plus[Complex[0.43301270189221935, 0.24999999999999997], Times[Complex[-0.3766936106342851, -1.225388931598258], Power[Times[Complex[-3.4853357377724805, -2.661778579257493], genJacobiellk], Rational[-1, 2]]]] Test Values: {Rule[k, 2], Rule[p, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[q, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[r, -1.5], Rule[s, -1.5], Rule[u, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]} ... skip entries to safe data
19.26.E1	${\displaystyle{\displaystyle R_{F}\left(x+\lambda,y+\lambda,z+\lambda\right)+R% _{F}\left(x+\mu,y+\mu,z+\mu\right)=R_{F}\left(x,y,z\right)}}$ `\CarlsonsymellintRF@{x+\lambda}{y+\lambda}{z+\lambda}+\CarlsonsymellintRF@{x+\mu}{y+\mu}{z+\mu} = \CarlsonsymellintRF@{x}{y}{z}`		0.5int(1/(sqrt(t+x + lambda)sqrt(t+y + lambda)sqrt(t+(x + yI)+ lambda)), t = 0..infinity)+ 0.5int(1/(sqrt(t+x + mu)sqrt(t+y + mu)sqrt(t+(x + yI)+ mu)), t = 0..infinity) = 0.5int(1/(sqrt(t+x)sqrt(t+y)sqrt(t+x + yI)), t = 0..infinity)	EllipticF[ArcCos[Sqrt[x + \[Lambda]/(x + yI)+ \[Lambda]]],((x + yI)+ \[Lambda]-y + \[Lambda])/((x + yI)+ \[Lambda]-x + \[Lambda])]/Sqrt[(x + yI)+ \[Lambda]-x + \[Lambda]]+ EllipticF[ArcCos[Sqrt[x + \[Mu]/(x + yI)+ \[Mu]]],((x + yI)+ \[Mu]-y + \[Mu])/((x + yI)+ \[Mu]-x + \[Mu])]/Sqrt[(x + yI)+ \[Mu]-x + \[Mu]] == EllipticF[ArcCos[Sqrt[x/x + yI]],(x + yI-y)/(x + yI-x)]/Sqrt[x + yI-x]	Aborted	Failure	Skipped - Because timed out	Failed [300 / 300] Result: Complex[0.6992255245511445, -1.8246422705609677] Test Values: {Rule[x, 1.5], Rule[y, -1.5], Rule[λ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[μ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]} Result: Complex[1.2162365888422955, -0.7585970772170993] Test Values: {Rule[x, 1.5], Rule[y, -1.5], Rule[λ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[μ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]]} ... skip entries to safe data
19.26.E2	${\displaystyle{\displaystyle x+\mu=\lambda^{-2}\left(\sqrt{(x+\lambda)yz}+% \sqrt{x(y+\lambda)(z+\lambda)}\right)^{2}}}$ `x+\mu = \lambda^{-2}\left(\sqrt{(x+\lambda)yz}+\sqrt{x(y+\lambda)(z+\lambda)}\right)^{2}`		x + mu = (lambda)^(- 2)(sqrt((x + lambda)y(x + yI))+sqrt(x(y + lambda)((x + y*I)+ lambda)))^(2)	x + \[Mu] == \[Lambda]^(- 2)(Sqrt[(x + \[Lambda])y(x + yI)]+Sqrt[x(y + \[Lambda])((x + y*I)+ \[Lambda])])^(2)	Skipped - no semantic math	Skipped - no semantic math	-	-
19.26#Ex1	${\displaystyle{\displaystyle(\xi,\eta,\zeta)=(x+\lambda,y+\lambda,z+\lambda)}}$ `(\xi,\eta,\zeta) = (x+\lambda,y+\lambda,z+\lambda)`		(xi , eta , zeta) = (x + lambda , y + lambda ,(x + y*I)+ lambda)	(\[Xi], \[Eta], \[Zeta]) == (x + \[Lambda], y + \[Lambda],(x + y*I)+ \[Lambda])	Skipped - no semantic math	Skipped - no semantic math	-	-
19.26.E5	${\displaystyle{\displaystyle\mu=\lambda^{-2}\left(\sqrt{xyz}+\sqrt{(x+\lambda)% (y+\lambda)(z+\lambda)}\right)^{2}-\lambda-x-y-z}}$ `\mu = \lambda^{-2}\left(\sqrt{xyz}+\sqrt{(x+\lambda)(y+\lambda)(z+\lambda)}\right)^{2}-\lambda-x-y-z`		mu = (lambda)^(- 2)(sqrt(xy(x + yI))+sqrt((x + lambda)(y + lambda)((x + yI)+ lambda)))^(2)- lambda - x - y -(x + yI)	\[Mu] == \[Lambda]^(- 2)(Sqrt[xy(x + yI)]+Sqrt[(x + \[Lambda])(y + \[Lambda])((x + yI)+ \[Lambda])])^(2)- \[Lambda]- x - y -(x + yI)	Skipped - no semantic math	Skipped - no semantic math	-	-
19.26.E6	${\displaystyle{\displaystyle(\lambda\mu-xy-xz-yz)^{2}=4xyz(\lambda+\mu+x+y+z)}}$ `(\lambda\mu-xy-xz-yz)^{2} = 4xyz(\lambda+\mu+x+y+z)`		(lambdamu - xy - x(x + yI)- y(x + yI))^(2) = 4xy(x + yI)(lambda + mu + x + y +(x + yI))	(\[Lambda]\[Mu]- xy - x(x + yI)- y(x + yI))^(2) == 4xy(x + yI)(\[Lambda]+ \[Mu]+ x + y +(x + yI))	Skipped - no semantic math	Skipped - no semantic math	-	-
19.26.E7	${\displaystyle{\displaystyle R_{D}\left(x+\lambda,y+\lambda,z+\lambda\right)+R% _{D}\left(x+\mu,y+\mu,z+\mu\right)=R_{D}\left(x,y,z\right)-\frac{3}{\sqrt{z(z+% \lambda)(z+\mu)}}}}$ `\CarlsonsymellintRD@{x+\lambda}{y+\lambda}{z+\lambda}+\CarlsonsymellintRD@{x+\mu}{y+\mu}{z+\mu} = \CarlsonsymellintRD@{x}{y}{z}-\frac{3}{\sqrt{z(z+\lambda)(z+\mu)}}`		Error	3(EllipticF[ArcCos[Sqrt[x + \[Lambda]/(x + yI)+ \[Lambda]]],((x + yI)+ \[Lambda]-y + \[Lambda])/((x + yI)+ \[Lambda]-x + \[Lambda])]-EllipticE[ArcCos[Sqrt[x + \[Lambda]/(x + yI)+ \[Lambda]]],((x + yI)+ \[Lambda]-y + \[Lambda])/((x + yI)+ \[Lambda]-x + \[Lambda])])/(((x + yI)+ \[Lambda]-y + \[Lambda])((x + yI)+ \[Lambda]-x + \[Lambda])^(1/2))+ 3(EllipticF[ArcCos[Sqrt[x + \[Mu]/(x + yI)+ \[Mu]]],((x + yI)+ \[Mu]-y + \[Mu])/((x + yI)+ \[Mu]-x + \[Mu])]-EllipticE[ArcCos[Sqrt[x + \[Mu]/(x + yI)+ \[Mu]]],((x + yI)+ \[Mu]-y + \[Mu])/((x + yI)+ \[Mu]-x + \[Mu])])/(((x + yI)+ \[Mu]-y + \[Mu])((x + yI)+ \[Mu]-x + \[Mu])^(1/2)) == 3(EllipticF[ArcCos[Sqrt[x/x + yI]],(x + yI-y)/(x + yI-x)]-EllipticE[ArcCos[Sqrt[x/x + yI]],(x + yI-y)/(x + yI-x)])/((x + yI-y)(x + yI-x)^(1/2))-Divide[3,Sqrt[(x + yI)((x + yI)+ \[Lambda])((x + y*I)+ \[Mu])]]	Missing Macro Error	Aborted	-	Failed [300 / 300] Result: Complex[-0.4984590390126629, 1.2092907867192135] Test Values: {Rule[x, 1.5], Rule[y, -1.5], Rule[λ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[μ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]} Result: Complex[0.01924185171185039, 1.9974068077017313] Test Values: {Rule[x, 1.5], Rule[y, -1.5], Rule[λ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[μ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]]} ... skip entries to safe data
19.26.E8	${\displaystyle{\displaystyle 2R_{G}\left(x+\lambda,y+\lambda,z+\lambda\right)+% 2R_{G}\left(x+\mu,y+\mu,z+\mu\right)=2R_{G}\left(x,y,z\right)+\lambda R_{F}% \left(x+\lambda,y+\lambda,z+\lambda\right)+\mu R_{F}\left(x+\mu,y+\mu,z+\mu% \right)+\sqrt{\lambda+\mu+x+y+z}}}$ `2\CarlsonsymellintRG@{x+\lambda}{y+\lambda}{z+\lambda}+2\CarlsonsymellintRG@{x+\mu}{y+\mu}{z+\mu} = 2\CarlsonsymellintRG@{x}{y}{z}+\lambda\CarlsonsymellintRF@{x+\lambda}{y+\lambda}{z+\lambda}+\mu\CarlsonsymellintRF@{x+\mu}{y+\mu}{z+\mu}+\sqrt{\lambda+\mu+x+y+z}`		Error	2Sqrt[(x + yI)+ \[Lambda]-x + \[Lambda]](EllipticE[ArcCos[Sqrt[x + \[Lambda]/(x + yI)+ \[Lambda]]],((x + yI)+ \[Lambda]-y + \[Lambda])/((x + yI)+ \[Lambda]-x + \[Lambda])]+(Cot[ArcCos[Sqrt[x + \[Lambda]/(x + yI)+ \[Lambda]]]])^2EllipticF[ArcCos[Sqrt[x + \[Lambda]/(x + yI)+ \[Lambda]]],((x + yI)+ \[Lambda]-y + \[Lambda])/((x + yI)+ \[Lambda]-x + \[Lambda])]+Cot[ArcCos[Sqrt[x + \[Lambda]/(x + yI)+ \[Lambda]]]]Sqrt[1-k^2Sin[ArcCos[Sqrt[x + \[Lambda]/(x + yI)+ \[Lambda]]]]^2])+ 2Sqrt[(x + yI)+ \[Mu]-x + \[Mu]](EllipticE[ArcCos[Sqrt[x + \[Mu]/(x + yI)+ \[Mu]]],((x + yI)+ \[Mu]-y + \[Mu])/((x + yI)+ \[Mu]-x + \[Mu])]+(Cot[ArcCos[Sqrt[x + \[Mu]/(x + yI)+ \[Mu]]]])^2EllipticF[ArcCos[Sqrt[x + \[Mu]/(x + yI)+ \[Mu]]],((x + yI)+ \[Mu]-y + \[Mu])/((x + yI)+ \[Mu]-x + \[Mu])]+Cot[ArcCos[Sqrt[x + \[Mu]/(x + yI)+ \[Mu]]]]Sqrt[1-k^2Sin[ArcCos[Sqrt[x + \[Mu]/(x + yI)+ \[Mu]]]]^2]) == 2Sqrt[x + yI-x](EllipticE[ArcCos[Sqrt[x/x + yI]],(x + yI-y)/(x + yI-x)]+(Cot[ArcCos[Sqrt[x/x + yI]]])^2EllipticF[ArcCos[Sqrt[x/x + yI]],(x + yI-y)/(x + yI-x)]+Cot[ArcCos[Sqrt[x/x + yI]]]Sqrt[1-k^2Sin[ArcCos[Sqrt[x/x + yI]]]^2])+ \[Lambda]EllipticF[ArcCos[Sqrt[x + \[Lambda]/(x + yI)+ \[Lambda]]],((x + yI)+ \[Lambda]-y + \[Lambda])/((x + yI)+ \[Lambda]-x + \[Lambda])]/Sqrt[(x + yI)+ \[Lambda]-x + \[Lambda]]+ \[Mu]EllipticF[ArcCos[Sqrt[x + \[Mu]/(x + yI)+ \[Mu]]],((x + yI)+ \[Mu]-y + \[Mu])/((x + yI)+ \[Mu]-x + \[Mu])]/Sqrt[(x + yI)+ \[Mu]-x + \[Mu]]+Sqrt[\[Lambda]+ \[Mu]+ x + y +(x + yI)]	Missing Macro Error	Aborted	-	Failed [300 / 300] Result: Plus[Complex[-2.0898920996046204, 0.6803615706262403], Times[Complex[-1.7320508075688772, 1.732050807568877], Plus[Complex[0.9985512968581824, 0.2012315241723115], Times[Complex[0.3176872874027722, -1.049249833251038], Power[Plus[1.0, Times[Complex[0.0, -1.5], Power[k, 2]]], Rational[1, 2]]]]], Times[Complex[4.184639587172815, -1.9117536488739475], Plus[Complex[0.7424137617640161, 0.220635885032481], Times[Complex[0.14483575015411373, 1.3558262394954135], Power[Plus[1.0, Times[Complex[0.9940169358562925, 0.4776709006307397], Power[k, 2]]], Rational[1, 2]]]]]] Test Values: {Rule[x, 1.5], Rule[y, -1.5], Rule[λ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[μ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]} Result: Plus[Complex[-1.182728387586514, 0.2705509888970101], Times[Complex[-1.7320508075688772, 1.732050807568877], Plus[Complex[0.9985512968581824, 0.2012315241723115], Times[Complex[0.3176872874027722, -1.049249833251038], Power[Plus[1.0, Times[Complex[0.0, -1.5], Power[k, 2]]], Rational[1, 2]]]]], Times[Complex[0.7841147574434748, -1.6170454393246465], Plus[Complex[0.3473840661116648, 1.4426085854555293], Times[Complex[0.7761183239980944, 1.3014092542459557], Power[Plus[1.0, Times[Complex[0.02232909936926042, 0.49401693585629247], Power[k, 2]]], Rational[1, 2]]]]], Times[Complex[2.0923197935864075, -0.9558768244369737], Plus[Complex[0.7424137617640161, 0.220635885032481], Times[Complex[0.14483575015411373, 1.3558262394954135], Power[Plus[1.0, Times[Complex[0.9940169358562925, 0.4776709006307397], Power[k, 2]]], Rational[1, 2]]]]]] Test Values: {Rule[x, 1.5], Rule[y, -1.5], Rule[λ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[μ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]]} ... skip entries to safe data
19.26.E9	${\displaystyle{\displaystyle R_{J}\left(x+\lambda,y+\lambda,z+\lambda,p+% \lambda\right)+R_{J}\left(x+\mu,y+\mu,z+\mu,p+\mu\right)=R_{J}\left(x,y,z,p% \right)-3R_{C}\left(\gamma-\delta,\gamma\right)}}$ `\CarlsonsymellintRJ@{x+\lambda}{y+\lambda}{z+\lambda}{p+\lambda}+\CarlsonsymellintRJ@{x+\mu}{y+\mu}{z+\mu}{p+\mu} = \CarlsonsymellintRJ@{x}{y}{z}{p}-3\CarlsonellintRC@{\gamma-\delta}{\gamma}`		Error	3((x + yI)+ \[Lambda]-x + \[Lambda])/((x + yI)+ \[Lambda]-p + \[Lambda])(EllipticPi[((x + yI)+ \[Lambda]-p + \[Lambda])/((x + yI)+ \[Lambda]-x + \[Lambda]),ArcCos[Sqrt[x + \[Lambda]/(x + yI)+ \[Lambda]]],((x + yI)+ \[Lambda]-y + \[Lambda])/((x + yI)+ \[Lambda]-x + \[Lambda])]-EllipticF[ArcCos[Sqrt[x + \[Lambda]/(x + yI)+ \[Lambda]]],((x + yI)+ \[Lambda]-y + \[Lambda])/((x + yI)+ \[Lambda]-x + \[Lambda])])/Sqrt[(x + yI)+ \[Lambda]-x + \[Lambda]]+ 3((x + yI)+ \[Mu]-x + \[Mu])/((x + yI)+ \[Mu]-p + \[Mu])(EllipticPi[((x + yI)+ \[Mu]-p + \[Mu])/((x + yI)+ \[Mu]-x + \[Mu]),ArcCos[Sqrt[x + \[Mu]/(x + yI)+ \[Mu]]],((x + yI)+ \[Mu]-y + \[Mu])/((x + yI)+ \[Mu]-x + \[Mu])]-EllipticF[ArcCos[Sqrt[x + \[Mu]/(x + yI)+ \[Mu]]],((x + yI)+ \[Mu]-y + \[Mu])/((x + yI)+ \[Mu]-x + \[Mu])])/Sqrt[(x + yI)+ \[Mu]-x + \[Mu]] == 3(x + yI-x)/(x + yI-p)(EllipticPi[(x + yI-p)/(x + yI-x),ArcCos[Sqrt[x/x + yI]],(x + yI-y)/(x + yI-x)]-EllipticF[ArcCos[Sqrt[x/x + yI]],(x + yI-y)/(x + yI-x)])/Sqrt[x + yI-x]- 31/Sqrt[\[Gamma]]*Hypergeometric2F1[1/2,1/2,3/2,1-(\[Gamma]- \[Delta])/(\[Gamma])]	Missing Macro Error	Failure	-	Failed [300 / 300] Result: Complex[6.482970499990588, -0.8807575715831795] Test Values: {Rule[p, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[x, 1.5], Rule[y, -1.5], Rule[γ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[δ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[λ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[μ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]} Result: Complex[7.020988185402777, -1.8389880807014276] Test Values: {Rule[p, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[x, 1.5], Rule[y, -1.5], Rule[γ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[δ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[λ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[μ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]]} ... skip entries to safe data
19.26#Ex3	${\displaystyle{\displaystyle\gamma=p(p+\lambda)(p+\mu)}}$ `\gamma = p(p+\lambda)(p+\mu)`		gamma = p(p + lambda)(p + mu)	\[Gamma] == p(p + \[Lambda])(p + \[Mu])	Skipped - no semantic math	Skipped - no semantic math	-	-
19.26#Ex4	${\displaystyle{\displaystyle\delta=(p-x)(p-y)(p-z)}}$ `\delta = (p-x)(p-y)(p-z)`		delta = (p - x)(p - y)(p -(x + y*I))	\[Delta] == (p - x)(p - y)(p -(x + y*I))	Skipped - no semantic math	Skipped - no semantic math	-	-
19.26.E11	${\displaystyle{\displaystyle R_{C}\left(x+\lambda,y+\lambda\right)+R_{C}\left(% x+\mu,y+\mu\right)=R_{C}\left(x,y\right)}}$ `\CarlsonellintRC@{x+\lambda}{y+\lambda}+\CarlsonellintRC@{x+\mu}{y+\mu} = \CarlsonellintRC@{x}{y}`		Error	1/Sqrt[y + \[Lambda]]Hypergeometric2F1[1/2,1/2,3/2,1-(x + \[Lambda])/(y + \[Lambda])]+ 1/Sqrt[y + \[Mu]]Hypergeometric2F1[1/2,1/2,3/2,1-(x + \[Mu])/(y + \[Mu])] == 1/Sqrt[y]*Hypergeometric2F1[1/2,1/2,3/2,1-(x)/(y)]	Missing Macro Error	Failure	-	Failed [300 / 300] Result: Complex[1.7722794006718585, -0.740880873447254] Test Values: {Rule[x, 1.5], Rule[y, -1.5], Rule[λ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[μ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]} Result: Complex[1.579678795390187, -0.7154745309495683] Test Values: {Rule[x, 1.5], Rule[y, -1.5], Rule[λ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[μ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]]} ... skip entries to safe data
19.26#Ex5	${\displaystyle{\displaystyle x+\mu=\lambda^{-2}(\sqrt{x+\lambda}y+\sqrt{x}(y+% \lambda))^{2}}}$ `x+\mu = \lambda^{-2}(\sqrt{x+\lambda}y+\sqrt{x}(y+\lambda))^{2}`		x + mu = (lambda)^(- 2)(sqrt(x + lambda)y +sqrt(x)*(y + lambda))^(2)	x + \[Mu] == \[Lambda]^(- 2)(Sqrt[x + \[Lambda]]y +Sqrt[x]*(y + \[Lambda]))^(2)	Skipped - no semantic math	Skipped - no semantic math	-	-
19.26#Ex6	${\displaystyle{\displaystyle y+\mu=(y(y+\lambda)/\lambda^{2})(\sqrt{x}+\sqrt{x% +\lambda})^{2}}}$ `y+\mu = (y(y+\lambda)/\lambda^{2})(\sqrt{x}+\sqrt{x+\lambda})^{2}`		y + mu = (y(y + lambda)/(lambda)^(2))(sqrt(x)+sqrt(x + lambda))^(2)	y + \[Mu] == (y(y + \[Lambda])/\[Lambda]^(2))(Sqrt[x]+Sqrt[x + \[Lambda]])^(2)	Skipped - no semantic math	Skipped - no semantic math	-	-
19.26.E13	${\displaystyle{\displaystyle R_{C}\left(\alpha^{2},\alpha^{2}-\theta\right)+R_% {C}\left(\beta^{2},\beta^{2}-\theta\right)=R_{C}\left(\sigma^{2},\sigma^{2}-% \theta\right)}}$ `\CarlsonellintRC@{\alpha^{2}}{\alpha^{2}-\theta}+\CarlsonellintRC@{\beta^{2}}{\beta^{2}-\theta} = \CarlsonellintRC@{\sigma^{2}}{\sigma^{2}-\theta}`	${\displaystyle{\displaystyle\sigma=(\alpha\beta+\theta)/(\alpha+\beta)}}$	Error	1/Sqrt[\[Alpha]^(2)- \[Theta]]Hypergeometric2F1[1/2,1/2,3/2,1-(\[Alpha]^(2))/(\[Alpha]^(2)- \[Theta])]+ 1/Sqrt[\[Beta]^(2)- \[Theta]]Hypergeometric2F1[1/2,1/2,3/2,1-(\[Beta]^(2))/(\[Beta]^(2)- \[Theta])] == 1/Sqrt[\[Sigma]^(2)- \[Theta]]*Hypergeometric2F1[1/2,1/2,3/2,1-(\[Sigma]^(2))/(\[Sigma]^(2)- \[Theta])]	Missing Macro Error	Aborted	-	Successful [Tested: 2]
19.26.E14	${\displaystyle{\displaystyle(p-y)R_{C}\left(x,p\right)+(q-y)R_{C}\left(x,q% \right)=(\eta-\xi)R_{C}\left(\xi,\eta\right)}}$ `(p-y)\CarlsonellintRC@{x}{p}+(q-y)\CarlsonellintRC@{x}{q} = (\eta-\xi)\CarlsonellintRC@{\xi}{\eta}`	${\displaystyle{\displaystyle x\geq 0,y\geq 0}}$	Error	(p - y)1/Sqrt[p]Hypergeometric2F1[1/2,1/2,3/2,1-(x)/(p)]+(q - y)1/Sqrt[q]Hypergeometric2F1[1/2,1/2,3/2,1-(x)/(q)] == (\[Eta]- \[Xi])1/Sqrt[\[Eta]]Hypergeometric2F1[1/2,1/2,3/2,1-(\[Xi])/(\[Eta])]	Missing Macro Error	Failure	-	Failed [300 / 300] Result: Indeterminate Test Values: {Rule[p, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[q, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[x, 1.5], Rule[y, 1.5], Rule[η, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[ξ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]} Result: Complex[-3.0971074607887266, 1.6817857583573725] Test Values: {Rule[p, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[q, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[x, 1.5], Rule[y, 1.5], Rule[η, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[ξ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]]} ... skip entries to safe data
19.26#Ex7	${\displaystyle{\displaystyle(p-x)(q-x)=(y-x)^{2}}}$ `(p-x)(q-x) = (y-x)^{2}`		(p - x)*(q - x) = (y - x)^(2)	(p - x)*(q - x) == (y - x)^(2)	Skipped - no semantic math	Skipped - no semantic math	-	-
19.26#Ex8	${\displaystyle{\displaystyle\xi=y^{2}/x}}$ `\xi = y^{2}/x`		xi = (y)^(2)/x	\[Xi] == (y)^(2)/x	Skipped - no semantic math	Skipped - no semantic math	-	-
19.26#Ex9	${\displaystyle{\displaystyle\eta=pq/x}}$ `\eta = pq/x`		eta = p*q/x	\[Eta] == p*q/x	Skipped - no semantic math	Skipped - no semantic math	-	-
19.26#Ex10	${\displaystyle{\displaystyle\eta-\xi=p+q-2y}}$ `\eta-\xi = p+q-2y`		eta - xi = p + q - 2*y	\[Eta]- \[Xi] == p + q - 2*y	Skipped - no semantic math	Skipped - no semantic math	-	-
19.26.E16	${\displaystyle{\displaystyle R_{F}\left(\lambda,y+\lambda,z+\lambda\right)={R_% {F}\left(0,y,z\right)-R_{F}\left(\mu,y+\mu,z+\mu\right),}}}$ `\CarlsonsymellintRF@{\lambda}{y+\lambda}{z+\lambda} = {\CarlsonsymellintRF@{0}{y}{z}-\CarlsonsymellintRF@{\mu}{y+\mu}{z+\mu},}`	${\displaystyle{\displaystyle\lambda\mu=yz}}$	0.5int(1/(sqrt(t+lambda)sqrt(t+y + lambda)sqrt(t+(x + yI)+ lambda)), t = 0..infinity) = 0.5int(1/(sqrt(t+0)sqrt(t+y)sqrt(t+x + yI)), t = 0..infinity)- 0.5int(1/(sqrt(t+mu)sqrt(t+y + mu)sqrt(t+(x + yI)+ mu)), t = 0..infinity)	EllipticF[ArcCos[Sqrt[\[Lambda]/(x + yI)+ \[Lambda]]],((x + yI)+ \[Lambda]-y + \[Lambda])/((x + yI)+ \[Lambda]-\[Lambda])]/Sqrt[(x + yI)+ \[Lambda]-\[Lambda]] == EllipticF[ArcCos[Sqrt[0/x + yI]],(x + yI-y)/(x + yI-0)]/Sqrt[x + yI-0]- EllipticF[ArcCos[Sqrt[\[Mu]/(x + yI)+ \[Mu]]],((x + yI)+ \[Mu]-y + \[Mu])/((x + yI)+ \[Mu]-\[Mu])]/Sqrt[(x + yI)+ \[Mu]-\[Mu]]	Error	Failure	-	Error
19.26.E17	${\displaystyle{\displaystyle\sqrt{\alpha}R_{C}\left(\beta,\alpha+\beta\right)+% \sqrt{\beta}R_{C}\left(\alpha,\alpha+\beta\right)=\pi/2}}$ `\sqrt{\alpha}\CarlsonellintRC@{\beta}{\alpha+\beta}+\sqrt{\beta}\CarlsonellintRC@{\alpha}{\alpha+\beta} = \pi/2`	${\displaystyle{\displaystyle\alpha+\beta>0}}$	Error	Sqrt[\[Alpha]]1/Sqrt[\[Alpha]+ \[Beta]]Hypergeometric2F1[1/2,1/2,3/2,1-(\[Beta])/(\[Alpha]+ \[Beta])]+Sqrt[\[Beta]]1/Sqrt[\[Alpha]+ \[Beta]]Hypergeometric2F1[1/2,1/2,3/2,1-(\[Alpha])/(\[Alpha]+ \[Beta])] == Pi/2	Missing Macro Error	Failure	-	Successful [Tested: 9]
19.26.E18	${\displaystyle{\displaystyle R_{F}\left(x,y,z\right)=2R_{F}\left(x+\lambda,y+% \lambda,z+\lambda\right)}}$ `\CarlsonsymellintRF@{x}{y}{z} = 2\CarlsonsymellintRF@{x+\lambda}{y+\lambda}{z+\lambda}`		0.5int(1/(sqrt(t+x)sqrt(t+y)sqrt(t+x + yI)), t = 0..infinity) = 20.5int(1/(sqrt(t+x + lambda)sqrt(t+y + lambda)sqrt(t+(x + y*I)+ lambda)), t = 0..infinity)	EllipticF[ArcCos[Sqrt[x/x + yI]],(x + yI-y)/(x + yI-x)]/Sqrt[x + yI-x] == 2EllipticF[ArcCos[Sqrt[x + \[Lambda]/(x + yI)+ \[Lambda]]],((x + yI)+ \[Lambda]-y + \[Lambda])/((x + yI)+ \[Lambda]-x + \[Lambda])]/Sqrt[(x + y*I)+ \[Lambda]-x + \[Lambda]]	Aborted	Failure	Skipped - Because timed out	Failed [180 / 180] Result: Complex[-0.6992255245511445, 1.8246422705609677] Test Values: {Rule[x, 1.5], Rule[y, -1.5], Rule[λ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]} Result: Complex[-1.7332476531334464, -0.3074481161267689] Test Values: {Rule[x, 1.5], Rule[y, -1.5], Rule[λ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]]} ... skip entries to safe data
19.26.E18	${\displaystyle{\displaystyle 2R_{F}\left(x+\lambda,y+\lambda,z+\lambda\right)=% R_{F}\left(\frac{x+\lambda}{4},\frac{y+\lambda}{4},\frac{z+\lambda}{4}\right)}}$ `2\CarlsonsymellintRF@{x+\lambda}{y+\lambda}{z+\lambda} = \CarlsonsymellintRF@{\frac{x+\lambda}{4}}{\frac{y+\lambda}{4}}{\frac{z+\lambda}{4}}`		20.5int(1/(sqrt(t+x + lambda)sqrt(t+y + lambda)sqrt(t+(x + yI)+ lambda)), t = 0..infinity) = 0.5int(1/(sqrt(t+(x + lambda)/(4))sqrt(t+(y + lambda)/(4))sqrt(t+((x + y*I)+ lambda)/(4))), t = 0..infinity)	2EllipticF[ArcCos[Sqrt[x + \[Lambda]/(x + yI)+ \[Lambda]]],((x + yI)+ \[Lambda]-y + \[Lambda])/((x + yI)+ \[Lambda]-x + \[Lambda])]/Sqrt[(x + yI)+ \[Lambda]-x + \[Lambda]] == EllipticF[ArcCos[Sqrt[Divide[x + \[Lambda],4]/Divide[(x + yI)+ \[Lambda],4]]],(Divide[(x + yI)+ \[Lambda],4]-Divide[y + \[Lambda],4])/(Divide[(x + yI)+ \[Lambda],4]-Divide[x + \[Lambda],4])]/Sqrt[Divide[(x + y*I)+ \[Lambda],4]-Divide[x + \[Lambda],4]]	Failure	Failure	Skipped - Because timed out	Failed [180 / 180] Result: Complex[-1.1343270456997319, -2.101834604175173] Test Values: {Rule[x, 1.5], Rule[y, -1.5], Rule[λ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]} Result: Complex[-0.07907692856233961, -0.3004487668798371] Test Values: {Rule[x, 1.5], Rule[y, -1.5], Rule[λ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]]} ... skip entries to safe data
19.26.E19	${\displaystyle{\displaystyle\lambda=\sqrt{x}\sqrt{y}+\sqrt{y}\sqrt{z}+\sqrt{z}% \sqrt{x}}}$ `\lambda = \sqrt{x}\sqrt{y}+\sqrt{y}\sqrt{z}+\sqrt{z}\sqrt{x}`		lambda = sqrt(x)sqrt(y)+sqrt(y)sqrt(x + yI)+sqrt(x + yI)*sqrt(x)	\[Lambda] == Sqrt[x]Sqrt[y]+Sqrt[y]Sqrt[x + yI]+Sqrt[x + yI]*Sqrt[x]	Skipped - no semantic math	Skipped - no semantic math	-	-
19.26.E20	${\displaystyle{\displaystyle R_{D}\left(x,y,z\right)=2R_{D}\left(x+\lambda,y+% \lambda,z+\lambda\right)+\frac{3}{\sqrt{z}(z+\lambda)}}}$ `\CarlsonsymellintRD@{x}{y}{z} = 2\CarlsonsymellintRD@{x+\lambda}{y+\lambda}{z+\lambda}+\frac{3}{\sqrt{z}(z+\lambda)}`		Error	3(EllipticF[ArcCos[Sqrt[x/x + yI]],(x + yI-y)/(x + yI-x)]-EllipticE[ArcCos[Sqrt[x/x + yI]],(x + yI-y)/(x + yI-x)])/((x + yI-y)(x + yI-x)^(1/2)) == 23(EllipticF[ArcCos[Sqrt[x + \[Lambda]/(x + yI)+ \[Lambda]]],((x + yI)+ \[Lambda]-y + \[Lambda])/((x + yI)+ \[Lambda]-x + \[Lambda])]-EllipticE[ArcCos[Sqrt[x + \[Lambda]/(x + yI)+ \[Lambda]]],((x + yI)+ \[Lambda]-y + \[Lambda])/((x + yI)+ \[Lambda]-x + \[Lambda])])/(((x + yI)+ \[Lambda]-y + \[Lambda])((x + yI)+ \[Lambda]-x + \[Lambda])^(1/2))+Divide[3,Sqrt[x + yI]((x + yI)+ \[Lambda])]	Missing Macro Error	Failure	-	Failed [180 / 180] Result: Complex[0.4984590390126629, -1.2092907867192135] Test Values: {Rule[x, 1.5], Rule[y, -1.5], Rule[λ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]} Result: Complex[-0.5295690158190058, -2.8195127867822802] Test Values: {Rule[x, 1.5], Rule[y, -1.5], Rule[λ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]]} ... skip entries to safe data
19.26.E21	${\displaystyle{\displaystyle 2R_{G}\left(x,y,z\right)=4R_{G}\left(x+\lambda,y+% \lambda,z+\lambda\right)-\lambda R_{F}\left(x,y,z\right)-\sqrt{x}-\sqrt{y}-% \sqrt{z}}}$ `2\CarlsonsymellintRG@{x}{y}{z} = 4\CarlsonsymellintRG@{x+\lambda}{y+\lambda}{z+\lambda}-\lambda\CarlsonsymellintRF@{x}{y}{z}-\sqrt{x}-\sqrt{y}-\sqrt{z}`		Error	2Sqrt[x + yI-x](EllipticE[ArcCos[Sqrt[x/x + yI]],(x + yI-y)/(x + yI-x)]+(Cot[ArcCos[Sqrt[x/x + yI]]])^2EllipticF[ArcCos[Sqrt[x/x + yI]],(x + yI-y)/(x + yI-x)]+Cot[ArcCos[Sqrt[x/x + yI]]]Sqrt[1-k^2Sin[ArcCos[Sqrt[x/x + yI]]]^2]) == 4Sqrt[(x + yI)+ \[Lambda]-x + \[Lambda]](EllipticE[ArcCos[Sqrt[x + \[Lambda]/(x + yI)+ \[Lambda]]],((x + yI)+ \[Lambda]-y + \[Lambda])/((x + yI)+ \[Lambda]-x + \[Lambda])]+(Cot[ArcCos[Sqrt[x + \[Lambda]/(x + yI)+ \[Lambda]]]])^2EllipticF[ArcCos[Sqrt[x + \[Lambda]/(x + yI)+ \[Lambda]]],((x + yI)+ \[Lambda]-y + \[Lambda])/((x + yI)+ \[Lambda]-x + \[Lambda])]+Cot[ArcCos[Sqrt[x + \[Lambda]/(x + yI)+ \[Lambda]]]]Sqrt[1-k^2Sin[ArcCos[Sqrt[x + \[Lambda]/(x + yI)+ \[Lambda]]]]^2])- \[Lambda]EllipticF[ArcCos[Sqrt[x/x + yI]],(x + yI-y)/(x + yI-x)]/Sqrt[x + yI-x]-Sqrt[x]-Sqrt[y]-Sqrt[x + yI]	Missing Macro Error	Aborted	-	Failed [180 / 180] Result: Plus[Complex[2.330530943809637, 0.9206144902290859], Times[Complex[1.7320508075688772, -1.732050807568877], Plus[Complex[0.9985512968581824, 0.2012315241723115], Times[Complex[0.3176872874027722, -1.049249833251038], Power[Plus[1.0, Times[Complex[0.0, -1.5], Power[k, 2]]], Rational[1, 2]]]]], Times[Complex[-4.184639587172815, 1.9117536488739475], Plus[Complex[0.7424137617640161, 0.220635885032481], Times[Complex[0.14483575015411373, 1.3558262394954135], Power[Plus[1.0, Times[Complex[0.9940169358562925, 0.4776709006307397], Power[k, 2]]], Rational[1, 2]]]]]] Test Values: {Rule[x, 1.5], Rule[y, -1.5], Rule[λ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]} Result: Plus[Complex[2.3171140130573056, 0.42755423781462054], Times[Complex[1.7320508075688772, -1.732050807568877], Plus[Complex[0.9985512968581824, 0.2012315241723115], Times[Complex[0.3176872874027722, -1.049249833251038], Power[Plus[1.0, Times[Complex[0.0, -1.5], Power[k, 2]]], Rational[1, 2]]]]], Times[Complex[-1.5682295148869496, 3.234090878649293], Plus[Complex[0.3473840661116648, 1.4426085854555293], Times[Complex[0.7761183239980944, 1.3014092542459557], Power[Plus[1.0, Times[Complex[0.02232909936926042, 0.49401693585629247], Power[k, 2]]], Rational[1, 2]]]]]] Test Values: {Rule[x, 1.5], Rule[y, -1.5], Rule[λ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]]} ... skip entries to safe data
19.26.E22	${\displaystyle{\displaystyle R_{J}\left(x,y,z,p\right)=2R_{J}\left(x+\lambda,y% +\lambda,z+\lambda,p+\lambda\right)+3R_{C}\left(\alpha^{2},\beta^{2}\right)}}$ `\CarlsonsymellintRJ@{x}{y}{z}{p} = 2\CarlsonsymellintRJ@{x+\lambda}{y+\lambda}{z+\lambda}{p+\lambda}+3\CarlsonellintRC@{\alpha^{2}}{\beta^{2}}`		Error	3(x + yI-x)/(x + yI-p)(EllipticPi[(x + yI-p)/(x + yI-x),ArcCos[Sqrt[x/x + yI]],(x + yI-y)/(x + yI-x)]-EllipticF[ArcCos[Sqrt[x/x + yI]],(x + yI-y)/(x + yI-x)])/Sqrt[x + yI-x] == 23((x + yI)+ \[Lambda]-x + \[Lambda])/((x + yI)+ \[Lambda]-p + \[Lambda])(EllipticPi[((x + yI)+ \[Lambda]-p + \[Lambda])/((x + yI)+ \[Lambda]-x + \[Lambda]),ArcCos[Sqrt[x + \[Lambda]/(x + yI)+ \[Lambda]]],((x + yI)+ \[Lambda]-y + \[Lambda])/((x + yI)+ \[Lambda]-x + \[Lambda])]-EllipticF[ArcCos[Sqrt[x + \[Lambda]/(x + yI)+ \[Lambda]]],((x + yI)+ \[Lambda]-y + \[Lambda])/((x + yI)+ \[Lambda]-x + \[Lambda])])/Sqrt[(x + yI)+ \[Lambda]-x + \[Lambda]]+ 31/Sqrt[\[Beta]^(2)]*Hypergeometric2F1[1/2,1/2,3/2,1-(\[Alpha]^(2))/(\[Beta]^(2))]	Missing Macro Error	Failure	-	Failed [300 / 300] Result: Indeterminate Test Values: {Rule[p, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[x, 1.5], Rule[y, -1.5], Rule[α, 1.5], Rule[β, 1.5], Rule[λ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]} Result: Indeterminate Test Values: {Rule[p, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[x, 1.5], Rule[y, -1.5], Rule[α, 1.5], Rule[β, 1.5], Rule[λ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]]} ... skip entries to safe data
19.26#Ex11	${\displaystyle{\displaystyle\alpha=p(\sqrt{x}+\sqrt{y}+\sqrt{z})+\sqrt{x}\sqrt% {y}\sqrt{z}}}$ `\alpha = p(\sqrt{x}+\sqrt{y}+\sqrt{z})+\sqrt{x}\sqrt{y}\sqrt{z}`		alpha = p(sqrt(x)+sqrt(y)+sqrt(x + yI))+sqrt(x)sqrt(y)sqrt(x + y*I)	\[Alpha] == p(Sqrt[x]+Sqrt[y]+Sqrt[x + yI])+Sqrt[x]Sqrt[y]Sqrt[x + y*I]	Skipped - no semantic math	Skipped - no semantic math	-	-
19.26#Ex12	${\displaystyle{\displaystyle\beta=\sqrt{p}(p+\lambda)}}$ `\beta = \sqrt{p}(p+\lambda)`		beta = sqrt(p)*(p + lambda)	\[Beta] == Sqrt[p]*(p + \[Lambda])	Skipped - no semantic math	Skipped - no semantic math	-	-
19.26#Ex13	${\displaystyle{\displaystyle\beta+\alpha=(\sqrt{p}+\sqrt{x})(\sqrt{p}+\sqrt{y}% )(\sqrt{p}+\sqrt{z})}}$ `\beta+\alpha = (\sqrt{p}+\sqrt{x})(\sqrt{p}+\sqrt{y})(\sqrt{p}+\sqrt{z})`		beta + alpha = (sqrt(p)+sqrt(x))(sqrt(p)+sqrt(y))(sqrt(p)+sqrt(x + y*I))	\[Beta]+ \[Alpha] == (Sqrt[p]+Sqrt[x])(Sqrt[p]+Sqrt[y])(Sqrt[p]+Sqrt[x + y*I])	Skipped - no semantic math	Skipped - no semantic math	-	-
19.26#Ex14	${\displaystyle{\displaystyle\beta^{2}-\alpha^{2}=(p-x)(p-y)(p-z)}}$ `\beta^{2}-\alpha^{2} = (p-x)(p-y)(p-z)`		(beta)^(2)- (alpha)^(2) = (p - x)(p - y)(p -(x + y*I))	\[Beta]^(2)- \[Alpha]^(2) == (p - x)(p - y)(p -(x + y*I))	Skipped - no semantic math	Skipped - no semantic math	-	-
19.26.E24	${\displaystyle{\displaystyle z=(\xi\zeta+\eta\zeta-\xi\eta)^{2}/(4\xi\eta\zeta% )}}$ `z = (\xi\zeta+\eta\zeta-\xi\eta)^{2}/(4\xi\eta\zeta)`	${\displaystyle{\displaystyle(\xi=(x+\lambda,\eta=(x+\lambda,\zeta)=(x+\lambda}}$	z = (xizeta + etazeta - xieta)^(2)/(4xietazeta)	z == (\[Xi]\[Zeta]+ \[Eta]\[Zeta]- \[Xi]\[Eta])^(2)/(4\[Xi]\[Eta]\[Zeta])	Skipped - no semantic math	Skipped - no semantic math	-	-
19.26.E25	${\displaystyle{\displaystyle R_{C}\left(x,y\right)=2R_{C}\left(x+\lambda,y+% \lambda\right)}}$ `\CarlsonellintRC@{x}{y} = 2\CarlsonellintRC@{x+\lambda}{y+\lambda}`	${\displaystyle{\displaystyle\lambda=y+2\sqrt{x}\sqrt{y}}}$	Error	1/Sqrt[y]Hypergeometric2F1[1/2,1/2,3/2,1-(x)/(y)] == 21/Sqrt[y + \[Lambda]]*Hypergeometric2F1[1/2,1/2,3/2,1-(x + \[Lambda])/(y + \[Lambda])]	Missing Macro Error	Failure	-	Failed [1 / 1] Result: Indeterminate Test Values: {Rule[x, 0.5], Rule[y, 0.5], Rule[λ, 1.5]}
19.26.E26	${\displaystyle{\displaystyle R_{C}\left(x^{2},y^{2}\right)=R_{C}\left(a^{2},ay% \right)}}$ `\CarlsonellintRC@{x^{2}}{y^{2}} = \CarlsonellintRC@{a^{2}}{ay}`	${\displaystyle{\displaystyle a=(x+y)/2,\Re x\geq 0,\Re y>0}}$	Error	1/Sqrt[(y)^(2)]Hypergeometric2F1[1/2,1/2,3/2,1-((x)^(2))/((y)^(2))] == 1/Sqrt[ay]Hypergeometric2F1[1/2,1/2,3/2,1-((a)^(2))/(ay)]	Missing Macro Error	Aborted	-	Failed [3 / 3] Result: Indeterminate Test Values: {Rule[a, 1.5], Rule[x, 1.5], Rule[y, 1.5]} Result: Indeterminate Test Values: {Rule[a, 0.5], Rule[x, 0.5], Rule[y, 0.5]} ... skip entries to safe data
19.26.E27	${\displaystyle{\displaystyle R_{C}\left(x^{2},x^{2}-\theta\right)=2R_{C}\left(% s^{2},s^{2}-\theta\right)}}$ `\CarlsonellintRC@{x^{2}}{x^{2}-\theta} = 2\CarlsonellintRC@{s^{2}}{s^{2}-\theta}`	${\displaystyle{\displaystyle s=x+\sqrt{x^{2}-\theta},\theta\neq x^{2}}}$	Error	1/Sqrt[(x)^(2)- \[Theta]]Hypergeometric2F1[1/2,1/2,3/2,1-((x)^(2))/((x)^(2)- \[Theta])] == 21/Sqrt[(s)^(2)- \[Theta]]*Hypergeometric2F1[1/2,1/2,3/2,1-((s)^(2))/((s)^(2)- \[Theta])]	Missing Macro Error	Failure	-	Successful [Tested: 2]
19.27#Ex1	${\displaystyle{\displaystyle a=\tfrac{1}{2}(x+y)}}$ `a = \tfrac{1}{2}(x+y)`		a = (1)/(2)*(x + y)	a == Divide[1,2]*(x + y)	Skipped - no semantic math	Skipped - no semantic math	-	-
19.27#Ex2	${\displaystyle{\displaystyle b=\tfrac{1}{2}(y+z)}}$ `b = \tfrac{1}{2}(y+z)`		b = (1)/(2)(y +(x + yI))	b == Divide[1,2](y +(x + yI))	Skipped - no semantic math	Skipped - no semantic math	-	-
19.27#Ex3	${\displaystyle{\displaystyle c=\tfrac{1}{3}(x+y+z)}}$ `c = \tfrac{1}{3}(x+y+z)`		c = (1)/(3)(x + y +(x + yI))	c == Divide[1,3](x + y +(x + yI))	Skipped - no semantic math	Skipped - no semantic math	-	-
19.27#Ex4	${\displaystyle{\displaystyle f=(xyz)^{1/3}}}$ `f = (xyz)^{1/3}`		f = (xy(x + y*I))^(1/3)	f == (xy(x + y*I))^(1/3)	Skipped - no semantic math	Skipped - no semantic math	-	-
19.27#Ex5	${\displaystyle{\displaystyle g=(xy)^{1/2}}}$ `g = (xy)^{1/2}`		g = (x*y)^(1/2)	g == (x*y)^(1/2)	Skipped - no semantic math	Skipped - no semantic math	-	-
19.27#Ex6	${\displaystyle{\displaystyle h=(yz)^{1/2}}}$ `h = (yz)^{1/2}`		h = (y(x + yI))^(1/2)	h == (y(x + yI))^(1/2)	Skipped - no semantic math	Skipped - no semantic math	-	-
19.28.E1	${\displaystyle{\displaystyle\int_{0}^{1}t^{\sigma-1}R_{F}\left(0,t,1\right)% \mathrm{d}t=\tfrac{1}{2}\left(\mathrm{B}\left(\sigma,\tfrac{1}{2}\right)\right% )^{2}}}$ `\int_{0}^{1}t^{\sigma-1}\CarlsonsymellintRF@{0}{t}{1}\diff{t} = \tfrac{1}{2}\left(\EulerBeta@{\sigma}{\tfrac{1}{2}}\right)^{2}`	${\displaystyle{\displaystyle\Re(\sigma)>0,\Re((\sigma)+b)>0,\Re(a+(\tfrac{1}{2% }))>0}}$	int((t)^(sigma - 1)* 0.5int(1/(sqrt(t+0)sqrt(t+t)sqrt(t+1)), t = 0..infinity), t = 0..1) = (1)/(2)(Beta(sigma, (1)/(2)))^(2)	Integrate[(t)^(\[Sigma]- 1)* EllipticF[ArcCos[Sqrt[0/1]],(1-t)/(1-0)]/Sqrt[1-0], {t, 0, 1}, GenerateConditions->None] == Divide[1,2]*(Beta[\[Sigma], Divide[1,2]])^(2)	Failure	Aborted	Failed [10 / 10] Result: Float(undefined)+1.162857938I Test Values: {sigma = 1/23^(1/2)+1/2I} Result: Float(undefined)+.9984297790I Test Values: {sigma = -1/2+1/2I3^(1/2)} ... skip entries to safe data	Skipped - Because timed out
19.28.E2	${\displaystyle{\displaystyle\int_{0}^{1}t^{\sigma-1}R_{G}\left(0,t,1\right)% \mathrm{d}t=\frac{\sigma}{4\sigma+2}\left(\mathrm{B}\left(\sigma,\tfrac{1}{2}% \right)\right)^{2}}}$ `\int_{0}^{1}t^{\sigma-1}\CarlsonsymellintRG@{0}{t}{1}\diff{t} = \frac{\sigma}{4\sigma+2}\left(\EulerBeta@{\sigma}{\tfrac{1}{2}}\right)^{2}`	${\displaystyle{\displaystyle\Re(\sigma)>0,\Re((\sigma)+b)>0,\Re(a+(\tfrac{1}{2% }))>0}}$	Error	Integrate[(t)^(\[Sigma]- 1)* Sqrt[1-0](EllipticE[ArcCos[Sqrt[0/1]],(1-t)/(1-0)]+(Cot[ArcCos[Sqrt[0/1]]])^2EllipticF[ArcCos[Sqrt[0/1]],(1-t)/(1-0)]+Cot[ArcCos[Sqrt[0/1]]]Sqrt[1-k^2Sin[ArcCos[Sqrt[0/1]]]^2]), {t, 0, 1}, GenerateConditions->None] == Divide[\[Sigma],4\[Sigma]+ 2](Beta[\[Sigma], Divide[1,2]])^(2)	Missing Macro Error	Aborted	-	Skipped - Because timed out
19.28.E3	${\displaystyle{\displaystyle\int_{0}^{1}t^{\sigma-1}(1-t)R_{D}\left(0,t,1% \right)\mathrm{d}t=\frac{3}{4\sigma+2}\left(\mathrm{B}\left(\sigma,\tfrac{1}{2% }\right)\right)^{2}}}$ `\int_{0}^{1}t^{\sigma-1}(1-t)\CarlsonsymellintRD@{0}{t}{1}\diff{t} = \frac{3}{4\sigma+2}\left(\EulerBeta@{\sigma}{\tfrac{1}{2}}\right)^{2}`	${\displaystyle{\displaystyle\Re(\sigma)>0,\Re((\sigma)+b)>0,\Re(a+(\tfrac{1}{2% }))>0}}$	Error	Integrate[(t)^(\[Sigma]- 1)(1 - t)3(EllipticF[ArcCos[Sqrt[0/1]],(1-t)/(1-0)]-EllipticE[ArcCos[Sqrt[0/1]],(1-t)/(1-0)])/((1-t)(1-0)^(1/2)), {t, 0, 1}, GenerateConditions->None] == Divide[3,4\[Sigma]+ 2](Beta[\[Sigma], Divide[1,2]])^(2)	Missing Macro Error	Aborted	-	Skipped - Because timed out
19.28.E5	${\displaystyle{\displaystyle\int_{z}^{\infty}R_{D}\left(x,y,t\right)\mathrm{d}% t=6R_{F}\left(x,y,z\right)}}$ `\int_{z}^{\infty}\CarlsonsymellintRD@{x}{y}{t}\diff{t} = 6\CarlsonsymellintRF@{x}{y}{z}`		Error	Integrate[3(EllipticF[ArcCos[Sqrt[x/t]],(t-y)/(t-x)]-EllipticE[ArcCos[Sqrt[x/t]],(t-y)/(t-x)])/((t-y)(t-x)^(1/2)), {t, (x + yI), Infinity}, GenerateConditions->None] == 6EllipticF[ArcCos[Sqrt[x/x + yI]],(x + yI-y)/(x + yI-x)]/Sqrt[x + yI-x]	Missing Macro Error	Aborted	-	Skipped - Because timed out
19.28.E6	${\displaystyle{\displaystyle\int_{0}^{1}R_{D}\left(x,y,v^{2}z+(1-v^{2})p\right% )\mathrm{d}v=R_{J}\left(x,y,z,p\right)}}$ `\int_{0}^{1}\CarlsonsymellintRD@{x}{y}{v^{2}z+(1-v^{2})p}\diff{v} = \CarlsonsymellintRJ@{x}{y}{z}{p}`		Error	Integrate[3(EllipticF[ArcCos[Sqrt[x/(v)^(2)(x + yI)+(1 - (v)^(2))p]],((v)^(2)(x + yI)+(1 - (v)^(2))p-y)/((v)^(2)(x + yI)+(1 - (v)^(2))p-x)]-EllipticE[ArcCos[Sqrt[x/(v)^(2)(x + yI)+(1 - (v)^(2))p]],((v)^(2)(x + yI)+(1 - (v)^(2))p-y)/((v)^(2)(x + yI)+(1 - (v)^(2))p-x)])/(((v)^(2)(x + yI)+(1 - (v)^(2))p-y)((v)^(2)(x + yI)+(1 - (v)^(2))p-x)^(1/2)), {v, 0, 1}, GenerateConditions->None] == 3(x + yI-x)/(x + yI-p)(EllipticPi[(x + yI-p)/(x + yI-x),ArcCos[Sqrt[x/x + yI]],(x + yI-y)/(x + yI-x)]-EllipticF[ArcCos[Sqrt[x/x + yI]],(x + yI-y)/(x + yI-x)])/Sqrt[x + y*I-x]	Missing Macro Error	Aborted	-	Skipped - Because timed out
19.28.E7	${\displaystyle{\displaystyle\int_{0}^{\infty}R_{J}\left(x,y,z,r^{2}\right)% \mathrm{d}r=\tfrac{3}{2}\pi R_{F}\left(xy,xz,yz\right)}}$ `\int_{0}^{\infty}\CarlsonsymellintRJ@{x}{y}{z}{r^{2}}\diff{r} = \tfrac{3}{2}\pi\CarlsonsymellintRF@{xy}{xz}{yz}`		Error	Integrate[3(x + yI-x)/(x + yI-(r)^(2))(EllipticPi[(x + yI-(r)^(2))/(x + yI-x),ArcCos[Sqrt[x/x + yI]],(x + yI-y)/(x + yI-x)]-EllipticF[ArcCos[Sqrt[x/x + yI]],(x + yI-y)/(x + yI-x)])/Sqrt[x + yI-x], {r, 0, Infinity}, GenerateConditions->None] == Divide[3,2]PiEllipticF[ArcCos[Sqrt[xy/y(x + yI)]],(y(x + yI)-x(x + yI))/(y(x + yI)-xy)]/Sqrt[y(x + yI)-xy]	Missing Macro Error	Aborted	-	Skipped - Because timed out
19.28.E8	${\displaystyle{\displaystyle\int_{0}^{\infty}R_{J}\left(tx,y,z,tp\right)% \mathrm{d}t=\frac{6}{\sqrt{p}}R_{C}\left(p,x\right)R_{F}\left(0,y,z\right)}}$ `\int_{0}^{\infty}\CarlsonsymellintRJ@{tx}{y}{z}{tp}\diff{t} = \frac{6}{\sqrt{p}}\CarlsonellintRC@{p}{x}\CarlsonsymellintRF@{0}{y}{z}`		Error	Integrate[3(x + yI-tx)/(x + yI-tp)(EllipticPi[(x + yI-tp)/(x + yI-tx),ArcCos[Sqrt[tx/x + yI]],(x + yI-y)/(x + yI-tx)]-EllipticF[ArcCos[Sqrt[tx/x + yI]],(x + yI-y)/(x + yI-tx)])/Sqrt[x + yI-tx], {t, 0, Infinity}, GenerateConditions->None] == Divide[6,Sqrt[p]]1/Sqrt[x]Hypergeometric2F1[1/2,1/2,3/2,1-(p)/(x)]EllipticF[ArcCos[Sqrt[0/x + yI]],(x + yI-y)/(x + yI-0)]/Sqrt[x + y*I-0]	Missing Macro Error	Aborted	-	Skipped - Because timed out
19.28.E9	${\displaystyle{\displaystyle\int_{0}^{\pi/2}R_{F}\left({\sin^{2}}\theta{\cos^{% 2}}\left(x+y\right),{\sin^{2}}\theta{\cos^{2}}\left(x-y\right),1\right)\mathrm% {d}\theta=R_{F}\left(0,{\cos^{2}}x,1\right)R_{F}\left(0,{\cos^{2}}y,1\right)}}$ `\int_{0}^{\pi/2}\CarlsonsymellintRF@{\sin^{2}@@{\theta}\cos^{2}@{x+y}}{\sin^{2}@@{\theta}\cos^{2}@{x-y}}{1}\diff{\theta} = \CarlsonsymellintRF@{0}{\cos^{2}@@{x}}{1}\CarlsonsymellintRF@{0}{\cos^{2}@@{y}}{1}`		int(0.5int(1/(sqrt(t+(sin(theta))^(2) (cos(x + y))^(2))sqrt(t+(sin(theta))^(2) (cos(x - y))^(2))sqrt(t+1)), t = 0..infinity), theta = 0..Pi/2) = 0.5int(1/(sqrt(t+0)sqrt(t+(cos(x))^(2))sqrt(t+1)), t = 0..infinity)0.5int(1/(sqrt(t+0)sqrt(t+(cos(y))^(2))sqrt(t+1)), t = 0..infinity)	Integrate[EllipticF[ArcCos[Sqrt[(Sin[\[Theta]])^(2)* (Cos[x + y])^(2)/1]],(1-(Sin[\[Theta]])^(2)* (Cos[x - y])^(2))/(1-(Sin[\[Theta]])^(2)* (Cos[x + y])^(2))]/Sqrt[1-(Sin[\[Theta]])^(2)* (Cos[x + y])^(2)], {\[Theta], 0, Pi/2}, GenerateConditions->None] == EllipticF[ArcCos[Sqrt[0/1]],(1-(Cos[x])^(2))/(1-0)]/Sqrt[1-0]*EllipticF[ArcCos[Sqrt[0/1]],(1-(Cos[y])^(2))/(1-0)]/Sqrt[1-0]	Aborted	Aborted	Skipped - Because timed out	Skipped - Because timed out
19.28.E10	${\displaystyle{\displaystyle\int_{0}^{\infty}R_{F}\left((ac+bd)^{2},(ad+bc)^{2% },4abcd{\cosh^{2}}z\right)\mathrm{d}z=\tfrac{1}{2}R_{F}\left(0,a^{2},b^{2}% \right)R_{F}\left(0,c^{2},d^{2}\right)}}$ `\int_{0}^{\infty}\CarlsonsymellintRF@{(ac+bd)^{2}}{(ad+bc)^{2}}{4abcd\cosh^{2}@@{z}}\diff{z} = \tfrac{1}{2}\CarlsonsymellintRF@{0}{a^{2}}{b^{2}}\CarlsonsymellintRF@{0}{c^{2}}{d^{2}}`		int(0.5int(1/(sqrt(t+(ac + bd)^(2))sqrt(t+(ad + bc)^(2))sqrt(t+4abcd(cosh(z))^(2))), t = 0..infinity), z = 0..infinity) = (1)/(2)0.5int(1/(sqrt(t+0)sqrt(t+(a)^(2))sqrt(t+(b)^(2))), t = 0..infinity)0.5int(1/(sqrt(t+0)sqrt(t+(c)^(2))sqrt(t+(d)^(2))), t = 0..infinity)	Integrate[EllipticF[ArcCos[Sqrt[(ac + bd)^(2)/4abcd(Cosh[z])^(2)]],(4abcd(Cosh[z])^(2)-(ad + bc)^(2))/(4abcd(Cosh[z])^(2)-(ac + bd)^(2))]/Sqrt[4abcd(Cosh[z])^(2)-(ac + bd)^(2)], {z, 0, Infinity}, GenerateConditions->None] == Divide[1,2]EllipticF[ArcCos[Sqrt[0/(b)^(2)]],((b)^(2)-(a)^(2))/((b)^(2)-0)]/Sqrt[(b)^(2)-0]EllipticF[ArcCos[Sqrt[0/(d)^(2)]],((d)^(2)-(c)^(2))/((d)^(2)-0)]/Sqrt[(d)^(2)-0]	Error	Aborted	-	Skipped - Because timed out
19.29#Ex1	${\displaystyle{\displaystyle X_{\alpha}=\sqrt{a_{\alpha}+b_{\alpha}x}}}$ `X_{\alpha} = \sqrt{a_{\alpha}+b_{\alpha}x}`		X[alpha] = sqrt(a[alpha]+ b[alpha]*x)	Subscript[X, \[Alpha]] == Sqrt[Subscript[a, \[Alpha]]+ Subscript[b, \[Alpha]]*x]	Skipped - no semantic math	Skipped - no semantic math	-	-
19.29#Ex2	${\displaystyle{\displaystyle Y_{\alpha}=\sqrt{a_{\alpha}+b_{\alpha}y}}}$ `Y_{\alpha} = \sqrt{a_{\alpha}+b_{\alpha}y}`	${\displaystyle{\displaystyle x>y,1\leq\alpha,\alpha\leq 5}}$	Y[alpha] = sqrt(a[alpha]+ b[alpha]*y)	Subscript[Y, \[Alpha]] == Sqrt[Subscript[a, \[Alpha]]+ Subscript[b, \[Alpha]]*y]	Skipped - no semantic math	Skipped - no semantic math	-	-
19.29.E2	${\displaystyle{\displaystyle d_{\alpha\beta}=a_{\alpha}b_{\beta}-a_{\beta}b_{% \alpha}}}$ `d_{\alpha\beta} = a_{\alpha}b_{\beta}-a_{\beta}b_{\alpha}`	${\displaystyle{\displaystyle d_{\alpha\beta}\neq 0,\alpha\neq\beta}}$	d[alphabeta] = a[alpha]b[beta]- a[beta]*b[alpha]	Subscript[d, \[Alpha]\[Beta]] == Subscript[a, \[Alpha]]Subscript[b, \[Beta]]- Subscript[a, \[Beta]]*Subscript[b, \[Alpha]]	Skipped - no semantic math	Skipped - no semantic math	-	-
19.29.E3	${\displaystyle{\displaystyle s(t)=\prod_{\alpha=1}^{4}\sqrt{a_{\alpha}+b_{% \alpha}t}}}$ `s(t) = \prod_{\alpha=1}^{4}\sqrt{a_{\alpha}+b_{\alpha}t}`		s(t) = product(sqrt(a[alpha]+ b[alpha]*t), alpha = 1..4)	s[t] == Product[Sqrt[Subscript[a, \[Alpha]]+ Subscript[b, \[Alpha]]*t], {\[Alpha], 1, 4}, GenerateConditions->None]	Skipped - no semantic math	Skipped - no semantic math	-	-
19.29.E4	${\displaystyle{\displaystyle\int_{y}^{x}\frac{\mathrm{d}t}{s(t)}=2R_{F}\left(U% _{12}^{2},U_{13}^{2},U_{23}^{2}\right)}}$ `\int_{y}^{x}\frac{\diff{t}}{s(t)} = 2\CarlsonsymellintRF@{U_{12}^{2}}{U_{13}^{2}}{U_{23}^{2}}`		int((1)/(s(t)), t = y..x) = 20.5int(1/(sqrt(t+(U[12])^(2))sqrt(t+(U[13])^(2))sqrt(t+(U[23])^(2))), t = 0..infinity)	Integrate[Divide[1,s[t]], {t, y, x}, GenerateConditions->None] == 2*EllipticF[ArcCos[Sqrt[(Subscript[U, 12])^(2)/(Subscript[U, 23])^(2)]],((Subscript[U, 23])^(2)-(Subscript[U, 13])^(2))/((Subscript[U, 23])^(2)-(Subscript[U, 12])^(2))]/Sqrt[(Subscript[U, 23])^(2)-(Subscript[U, 12])^(2)]	Aborted	Aborted	Skipped - Because timed out	Skipped - Because timed out
19.29#Ex3	${\displaystyle{\displaystyle U_{\alpha\beta}=(X_{\alpha}X_{\beta}Y_{\gamma}Y_{% \delta}+Y_{\alpha}Y_{\beta}X_{\gamma}X_{\delta})/(x-y)}}$ `U_{\alpha\beta} = (X_{\alpha}X_{\beta}Y_{\gamma}Y_{\delta}+Y_{\alpha}Y_{\beta}X_{\gamma}X_{\delta})/(x-y)`		U[alphabeta] = (X[alpha]X[beta]Y[gamma]Y[delta]+ Y[alpha]Y[beta]X[gamma]*X[delta])/(x - y)	Subscript[U, \[Alpha]\[Beta]] == (Subscript[X, \[Alpha]]Subscript[X, \[Beta]]Subscript[Y, \[Gamma]]Subscript[Y, \[Delta]]+ Subscript[Y, \[Alpha]]Subscript[Y, \[Beta]]Subscript[X, \[Gamma]]*Subscript[X, \[Delta]])/(x - y)	Skipped - no semantic math	Skipped - no semantic math	-	-
19.29#Ex4	${\displaystyle{\displaystyle U_{\alpha\beta}=U_{\beta\alpha}}}$ `U_{\alpha\beta} = U_{\beta\alpha}`		U[alphabeta] = U[betaalpha]	Subscript[U, \[Alpha]\[Beta]] == Subscript[U, \[Beta]\[Alpha]]	Skipped - no semantic math	Skipped - no semantic math	-	-
19.29#Ex5	${\displaystyle{\displaystyle U_{\alpha\beta}^{2}-U_{\alpha\gamma}^{2}=d_{% \alpha\delta}d_{\beta\gamma}}}$ `U_{\alpha\beta}^{2}-U_{\alpha\gamma}^{2} = d_{\alpha\delta}d_{\beta\gamma}`		(U[alphabeta])^(2)- (U[alphagamma])^(2) = d[alphadelta]d[beta*gamma]	(Subscript[U, \[Alpha]\[Beta]])^(2)- (Subscript[U, \[Alpha]\[Gamma]])^(2) == Subscript[d, \[Alpha]\[Delta]]Subscript[d, \[Beta]*\[Gamma]]	Skipped - no semantic math	Skipped - no semantic math	-	-
19.29#Ex6	${\displaystyle{\displaystyle U_{\alpha\beta}=\sqrt{b_{\alpha}}\sqrt{b_{\beta}}% Y_{\gamma}Y_{\delta}+Y_{\alpha}Y_{\beta}\sqrt{b_{\gamma}}\sqrt{b_{\delta}},}}$ `U_{\alpha\beta} = \sqrt{b_{\alpha}}\sqrt{b_{\beta}}Y_{\gamma}Y_{\delta}+Y_{\alpha}Y_{\beta}\sqrt{b_{\gamma}}\sqrt{b_{\delta}},`	${\displaystyle{\displaystyle x=\infty}}$	U[alphabeta] = sqrt(b[alpha])sqrt(b[beta])Y[gamma]Y[delta]+ Y[alpha]Y[beta]sqrt(b[gamma])*sqrt(b[delta])	Subscript[U, \[Alpha]\[Beta]] == Sqrt[Subscript[b, \[Alpha]]]Sqrt[Subscript[b, \[Beta]]]Subscript[Y, \[Gamma]]Subscript[Y, \[Delta]]+ Subscript[Y, \[Alpha]]Subscript[Y, \[Beta]]Sqrt[Subscript[b, \[Gamma]]]*Sqrt[Subscript[b, \[Delta]]]	Skipped - no semantic math	Skipped - no semantic math	-	-
19.29#Ex7	${\displaystyle{\displaystyle U_{\alpha\beta}=X_{\alpha}X_{\beta}\sqrt{-b_{% \gamma}}\sqrt{-b_{\delta}}+\sqrt{-b_{\alpha}}\sqrt{-b_{\beta}}X_{\gamma}X_{% \delta}}}$ `U_{\alpha\beta} = X_{\alpha}X_{\beta}\sqrt{-b_{\gamma}}\sqrt{-b_{\delta}}+\sqrt{-b_{\alpha}}\sqrt{-b_{\beta}}X_{\gamma}X_{\delta}`	${\displaystyle{\displaystyle y=-\infty}}$	U[alphabeta] = X[alpha]X[beta]sqrt(- b[gamma])sqrt(- b[delta])+sqrt(- b[alpha])sqrt(- b[beta])X[gamma]*X[delta]	Subscript[U, \[Alpha]\[Beta]] == Subscript[X, \[Alpha]]Subscript[X, \[Beta]]Sqrt[- Subscript[b, \[Gamma]]]Sqrt[- Subscript[b, \[Delta]]]+Sqrt[- Subscript[b, \[Alpha]]]Sqrt[- Subscript[b, \[Beta]]]Subscript[X, \[Gamma]]*Subscript[X, \[Delta]]	Skipped - no semantic math	Skipped - no semantic math	-	-
19.29.E7	${\displaystyle{\displaystyle\int_{y}^{x}\frac{a_{\alpha}+b_{\alpha}t}{a_{% \delta}+b_{\delta}t}\frac{\mathrm{d}t}{s(t)}=\tfrac{2}{3}d_{\alpha\beta}d_{% \alpha\gamma}R_{D}\left(U_{\alpha\beta}^{2},U_{\alpha\gamma}^{2},U_{\alpha% \delta}^{2}\right)+\frac{2X_{\alpha}Y_{\alpha}}{X_{\delta}Y_{\delta}U_{\alpha% \delta}}}}$ `\int_{y}^{x}\frac{a_{\alpha}+b_{\alpha}t}{a_{\delta}+b_{\delta}t}\frac{\diff{t}}{s(t)} = \tfrac{2}{3}d_{\alpha\beta}d_{\alpha\gamma}\CarlsonsymellintRD@{U_{\alpha\beta}^{2}}{U_{\alpha\gamma}^{2}}{U_{\alpha\delta}^{2}}+\frac{2X_{\alpha}Y_{\alpha}}{X_{\delta}Y_{\delta}U_{\alpha\delta}}`	${\displaystyle{\displaystyle U_{\alpha\delta}\neq 0}}$	Error	Integrate[Divide[Subscript[a, \[Alpha]]+ Subscript[b, \[Alpha]]t,Subscript[a, \[Delta]]+ Subscript[b, \[Delta]]t]Divide[1,s[t]], {t, y, x}, GenerateConditions->None] == Divide[2,3]Subscript[d, \[Alpha]\[Beta]]Subscript[d, \[Alpha]\[Gamma]]3(EllipticF[ArcCos[Sqrt[(Subscript[U, \[Alpha]\[Beta]])^(2)/(Subscript[U, \[Alpha]\[Delta]])^(2)]],((Subscript[U, \[Alpha]\[Delta]])^(2)-(Subscript[U, \[Alpha]\[Gamma]])^(2))/((Subscript[U, \[Alpha]\[Delta]])^(2)-(Subscript[U, \[Alpha]\[Beta]])^(2))]-EllipticE[ArcCos[Sqrt[(Subscript[U, \[Alpha]\[Beta]])^(2)/(Subscript[U, \[Alpha]\[Delta]])^(2)]],((Subscript[U, \[Alpha]\[Delta]])^(2)-(Subscript[U, \[Alpha]\[Gamma]])^(2))/((Subscript[U, \[Alpha]\[Delta]])^(2)-(Subscript[U, \[Alpha]\[Beta]])^(2))])/(((Subscript[U, \[Alpha]\[Delta]])^(2)-(Subscript[U, \[Alpha]\[Gamma]])^(2))((Subscript[U, \[Alpha]\[Delta]])^(2)-(Subscript[U, \[Alpha]\[Beta]])^(2))^(1/2))+Divide[2Subscript[X, \[Alpha]]Subscript[Y, \[Alpha]],Subscript[X, \[Delta]]Subscript[Y, \[Delta]]Subscript[U, \[Alpha]*\[Delta]]]	Missing Macro Error	Aborted	-	Skipped - Because timed out
19.29.E8	${\displaystyle{\displaystyle\int_{y}^{x}\frac{a_{\alpha}+b_{\alpha}t}{a_{5}+b_% {5}t}\frac{\mathrm{d}t}{s(t)}=\frac{2}{3}\frac{d_{\alpha\beta}d_{\alpha\gamma}% d_{\alpha\delta}}{d_{\alpha 5}}R_{J}\left(U_{12}^{2},U_{13}^{2},U_{23}^{2},U_{% \alpha 5}^{2}\right)+2R_{C}\left(S_{\alpha 5}^{2},Q_{\alpha 5}^{2}\right)}}$ `\int_{y}^{x}\frac{a_{\alpha}+b_{\alpha}t}{a_{5}+b_{5}t}\frac{\diff{t}}{s(t)} = \frac{2}{3}\frac{d_{\alpha\beta}d_{\alpha\gamma}d_{\alpha\delta}}{d_{\alpha 5}}\CarlsonsymellintRJ@{U_{12}^{2}}{U_{13}^{2}}{U_{23}^{2}}{U_{\alpha 5}^{2}}+2\CarlsonellintRC@{S_{\alpha 5}^{2}}{Q_{\alpha 5}^{2}}`		Error	Integrate[Divide[Subscript[a, \[Alpha]]+ Subscript[b, \[Alpha]]t,Subscript[a, 5]+ Subscript[b, 5]t]Divide[1,s[t]], {t, y, x}, GenerateConditions->None] == Divide[2,3]Divide[Subscript[d, \[Alpha]\[Beta]]Subscript[d, \[Alpha]\[Gamma]]Subscript[d, \[Alpha]\[Delta]],Subscript[d, \[Alpha]5]]3((Subscript[U, 23])^(2)-(Subscript[U, 12])^(2))/((Subscript[U, 23])^(2)-(Subscript[U, \[Alpha]5])^(2))(EllipticPi[((Subscript[U, 23])^(2)-(Subscript[U, \[Alpha]5])^(2))/((Subscript[U, 23])^(2)-(Subscript[U, 12])^(2)),ArcCos[Sqrt[(Subscript[U, 12])^(2)/(Subscript[U, 23])^(2)]],((Subscript[U, 23])^(2)-(Subscript[U, 13])^(2))/((Subscript[U, 23])^(2)-(Subscript[U, 12])^(2))]-EllipticF[ArcCos[Sqrt[(Subscript[U, 12])^(2)/(Subscript[U, 23])^(2)]],((Subscript[U, 23])^(2)-(Subscript[U, 13])^(2))/((Subscript[U, 23])^(2)-(Subscript[U, 12])^(2))])/Sqrt[(Subscript[U, 23])^(2)-(Subscript[U, 12])^(2)]+ 21/Sqrt[(Subscript[Q, \[Alpha]5])^(2)]Hypergeometric2F1[1/2,1/2,3/2,1-((Subscript[S, \[Alpha]5])^(2))/((Subscript[Q, \[Alpha]5])^(2))]	Missing Macro Error	Aborted	-	Skipped - Because timed out
19.29#Ex8	${\displaystyle{\displaystyle U_{\alpha 5}^{2}=U_{\alpha\beta}^{2}-\frac{d_{% \alpha\gamma}d_{\alpha\delta}d_{\beta 5}}{d_{\alpha 5}}}}$ `U_{\alpha 5}^{2} = U_{\alpha\beta}^{2}-\frac{d_{\alpha\gamma}d_{\alpha\delta}d_{\beta 5}}{d_{\alpha 5}}`		(U[alpha5])^(2) = (U[alphabeta])^(2)-(d[alphagamma]d[alphadelta]d[beta5])/(d[alpha5])	(Subscript[U, \[Alpha]5])^(2) == (Subscript[U, \[Alpha]\[Beta]])^(2)-Divide[Subscript[d, \[Alpha]\[Gamma]]Subscript[d, \[Alpha]\[Delta]]Subscript[d, \[Beta]5],Subscript[d, \[Alpha]5]]	Skipped - no semantic math	Skipped - no semantic math	-	-
19.29#Ex9	${\displaystyle{\displaystyle S_{\alpha 5}=\frac{1}{x-y}\left(\frac{X_{\beta}X_% {\gamma}X_{\delta}}{X_{\alpha}}Y_{5}^{2}+\frac{Y_{\beta}Y_{\gamma}Y_{\delta}}{% Y_{\alpha}}X_{5}^{2}\right)}}$ `S_{\alpha 5} = \frac{1}{x-y}\left(\frac{X_{\beta}X_{\gamma}X_{\delta}}{X_{\alpha}}Y_{5}^{2}+\frac{Y_{\beta}Y_{\gamma}Y_{\delta}}{Y_{\alpha}}X_{5}^{2}\right)`		S[alpha5] = (1)/(x - y)((X[beta]X[gamma]X[delta])/(X[alpha])(Y[5])^(2)+(Y[beta]Y[gamma]Y[delta])/(Y[alpha])(X[5])^(2))	Subscript[S, \[Alpha]5] == Divide[1,x - y](Divide[Subscript[X, \[Beta]]Subscript[X, \[Gamma]]Subscript[X, \[Delta]],Subscript[X, \[Alpha]]](Subscript[Y, 5])^(2)+Divide[Subscript[Y, \[Beta]]Subscript[Y, \[Gamma]]Subscript[Y, \[Delta]],Subscript[Y, \[Alpha]]](Subscript[X, 5])^(2))	Skipped - no semantic math	Skipped - no semantic math	-	-
19.29#Ex10	${\displaystyle{\displaystyle Q_{\alpha 5}=\frac{X_{5}Y_{5}}{X_{\alpha}Y_{% \alpha}}U_{\alpha 5}}}$ `Q_{\alpha 5} = \frac{X_{5}Y_{5}}{X_{\alpha}Y_{\alpha}}U_{\alpha 5}`		Q[alpha5] = (X[5]Y[5])/(X[alpha]Y[alpha])U[alpha*5]	Subscript[Q, \[Alpha]5] == Divide[Subscript[X, 5]Subscript[Y, 5],Subscript[X, \[Alpha]]Subscript[Y, \[Alpha]]]Subscript[U, \[Alpha]*5]	Skipped - no semantic math	Skipped - no semantic math	-	-
19.29#Ex11	${\displaystyle{\displaystyle S_{\alpha 5}^{2}-Q_{\alpha 5}^{2}=\frac{d_{\beta 5% }d_{\gamma 5}d_{\delta 5}}{d_{\alpha 5}}}}$ `S_{\alpha 5}^{2}-Q_{\alpha 5}^{2} = \frac{d_{\beta 5}d_{\gamma 5}d_{\delta 5}}{d_{\alpha 5}}`		(S[alpha5])^(2)- (Q[alpha5])^(2) = (d[beta5]d[gamma5]d[delta5])/(d[alpha5])	(Subscript[S, \[Alpha]5])^(2)- (Subscript[Q, \[Alpha]5])^(2) == Divide[Subscript[d, \[Beta]5]Subscript[d, \[Gamma]5]Subscript[d, \[Delta]5],Subscript[d, \[Alpha]5]]	Skipped - no semantic math	Skipped - no semantic math	-	-
19.29.E10	${\displaystyle{\displaystyle\int_{u}^{b}\sqrt{\frac{a-t}{(b-t)(t-c)^{3}}}% \mathrm{d}t=-\tfrac{2}{3}{(a-b)}{(b-u)}^{3/2}R_{D}+\frac{2}{b-c}\sqrt{\frac{(a% -u)(b-u)}{u-c}}}}$ `\int_{u}^{b}\sqrt{\frac{a-t}{(b-t)(t-c)^{3}}}\diff{t} = -\tfrac{2}{3}{(a-b)}{(b-u)}^{3/2}\CarlsonsymellintRD@@{(a-b)(u-c)}{(b-c)(a-u)}{(a-b)(b-c)}+\frac{2}{b-c}\sqrt{\frac{(a-u)(b-u)}{u-c}}`	${\displaystyle{\displaystyle a>b,b>u,u>c}}$	Error	Integrate[Sqrt[Divide[a - t,(b - t)(t - c)^(3)]], {t, u, b}, GenerateConditions->None] == -Divide[2,3](a - b)(b - u)^(3/2) 3(EllipticF[ArcCos[Sqrt[(a - b)(u - c)/(a - b)(b - c)]],((a - b)(b - c)-(b - c)(a - u))/((a - b)(b - c)-(a - b)(u - c))]-EllipticE[ArcCos[Sqrt[(a - b)(u - c)/(a - b)(b - c)]],((a - b)(b - c)-(b - c)(a - u))/((a - b)(b - c)-(a - b)(u - c))])/(((a - b)(b - c)-(b - c)(a - u))((a - b)(b - c)-(a - b)(u - c))^(1/2))+Divide[2,b - c]Sqrt[Divide[(a - u)(b - u),u - c]]	Missing Macro Error	Aborted	-	Skipped - Because timed out
19.29.E11	${\displaystyle{\displaystyle I(\mathbf{m})=\int_{y}^{x}\prod_{\alpha=1}^{h}(a_% {\alpha}+b_{\alpha}t)^{-1/2}\prod_{j=1}^{n}(a_{j}+b_{j}t)^{m_{j}}\mathrm{d}t}}$ `I(\mathbf{m}) = \int_{y}^{x}\prod_{\alpha=1}^{h}(a_{\alpha}+b_{\alpha}t)^{-1/2}\prod_{j=1}^{n}(a_{j}+b_{j}t)^{m_{j}}\diff{t}`		I(m) = int(product((a[alpha]+ b[alpha]t)^(- 1/2) product((a[j]+ b[j]*t)^(m[j]), j = 1..n), alpha = 1..h), t = y..x)	I[m] == Integrate[Product[(Subscript[a, \[Alpha]]+ Subscript[b, \[Alpha]]t)^(- 1/2) Product[(Subscript[a, j]+ Subscript[b, j]*t)^(Subscript[m, j]), {j, 1, n}, GenerateConditions->None], {\[Alpha], 1, h}, GenerateConditions->None], {t, y, x}, GenerateConditions->None]	Aborted	Aborted	Error	Skipped - Because timed out
19.29.E15	${\displaystyle{\displaystyle b_{j}I(\mathbf{e}_{l}-\mathbf{e}_{j})=d_{lj}I(-% \mathbf{e}_{j})+b_{l}I(\boldsymbol{{0}})}}$ `b_{j}I(\mathbf{e}_{l}-\mathbf{e}_{j}) = d_{lj}I(-\mathbf{e}_{j})+b_{l}I(\boldsymbol{{0}})`	${\displaystyle{\displaystyle j=1,l=1}}$	b[j]I(e[l]- e[j]) = d[l, j]I(- e[j])+ b[l]*I(0)	Subscript[b, j]I[Subscript[e, l]- Subscript[e, j]] == Subscript[d, l, j]I[- Subscript[e, j]]+ Subscript[b, l]*I[0]	Skipped - no semantic math	Skipped - no semantic math	-	-
19.29.E16	${\displaystyle{\displaystyle b_{\beta}b_{\gamma}I(\mathbf{e}_{\alpha})=d_{% \alpha\beta}d_{\alpha\gamma}I(-\mathbf{e}_{\alpha})+2b_{\alpha}\left(\frac{s(x% )}{a_{\alpha}+b_{\alpha}x}-\frac{s(y)}{a_{\alpha}+b_{\alpha}y}\right)}}$ `b_{\beta}b_{\gamma}I(\mathbf{e}_{\alpha}) = d_{\alpha\beta}d_{\alpha\gamma}I(-\mathbf{e}_{\alpha})+2b_{\alpha}\left(\frac{s(x)}{a_{\alpha}+b_{\alpha}x}-\frac{s(y)}{a_{\alpha}+b_{\alpha}y}\right)`		b[beta]b[gamma]I(e[alpha]) = d[alphabeta]d[alphagamma]I(- e[alpha])+ 2b[alpha]((s(x))/(a[alpha]+ b[alpha]x)-(s(y))/(a[alpha]+ b[alpha]y))	Subscript[b, \[Beta]]Subscript[b, \[Gamma]]I[Subscript[e, \[Alpha]]] == Subscript[d, \[Alpha]\[Beta]]Subscript[d, \[Alpha]\[Gamma]]I[- Subscript[e, \[Alpha]]]+ 2Subscript[b, \[Alpha]](Divide[s[x],Subscript[a, \[Alpha]]+ Subscript[b, \[Alpha]]x]-Divide[s[y],Subscript[a, \[Alpha]]+ Subscript[b, \[Alpha]]y])	Skipped - no semantic math	Skipped - no semantic math	-	-
19.29.E17	${\displaystyle{\displaystyle s(t)=\prod_{\alpha=1}^{3}\sqrt{a_{\alpha}+b_{% \alpha}t}}}$ `s(t) = \prod_{\alpha=1}^{3}\sqrt{a_{\alpha}+b_{\alpha}t}`		s(t) = product(sqrt(a[alpha]+ b[alpha]*t), alpha = 1..3)	s[t] == Product[Sqrt[Subscript[a, \[Alpha]]+ Subscript[b, \[Alpha]]*t], {\[Alpha], 1, 3}, GenerateConditions->None]	Skipped - no semantic math	Skipped - no semantic math	-	-
19.29.E18	${\displaystyle{\displaystyle b_{j}^{q}I(q\mathbf{e}_{l})=\sum_{r=0}^{q}% \genfrac{(}{)}{0.0pt}{}{q}{r}b_{l}^{r}d_{lj}^{q-r}I(r\mathbf{e}_{j})}}$ `b_{j}^{q}I(q\mathbf{e}_{l}) = \sum_{r=0}^{q}\binom{q}{r}b_{l}^{r}d_{lj}^{q-r}I(r\mathbf{e}_{j})`	${\displaystyle{\displaystyle j=1,l=1}}$	(b[j])^(q)I(qe[l]) = sum(binomial(q,r)(b[l])^(r)(d[l, j])^(q - r)I(re[j]), r = 0..q)	(Subscript[b, j])^(q)I[qSubscript[e, l]] == Sum[Binomial[q,r](Subscript[b, l])^(r)(Subscript[d, l, j])^(q - r)I[rSubscript[e, j]], {r, 0, q}, GenerateConditions->None]	Failure	Failure	Error	Skipped - Because timed out
19.29.E19	${\displaystyle{\displaystyle\int_{y}^{x}\frac{\mathrm{d}t}{\sqrt{Q_{1}(t)Q_{2}% (t)}}=R_{F}\left(U^{2}+a_{1}b_{2},U^{2}+a_{2}b_{1},U^{2}\right)}}$ `\int_{y}^{x}\frac{\diff{t}}{\sqrt{Q_{1}(t)Q_{2}(t)}} = \CarlsonsymellintRF@{U^{2}+a_{1}b_{2}}{U^{2}+a_{2}b_{1}}{U^{2}}`		int((1)/(sqrt(Q[1](t)* Q[2](t))), t = y..x) = 0.5int(1/(sqrt(t+(U)^(2)+ a[1]b[2])sqrt(t+(U)^(2)+ a[2]b[1])*sqrt(t+(U)^(2))), t = 0..infinity)	Integrate[Divide[1,Sqrt[Subscript[Q, 1][t]* Subscript[Q, 2][t]]], {t, y, x}, GenerateConditions->None] == EllipticF[ArcCos[Sqrt[(U)^(2)+ Subscript[a, 1]Subscript[b, 2]/(U)^(2)]],((U)^(2)-(U)^(2)+ Subscript[a, 2]Subscript[b, 1])/((U)^(2)-(U)^(2)+ Subscript[a, 1]Subscript[b, 2])]/Sqrt[(U)^(2)-(U)^(2)+ Subscript[a, 1]Subscript[b, 2]]	Aborted	Aborted	Manual Skip!	Skipped - Because timed out
19.29.E20	${\displaystyle{\displaystyle\int_{y}^{x}\frac{t^{2}\mathrm{d}t}{\sqrt{Q_{1}(t)% Q_{2}(t)}}=\tfrac{1}{3}a_{1}a_{2}R_{D}\left(U^{2}+a_{1}b_{2},U^{2}+a_{2}b_{1},% U^{2}\right)+(xy/U)}}$ `\int_{y}^{x}\frac{t^{2}\diff{t}}{\sqrt{Q_{1}(t)Q_{2}(t)}} = \tfrac{1}{3}a_{1}a_{2}\CarlsonsymellintRD@{U^{2}+a_{1}b_{2}}{U^{2}+a_{2}b_{1}}{U^{2}}+(xy/U)`		Error	Integrate[Divide[(t)^(2),Sqrt[Subscript[Q, 1][t]* Subscript[Q, 2][t]]], {t, y, x}, GenerateConditions->None] == Divide[1,3]Subscript[a, 1]Subscript[a, 2]3(EllipticF[ArcCos[Sqrt[(U)^(2)+ Subscript[a, 1]Subscript[b, 2]/(U)^(2)]],((U)^(2)-(U)^(2)+ Subscript[a, 2]Subscript[b, 1])/((U)^(2)-(U)^(2)+ Subscript[a, 1]Subscript[b, 2])]-EllipticE[ArcCos[Sqrt[(U)^(2)+ Subscript[a, 1]Subscript[b, 2]/(U)^(2)]],((U)^(2)-(U)^(2)+ Subscript[a, 2]Subscript[b, 1])/((U)^(2)-(U)^(2)+ Subscript[a, 1]Subscript[b, 2])])/(((U)^(2)-(U)^(2)+ Subscript[a, 2]Subscript[b, 1])((U)^(2)-(U)^(2)+ Subscript[a, 1]Subscript[b, 2])^(1/2))+(xy/U)	Missing Macro Error	Aborted	-	Skipped - Because timed out
19.29.E21	${\displaystyle{\displaystyle\int_{y}^{x}\frac{\mathrm{d}t}{t^{2}\sqrt{Q_{1}(t)% Q_{2}(t)}}=\tfrac{1}{3}b_{1}b_{2}R_{D}\left(U^{2}+a_{1}b_{2},U^{2}+a_{2}b_{1},% U^{2}\right)+(xyU)^{-1}}}$ `\int_{y}^{x}\frac{\diff{t}}{t^{2}\sqrt{Q_{1}(t)Q_{2}(t)}} = \tfrac{1}{3}b_{1}b_{2}\CarlsonsymellintRD@{U^{2}+a_{1}b_{2}}{U^{2}+a_{2}b_{1}}{U^{2}}+(xyU)^{-1}`		Error	Integrate[Divide[1,(t)^(2)Sqrt[Subscript[Q, 1][t] Subscript[Q, 2][t]]], {t, y, x}, GenerateConditions->None] == Divide[1,3]Subscript[b, 1]Subscript[b, 2]3(EllipticF[ArcCos[Sqrt[(U)^(2)+ Subscript[a, 1]Subscript[b, 2]/(U)^(2)]],((U)^(2)-(U)^(2)+ Subscript[a, 2]Subscript[b, 1])/((U)^(2)-(U)^(2)+ Subscript[a, 1]Subscript[b, 2])]-EllipticE[ArcCos[Sqrt[(U)^(2)+ Subscript[a, 1]Subscript[b, 2]/(U)^(2)]],((U)^(2)-(U)^(2)+ Subscript[a, 2]Subscript[b, 1])/((U)^(2)-(U)^(2)+ Subscript[a, 1]Subscript[b, 2])])/(((U)^(2)-(U)^(2)+ Subscript[a, 2]Subscript[b, 1])((U)^(2)-(U)^(2)+ Subscript[a, 1]Subscript[b, 2])^(1/2))+(xy*U)^(- 1)	Missing Macro Error	Aborted	-	Skipped - Because timed out
19.29.E22	${\displaystyle{\displaystyle(x^{2}-y^{2})U=x\sqrt{Q_{1}(y)Q_{2}(y)}+y\sqrt{Q_{% 1}(x)Q_{2}(x)}}}$ `(x^{2}-y^{2})U = x\sqrt{Q_{1}(y)Q_{2}(y)}+y\sqrt{Q_{1}(x)Q_{2}(x)}`		((x)^(2)- (y)^(2))U = xsqrt(Q[1](y)* Q[2](y))+ ysqrt(Q[1](x) Q[2](x))	((x)^(2)- (y)^(2))U == xSqrt[Subscript[Q, 1][y]* Subscript[Q, 2][y]]+ ySqrt[Subscript[Q, 1][x] Subscript[Q, 2][x]]	Skipped - no semantic math	Skipped - no semantic math	-	-
19.29.E23	${\displaystyle{\displaystyle\int_{y}^{\infty}\frac{\mathrm{d}t}{\sqrt{(t^{2}+a% ^{2})(t^{2}-b^{2})}}=R_{F}\left(y^{2}+a^{2},y^{2}-b^{2},y^{2}\right)}}$ `\int_{y}^{\infty}\frac{\diff{t}}{\sqrt{(t^{2}+a^{2})(t^{2}-b^{2})}} = \CarlsonsymellintRF@{y^{2}+a^{2}}{y^{2}-b^{2}}{y^{2}}`		int((1)/(sqrt(((t)^(2)+ (a)^(2))((t)^(2)- (b)^(2)))), t = y..infinity) = 0.5int(1/(sqrt(t+(y)^(2)+ (a)^(2))sqrt(t+(y)^(2)- (b)^(2))sqrt(t+(y)^(2))), t = 0..infinity)	Integrate[Divide[1,Sqrt[((t)^(2)+ (a)^(2))*((t)^(2)- (b)^(2))]], {t, y, Infinity}, GenerateConditions->None] == EllipticF[ArcCos[Sqrt[(y)^(2)+ (a)^(2)/(y)^(2)]],((y)^(2)-(y)^(2)- (b)^(2))/((y)^(2)-(y)^(2)+ (a)^(2))]/Sqrt[(y)^(2)-(y)^(2)+ (a)^(2)]	Aborted	Aborted	Skipped - Because timed out	Skipped - Because timed out
19.29.E24	${\displaystyle{\displaystyle\int_{y}^{x}\frac{\mathrm{d}t}{\sqrt{Q_{1}(t)Q_{2}% (t)}}=4R_{F}\left(U,U+D_{12}+V,U+D_{12}-V\right)}}$ `\int_{y}^{x}\frac{\diff{t}}{\sqrt{Q_{1}(t)Q_{2}(t)}} = 4\CarlsonsymellintRF@{U}{U+D_{12}+V}{U+D_{12}-V}`		int((1)/(sqrt(Q[1](t)* Q[2](t))), t = y..x) = 40.5int(1/(sqrt(t+U)sqrt(t+U + D[12]+ V)sqrt(t+U + D[12]- V)), t = 0..infinity)	Integrate[Divide[1,Sqrt[Subscript[Q, 1][t]* Subscript[Q, 2][t]]], {t, y, x}, GenerateConditions->None] == 4*EllipticF[ArcCos[Sqrt[U/U + Subscript[D, 12]- V]],(U + Subscript[D, 12]- V-U + Subscript[D, 12]+ V)/(U + Subscript[D, 12]- V-U)]/Sqrt[U + Subscript[D, 12]- V-U]	Aborted	Aborted	Skipped - Because timed out	Skipped - Because timed out
19.29#Ex17	${\displaystyle{\displaystyle(x-y)^{2}U=S_{1}S_{2}}}$ `(x-y)^{2}U = S_{1}S_{2}`		(x - y)^(2)* U = S[1]*S[2]	(x - y)^(2)* U == Subscript[S, 1]*Subscript[S, 2]	Skipped - no semantic math	Skipped - no semantic math	-	-
19.29#Ex18	${\displaystyle{\displaystyle S_{j}=\left(\sqrt{Q_{j}(x)}+\sqrt{Q_{j}(y)}\right% )^{2}-h_{j}(x-y)^{2}}}$ `S_{j} = \left(\sqrt{Q_{j}(x)}+\sqrt{Q_{j}(y)}\right)^{2}-h_{j}(x-y)^{2}`		S[j] = (sqrt(Q[j](x))+sqrt(Q[j](y)))^(2)- h[j]*(x - y)^(2)	Subscript[S, j] == (Sqrt[Subscript[Q, j][x]]+Sqrt[Subscript[Q, j][y]])^(2)- Subscript[h, j]*(x - y)^(2)	Skipped - no semantic math	Skipped - no semantic math	-	-
19.29#Ex19	${\displaystyle{\displaystyle D_{jl}=2f_{j}h_{l}+2h_{j}f_{l}-g_{j}g_{l}}}$ `D_{jl} = 2f_{j}h_{l}+2h_{j}f_{l}-g_{j}g_{l}`		D[j, l] = 2f[j]h[l]+ 2h[j]f[l]- g[j]*g[l]	Subscript[D, j, l] == 2Subscript[f, j]Subscript[h, l]+ 2Subscript[h, j]Subscript[f, l]- Subscript[g, j]*Subscript[g, l]	Skipped - no semantic math	Skipped - no semantic math	-	-
19.29#Ex20	${\displaystyle{\displaystyle V=\sqrt{D_{12}^{2}-D_{11}D_{22}}}}$ `V = \sqrt{D_{12}^{2}-D_{11}D_{22}}`		V = sqrt((D[12])^(2)- D[11]*D[22])	V == Sqrt[(Subscript[D, 12])^(2)- Subscript[D, 11]*Subscript[D, 22]]	Skipped - no semantic math	Skipped - no semantic math	-	-
19.29#Ex21	${\displaystyle{\displaystyle S_{1}=(X_{1}Y_{2}+Y_{1}X_{2})^{2}}}$ `S_{1} = (X_{1}Y_{2}+Y_{1}X_{2})^{2}`		S[1] = (X[1]Y[2]+ Y[1]X[2])^(2)	Subscript[S, 1] == (Subscript[X, 1]Subscript[Y, 2]+ Subscript[Y, 1]Subscript[X, 2])^(2)	Skipped - no semantic math	Skipped - no semantic math	-	-
19.29#Ex22	${\displaystyle{\displaystyle X_{j}=\sqrt{a_{j}+b_{j}x}}}$ `X_{j} = \sqrt{a_{j}+b_{j}x}`		X[j] = sqrt(a[j]+ b[j]*x)	Subscript[X, j] == Sqrt[Subscript[a, j]+ Subscript[b, j]*x]	Skipped - no semantic math	Skipped - no semantic math	-	-
19.29#Ex23	${\displaystyle{\displaystyle Y_{j}=\sqrt{a_{j}+b_{j}y}}}$ `Y_{j} = \sqrt{a_{j}+b_{j}y}`		Y[j] = sqrt(a[j]+ b[j]*y)	Subscript[Y, j] == Sqrt[Subscript[a, j]+ Subscript[b, j]*y]	Skipped - no semantic math	Skipped - no semantic math	-	-
19.29#Ex24	${\displaystyle{\displaystyle D_{12}=2a_{1}a_{2}h_{2}+2b_{1}b_{2}f_{2}-(a_{1}b_% {2}+a_{2}b_{1})g_{2}}}$ `D_{12} = 2a_{1}a_{2}h_{2}+2b_{1}b_{2}f_{2}-(a_{1}b_{2}+a_{2}b_{1})g_{2}`		D[12] = 2a[1]a[2]h[2]+ 2b[1]b[2]f[2]-(a[1]b[2]+ a[2]b[1])*g[2]	Subscript[D, 12] == 2Subscript[a, 1]Subscript[a, 2]Subscript[h, 2]+ 2Subscript[b, 1]Subscript[b, 2]Subscript[f, 2]-(Subscript[a, 1]Subscript[b, 2]+ Subscript[a, 2]Subscript[b, 1])*Subscript[g, 2]	Skipped - no semantic math	Skipped - no semantic math	-	-
19.29#Ex25	${\displaystyle{\displaystyle D_{11}=-(a_{1}b_{2}-a_{2}b_{1})^{2}}}$ `D_{11} = -(a_{1}b_{2}-a_{2}b_{1})^{2}`		D[11] = -(a[1]b[2]- a[2]b[1])^(2)	Subscript[D, 11] == -(Subscript[a, 1]Subscript[b, 2]- Subscript[a, 2]Subscript[b, 1])^(2)	Skipped - no semantic math	Skipped - no semantic math	-	-
19.29#Ex26	${\displaystyle{\displaystyle S_{1}=(X_{1}+Y_{1})^{2}}}$ `S_{1} = (X_{1}+Y_{1})^{2}`		S[1] = (X[1]+ Y[1])^(2)	Subscript[S, 1] == (Subscript[X, 1]+ Subscript[Y, 1])^(2)	Skipped - no semantic math	Skipped - no semantic math	-	-
19.29#Ex27	${\displaystyle{\displaystyle D_{12}=2a_{1}h_{2}-b_{1}g_{2}}}$ `D_{12} = 2a_{1}h_{2}-b_{1}g_{2}`		D[12] = 2a[1]h[2]- b[1]*g[2]	Subscript[D, 12] == 2Subscript[a, 1]Subscript[h, 2]- Subscript[b, 1]*Subscript[g, 2]	Skipped - no semantic math	Skipped - no semantic math	-	-
19.29#Ex28	${\displaystyle{\displaystyle D_{11}=-b_{1}^{2}}}$ `D_{11} = -b_{1}^{2}`		D[11] = - (b[1])^(2)	Subscript[D, 11] == - (Subscript[b, 1])^(2)	Skipped - no semantic math	Skipped - no semantic math	-	-
19.29.E28	${\displaystyle{\displaystyle\int_{y}^{x}\frac{\mathrm{d}t}{\sqrt{t^{3}-a^{3}}}% =4R_{F}\left(U,U-3a+2\sqrt{3}a,U-3a-2\sqrt{3}a\right)}}$ `\int_{y}^{x}\frac{\diff{t}}{\sqrt{t^{3}-a^{3}}} = 4\CarlsonsymellintRF@{U}{U-3a+2\sqrt{3}a}{U-3a-2\sqrt{3}a}`		int((1)/(sqrt((t)^(3)- (a)^(3))), t = y..x) = 40.5int(1/(sqrt(t+U)sqrt(t+U - 3a + 2sqrt(3)a)sqrt(t+U - 3a - 2sqrt(3)a)), t = 0..infinity)	Integrate[Divide[1,Sqrt[(t)^(3)- (a)^(3)]], {t, y, x}, GenerateConditions->None] == 4EllipticF[ArcCos[Sqrt[U/U - 3a - 2Sqrt[3]a]],(U - 3a - 2Sqrt[3]a-U - 3a + 2Sqrt[3]a)/(U - 3a - 2Sqrt[3]a-U)]/Sqrt[U - 3a - 2Sqrt[3]a-U]	Aborted	Aborted	Skipped - Because timed out	Skipped - Because timed out
19.29#Ex29	${\displaystyle{\displaystyle(x-y)^{2}U=(\sqrt{x-a}+\sqrt{y-a})^{2}\left((\xi+% \eta)^{2}-(x-y)^{2}\right)}}$ `(x-y)^{2}U = (\sqrt{x-a}+\sqrt{y-a})^{2}\left((\xi+\eta)^{2}-(x-y)^{2}\right)`		(x - y)^(2)* U = (sqrt(x - a)+sqrt(y - a))^(2)*((xi + eta)^(2)-(x - y)^(2))	(x - y)^(2)* U == (Sqrt[x - a]+Sqrt[y - a])^(2)*((\[Xi]+ \[Eta])^(2)-(x - y)^(2))	Skipped - no semantic math	Skipped - no semantic math	-	-
19.29#Ex30	${\displaystyle{\displaystyle\xi=\sqrt{x^{2}+ax+a^{2}}}}$ `\xi = \sqrt{x^{2}+ax+a^{2}}`		xi = sqrt((x)^(2)+ a*x + (a)^(2))	\[Xi] == Sqrt[(x)^(2)+ a*x + (a)^(2)]	Skipped - no semantic math	Skipped - no semantic math	-	-
19.29#Ex31	${\displaystyle{\displaystyle\eta=\sqrt{y^{2}+ay+a^{2}}}}$ `\eta = \sqrt{y^{2}+ay+a^{2}}`		eta = sqrt((y)^(2)+ a*y + (a)^(2))	\[Eta] == Sqrt[(y)^(2)+ a*y + (a)^(2)]	Skipped - no semantic math	Skipped - no semantic math	-	-
19.29.E30	${\displaystyle{\displaystyle\int_{y}^{x}\frac{\mathrm{d}t}{\sqrt{Q(t^{2})}}=2R% _{F}\left(U,U-g+2\sqrt{fh},U-g-2\sqrt{fh}\right)}}$ `\int_{y}^{x}\frac{\diff{t}}{\sqrt{Q(t^{2})}} = 2\CarlsonsymellintRF@{U}{U-g+2\sqrt{fh}}{U-g-2\sqrt{fh}}`		int((1)/(sqrt(Q((t)^(2)))), t = y..x) = 20.5int(1/(sqrt(t+U)sqrt(t+U - g + 2sqrt(fh))sqrt(t+U - g - 2sqrt(fh))), t = 0..infinity)	Integrate[Divide[1,Sqrt[Q[(t)^(2)]]], {t, y, x}, GenerateConditions->None] == 2EllipticF[ArcCos[Sqrt[U/U - g - 2Sqrt[fh]]],(U - g - 2Sqrt[fh]-U - g + 2Sqrt[fh])/(U - g - 2Sqrt[fh]-U)]/Sqrt[U - g - 2Sqrt[f*h]-U]	Aborted	Aborted	Skipped - Because timed out	Skipped - Because timed out
19.29.E31	${\displaystyle{\displaystyle(x-y)^{2}U=\left(\sqrt{Q(x^{2})}+\sqrt{Q(y^{2})}% \right)^{2}-h(x^{2}-y^{2})^{2}}}$ `(x-y)^{2}U = \left(\sqrt{Q(x^{2})}+\sqrt{Q(y^{2})}\right)^{2}-h(x^{2}-y^{2})^{2}`		(x - y)^(2)* U = (sqrt(Q((x)^(2)))+sqrt(Q((y)^(2))))^(2)- h*((x)^(2)- (y)^(2))^(2)	(x - y)^(2)* U == (Sqrt[Q[(x)^(2)]]+Sqrt[Q[(y)^(2)]])^(2)- h*((x)^(2)- (y)^(2))^(2)	Skipped - no semantic math	Skipped - no semantic math	-	-
19.29.E32	${\displaystyle{\displaystyle\int_{y}^{x}\frac{\mathrm{d}t}{\sqrt{t^{4}+a^{4}}}% =2R_{F}\left(U,U+2a^{2},U-2a^{2}\right)}}$ `\int_{y}^{x}\frac{\diff{t}}{\sqrt{t^{4}+a^{4}}} = 2\CarlsonsymellintRF@{U}{U+2a^{2}}{U-2a^{2}}`		int((1)/(sqrt((t)^(4)+ (a)^(4))), t = y..x) = 20.5int(1/(sqrt(t+U)sqrt(t+U + 2(a)^(2))sqrt(t+U - 2(a)^(2))), t = 0..infinity)	Integrate[Divide[1,Sqrt[(t)^(4)+ (a)^(4)]], {t, y, x}, GenerateConditions->None] == 2EllipticF[ArcCos[Sqrt[U/U - 2(a)^(2)]],(U - 2(a)^(2)-U + 2(a)^(2))/(U - 2(a)^(2)-U)]/Sqrt[U - 2(a)^(2)-U]	Aborted	Failure	Skipped - Because timed out	Failed [300 / 300] Result: Complex[0.06910876495694751, 1.480960979386122] Test Values: {Rule[a, -1.5], Rule[U, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[x, 1.5], Rule[y, -1.5]} Result: Complex[1.3051585498245286, 1.480960979386122] Test Values: {Rule[a, -1.5], Rule[U, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[x, 1.5], Rule[y, 1.5]} ... skip entries to safe data
19.29.E33	${\displaystyle{\displaystyle(x-y)^{2}U=\left(\sqrt{x^{4}+a^{4}}+\sqrt{y^{4}+a^% {4}}\right)^{2}-(x^{2}-y^{2})^{2}}}$ `(x-y)^{2}U = \left(\sqrt{x^{4}+a^{4}}+\sqrt{y^{4}+a^{4}}\right)^{2}-(x^{2}-y^{2})^{2}`		(x - y)^(2)* U = (sqrt((x)^(4)+ (a)^(4))+sqrt((y)^(4)+ (a)^(4)))^(2)-((x)^(2)- (y)^(2))^(2)	(x - y)^(2)* U == (Sqrt[(x)^(4)+ (a)^(4)]+Sqrt[(y)^(4)+ (a)^(4)])^(2)-((x)^(2)- (y)^(2))^(2)	Skipped - no semantic math	Skipped - no semantic math	-	-
19.30#Ex1	${\displaystyle{\displaystyle x=a\sin\phi}}$ `x = a\sin@@{\phi}`		x = a*sin(phi)	x == a*Sin[\[Phi]]	Failure	Failure	Failed [180 / 180] Result: 2.788470502+.5063946946I Test Values: {a = -3/2, phi = 1/23^(1/2)+1/2I, x = 3/2} Result: 1.788470502+.5063946946I Test Values: {a = -3/2, phi = 1/23^(1/2)+1/2I, x = 1/2} ... skip entries to safe data	Failed [180 / 180] Result: Complex[2.1491827752870476, 0.34394646701016035] Test Values: {Rule[a, -1.5], Rule[x, 1.5], Rule[ϕ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]} Result: Complex[1.093555858156998, 0.6491787480429551] Test Values: {Rule[a, -1.5], Rule[x, 1.5], Rule[ϕ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]]} ... skip entries to safe data
19.30#Ex2	${\displaystyle{\displaystyle y=b\cos\phi}}$ `y = b\cos@@{\phi}`	${\displaystyle{\displaystyle 0\leq\phi,\phi\leq 2\pi}}$	y = b*cos(phi)	y == b*Cos[\[Phi]]	Failure	Failure	Failed [108 / 108] Result: -1.393894198 Test Values: {b = -3/2, phi = 3/2, y = -3/2} Result: 1.606105802 Test Values: {b = -3/2, phi = 3/2, y = 3/2} ... skip entries to safe data	Failed [108 / 108] Result: -1.3938941974984456 Test Values: {Rule[b, -1.5], Rule[y, -1.5], Rule[ϕ, 1.5]} Result: -0.18362615716444086 Test Values: {Rule[b, -1.5], Rule[y, -1.5], Rule[ϕ, 0.5]} ... skip entries to safe data
19.30.E2	${\displaystyle{\displaystyle s=a\int_{0}^{\phi}\sqrt{1-k^{2}{\sin^{2}}\theta}% \mathrm{d}\theta}}$ `s = a\int_{0}^{\phi}\sqrt{1-k^{2}\sin^{2}@@{\theta}}\diff{\theta}`		s = aint(sqrt(1 - (k)^(2) (sin(theta))^(2)), theta = 0..phi)	s == aIntegrate[Sqrt[1 - (k)^(2) (Sin[\[Theta]])^(2)], {\[Theta], 0, \[Phi]}, GenerateConditions->None]	Aborted	Aborted	Skipped - Because timed out	Skipped - Because timed out
19.30.E3	${\displaystyle{\displaystyle s/a=E\left(\phi,k\right)}}$ `s/a = \incellintEk@{\phi}{k}`		s/a = EllipticE(sin(phi), k)	s/a == EllipticE[\[Phi], (k)^2]	Failure	Failure	Failed [300 / 300] Result: .1410196655-.3375964631I Test Values: {a = -3/2, phi = 1/23^(1/2)+1/2I, s = -3/2, k = 1} Result: -.36391978e-1+.5433649104e-1I Test Values: {a = -3/2, phi = 1/23^(1/2)+1/2I, s = -3/2, k = 2} ... skip entries to safe data	Failed [300 / 300] Result: Complex[0.5672114831419685, -0.22929764467344024] Test Values: {Rule[a, -1.5], Rule[k, 1], Rule[s, -1.5], Rule[ϕ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]} Result: Complex[0.5579190406370536, -0.16535187593702125] Test Values: {Rule[a, -1.5], Rule[k, 2], Rule[s, -1.5], Rule[ϕ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]} ... skip entries to safe data
19.30.E3	${\displaystyle{\displaystyle E\left(\phi,k\right)={R_{F}\left(c-1,c-k^{2},c% \right)-\tfrac{1}{3}k^{2}R_{D}\left(c-1,c-k^{2},c\right)}}}$ `\incellintEk@{\phi}{k} = {\CarlsonsymellintRF@{c-1}{c-k^{2}}{c}-\tfrac{1}{3}k^{2}\CarlsonsymellintRD@{c-1}{c-k^{2}}{c}}`		Error	EllipticE[\[Phi], (k)^2] == EllipticF[ArcCos[Sqrt[c - 1/c]],(c-c - (k)^(2))/(c-c - 1)]/Sqrt[c-c - 1]-Divide[1,3](k)^(2) 3(EllipticF[ArcCos[Sqrt[c - 1/c]],(c-c - (k)^(2))/(c-c - 1)]-EllipticE[ArcCos[Sqrt[c - 1/c]],(c-c - (k)^(2))/(c-c - 1)])/((c-c - (k)^(2))(c-c - 1)^(1/2))	Missing Macro Error	Failure	Skip - symbolical successful subtest	Failed [180 / 180] Result: Complex[3.5743811704478246, 0.7698502565730785] Test Values: {Rule[c, -1.5], Rule[k, 1], Rule[ϕ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]} Result: Complex[3.9424508382496875, -1.017653751864599] Test Values: {Rule[c, -1.5], Rule[k, 2], Rule[ϕ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]} ... skip entries to safe data
19.30#Ex3	${\displaystyle{\displaystyle k^{2}=1-(b^{2}/a^{2})}}$ `k^{2} = 1-(b^{2}/a^{2})`		(k)^(2) = 1 -((b)^(2)/(a)^(2))	(k)^(2) == 1 -((b)^(2)/(a)^(2))	Skipped - no semantic math	Skipped - no semantic math	-	-
19.30#Ex4	${\displaystyle{\displaystyle c={\csc^{2}}\phi}}$ `c = \csc^{2}@@{\phi}`		c = (csc(phi))^(2)	c == (Csc[\[Phi]])^(2)	Failure	Failure	Failed [60 / 60] Result: -2.359812877+.7993130071I Test Values: {c = -3/2, phi = 1/23^(1/2)+1/2I} Result: -1.296085040-.8173084059I Test Values: {c = -3/2, phi = -1/2+1/2I3^(1/2)} ... skip entries to safe data	Failed [60 / 60] Result: Complex[-3.841312467237177, 3.4490957612740374] Test Values: {Rule[c, -1.5], Rule[ϕ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]} Result: Complex[0.17530792640393877, -3.4502399957777015] Test Values: {Rule[c, -1.5], Rule[ϕ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]]} ... skip entries to safe data
19.30.E5	${\displaystyle{\displaystyle L(a,b)=4aE\left(k\right)}}$ `L(a,b) = 4a\compellintEk@{k}`		L(a , b) = 4aEllipticE(k)	L[a , b] == 4aEllipticE[(k)^2]	Failure	Failure	Failed [300 / 300] Result: (.8660254040+.5000000000I)(-1.500000000, -1.500000000)+6.000000000 Test Values: {L = 1/23^(1/2)+1/2I, a = -3/2, b = -3/2, k = 1} Result: (.8660254040+.5000000000I)(-1.500000000, -1.500000000)+2.437793319+8.063125386I Test Values: {L = 1/23^(1/2)+1/2*I, a = -3/2, b = -3/2, k = 2} ... skip entries to safe data	Error
19.30.E5	${\displaystyle{\displaystyle 4aE\left(k\right)=8aR_{G}\left(0,b^{2}/a^{2},1% \right)}}$ `4a\compellintEk@{k} = 8a\CarlsonsymellintRG@{0}{b^{2}/a^{2}}{1}`		Error	4aEllipticE[(k)^2] == 8aSqrt[1-0](EllipticE[ArcCos[Sqrt[0/1]],(1-(b)^(2)/(a)^(2))/(1-0)]+(Cot[ArcCos[Sqrt[0/1]]])^2EllipticF[ArcCos[Sqrt[0/1]],(1-(b)^(2)/(a)^(2))/(1-0)]+Cot[ArcCos[Sqrt[0/1]]]Sqrt[1-k^2Sin[ArcCos[Sqrt[0/1]]]^2])	Missing Macro Error	Failure	Skip - symbolical successful subtest	Failed [108 / 108] Result: 12.849555921538759 Test Values: {Rule[a, -1.5], Rule[b, -1.5], Rule[k, 1]} Result: Complex[16.411762602778996, -8.063125388322588] Test Values: {Rule[a, -1.5], Rule[b, -1.5], Rule[k, 2]} ... skip entries to safe data
19.30.E5	${\displaystyle{\displaystyle 8aR_{G}\left(0,b^{2}/a^{2},1\right)=8R_{G}\left(0% ,a^{2},b^{2}\right)}}$ `8a\CarlsonsymellintRG@{0}{b^{2}/a^{2}}{1} = 8\CarlsonsymellintRG@{0}{a^{2}}{b^{2}}`		Error	8aSqrt[1-0](EllipticE[ArcCos[Sqrt[0/1]],(1-(b)^(2)/(a)^(2))/(1-0)]+(Cot[ArcCos[Sqrt[0/1]]])^2EllipticF[ArcCos[Sqrt[0/1]],(1-(b)^(2)/(a)^(2))/(1-0)]+Cot[ArcCos[Sqrt[0/1]]]Sqrt[1-k^2Sin[ArcCos[Sqrt[0/1]]]^2]) == 8Sqrt[(b)^(2)-0](EllipticE[ArcCos[Sqrt[0/(b)^(2)]],((b)^(2)-(a)^(2))/((b)^(2)-0)]+(Cot[ArcCos[Sqrt[0/(b)^(2)]]])^2EllipticF[ArcCos[Sqrt[0/(b)^(2)]],((b)^(2)-(a)^(2))/((b)^(2)-0)]+Cot[ArcCos[Sqrt[0/(b)^(2)]]]Sqrt[1-k^2*Sin[ArcCos[Sqrt[0/(b)^(2)]]]^2])	Missing Macro Error	Failure	Skip - symbolical successful subtest	Failed [18 / 36] Result: -37.69911184307752 Test Values: {Rule[a, -1.5], Rule[b, -1.5]} Result: -37.69911184307752 Test Values: {Rule[a, -1.5], Rule[b, 1.5]} ... skip entries to safe data
19.30.E5	${\displaystyle{\displaystyle 8R_{G}\left(0,a^{2},b^{2}\right)=8abR_{G}\left(0,% a^{-2},b^{-2}\right)}}$ `8\CarlsonsymellintRG@{0}{a^{2}}{b^{2}} = 8ab\CarlsonsymellintRG@{0}{a^{-2}}{b^{-2}}`		Error	8Sqrt[(b)^(2)-0](EllipticE[ArcCos[Sqrt[0/(b)^(2)]],((b)^(2)-(a)^(2))/((b)^(2)-0)]+(Cot[ArcCos[Sqrt[0/(b)^(2)]]])^2EllipticF[ArcCos[Sqrt[0/(b)^(2)]],((b)^(2)-(a)^(2))/((b)^(2)-0)]+Cot[ArcCos[Sqrt[0/(b)^(2)]]]Sqrt[1-k^2Sin[ArcCos[Sqrt[0/(b)^(2)]]]^2]) == 8abSqrt[(b)^(- 2)-0](EllipticE[ArcCos[Sqrt[0/(b)^(- 2)]],((b)^(- 2)-(a)^(- 2))/((b)^(- 2)-0)]+(Cot[ArcCos[Sqrt[0/(b)^(- 2)]]])^2EllipticF[ArcCos[Sqrt[0/(b)^(- 2)]],((b)^(- 2)-(a)^(- 2))/((b)^(- 2)-0)]+Cot[ArcCos[Sqrt[0/(b)^(- 2)]]]Sqrt[1-k^2Sin[ArcCos[Sqrt[0/(b)^(- 2)]]]^2])	Missing Macro Error	Failure	Skip - symbolical successful subtest	Failed [18 / 36] Result: 37.69911184307752 Test Values: {Rule[a, -1.5], Rule[b, 1.5]} Result: 26.729786441110512 Test Values: {Rule[a, -1.5], Rule[b, 0.5]} ... skip entries to safe data
19.30.E6	${\displaystyle{\displaystyle\frac{\partial s}{\partial(1/k)}=\sqrt{a^{2}-b^{2}% }F\left(\phi,k\right)}}$ `\pderiv{s}{(1/k)} = \sqrt{a^{2}-b^{2}}\incellintFk@{\phi}{k}`	${\displaystyle{\displaystyle k^{2}=(a^{2}-b^{2})/(a^{2}+\lambda),c={\csc^{2}}% \phi}}$	subs( temp=(1/k), diff( s, temp$(1) ) ) = sqrt((a)^(2)- (b)^(2))*EllipticF(sin(phi), k)	(D[s, {temp, 1}]/.temp-> (1/k)) == Sqrt[(a)^(2)- (b)^(2)]*EllipticF[\[Phi], (k)^2]	Failure	Failure	Successful [Tested: 300]	Failed [20 / 300] Result: Indeterminate Test Values: {Rule[a, -1.5], Rule[b, -1.5], Rule[k, 1], Rule[s, -1.5], Rule[ϕ, -2]} Result: Indeterminate Test Values: {Rule[a, -1.5], Rule[b, -1.5], Rule[k, 1], Rule[s, -1.5], Rule[ϕ, 2]} ... skip entries to safe data
19.30.E6	${\displaystyle{\displaystyle\sqrt{a^{2}-b^{2}}F\left(\phi,k\right)=\sqrt{a^{2}% -b^{2}}R_{F}\left(c-1,c-k^{2},c\right)}}$ `\sqrt{a^{2}-b^{2}}\incellintFk@{\phi}{k} = \sqrt{a^{2}-b^{2}}\CarlsonsymellintRF@{c-1}{c-k^{2}}{c}`	${\displaystyle{\displaystyle k^{2}=(a^{2}-b^{2})/(a^{2}+\lambda),c={\csc^{2}}% \phi}}$	sqrt((a)^(2)- (b)^(2))EllipticF(sin(phi), k) = sqrt((a)^(2)- (b)^(2))0.5int(1/(sqrt(t+c - 1)sqrt(t+c - (k)^(2))*sqrt(t+c)), t = 0..infinity)	Sqrt[(a)^(2)- (b)^(2)]EllipticF[\[Phi], (k)^2] == Sqrt[(a)^(2)- (b)^(2)]EllipticF[ArcCos[Sqrt[c - 1/c]],(c-c - (k)^(2))/(c-c - 1)]/Sqrt[c-c - 1]	Error	Failure	Skip - symbolical successful subtest	Skip - No test values generated
19.30#Ex5	${\displaystyle{\displaystyle x=a\sqrt{t+1}}}$ `x = a\sqrt{t+1}`		x = a*sqrt(t + 1)	x == a*Sqrt[t + 1]	Skipped - no semantic math	Skipped - no semantic math	-	-
19.30#Ex6	${\displaystyle{\displaystyle y=b\sqrt{t}}}$ `y = b\sqrt{t}`		y = b*sqrt(t)	y == b*Sqrt[t]	Skipped - no semantic math	Skipped - no semantic math	-	-
19.30.E8	${\displaystyle{\displaystyle s=\frac{1}{2}\int_{0}^{y^{2}/b^{2}}\sqrt{\frac{(a% ^{2}+b^{2})t+b^{2}}{t(t+1)}}\mathrm{d}t}}$ `s = \frac{1}{2}\int_{0}^{y^{2}/b^{2}}\sqrt{\frac{(a^{2}+b^{2})t+b^{2}}{t(t+1)}}\diff{t}`		s = (1)/(2)int(sqrt((((a)^(2)+ (b)^(2))t + (b)^(2))/(t*(t + 1))), t = 0..(y)^(2)/(b)^(2))	s == Divide[1,2]Integrate[Sqrt[Divide[((a)^(2)+ (b)^(2))t + (b)^(2),t*(t + 1)]], {t, 0, (y)^(2)/(b)^(2)}, GenerateConditions->None]	Failure	Aborted	Failed [300 / 300] Result: -3.149531120 Test Values: {a = -3/2, b = -3/2, s = -3/2, y = -3/2} Result: -3.149531120 Test Values: {a = -3/2, b = -3/2, s = -3/2, y = 3/2} ... skip entries to safe data	Skipped - Because timed out
19.30.E9	${\displaystyle{\displaystyle s=\tfrac{1}{2}I(\mathbf{e}_{1})}}$ `s = \tfrac{1}{2}I(\mathbf{e}_{1})`	${\displaystyle{\displaystyle r=b^{4}/y^{2}}}$	s = (1)/(2)*I(e[1])	s == Divide[1,2]*I[Subscript[e, 1]]	Failure	Failure	Failed [298 / 300] Result: -1.750000000-.4330127020I Test Values: {I = 1/23^(1/2)+1/2I, s = -3/2, e[1] = 1/23^(1/2)+1/2I} Result: -1.066987298-.2500000002I Test Values: {I = 1/23^(1/2)+1/2I, s = -3/2, e[1] = -1/2+1/2I3^(1/2)} ... skip entries to safe data	Failed [180 / 180] Result: Complex[-1.375, -0.21650635094610968] Test Values: {Rule[Complex[0, 1], 1], Rule[s, -1.5], Rule[Subscript[e, 1], Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]} Result: Complex[-1.375, -0.21650635094610968] Test Values: {Rule[Complex[0, 1], 2], Rule[s, -1.5], Rule[Subscript[e, 1], Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]} ... skip entries to safe data
19.30.E9	${\displaystyle{\displaystyle\tfrac{1}{2}I(\mathbf{e}_{1})=-\tfrac{1}{3}a^{2}b^% {2}R_{D}\left(r,r+b^{2}+a^{2},r+b^{2}\right)+y\sqrt{\frac{r+b^{2}+a^{2}}{r+b^{% 2}}}}}$ `\tfrac{1}{2}I(\mathbf{e}_{1}) = -\tfrac{1}{3}a^{2}b^{2}\CarlsonsymellintRD@{r}{r+b^{2}+a^{2}}{r+b^{2}}+y\sqrt{\frac{r+b^{2}+a^{2}}{r+b^{2}}}`	${\displaystyle{\displaystyle r=b^{4}/y^{2}}}$	Error	Divide[1,2]I[Subscript[e, 1]] == -Divide[1,3](a)^(2)* (b)^(2)* 3(EllipticF[ArcCos[Sqrt[r/r + (b)^(2)]],(r + (b)^(2)-r + (b)^(2)+ (a)^(2))/(r + (b)^(2)-r)]-EllipticE[ArcCos[Sqrt[r/r + (b)^(2)]],(r + (b)^(2)-r + (b)^(2)+ (a)^(2))/(r + (b)^(2)-r)])/((r + (b)^(2)-r + (b)^(2)+ (a)^(2))(r + (b)^(2)-r)^(1/2))+ y*Sqrt[Divide[r + (b)^(2)+ (a)^(2),r + (b)^(2)]]	Missing Macro Error	Failure	Skip - symbolical successful subtest	Skip - No test values generated
19.30.E10	${\displaystyle{\displaystyle r^{2}=2a^{2}\cos\left(2\theta\right)}}$ `r^{2} = 2a^{2}\cos@{2\theta}`	${\displaystyle{\displaystyle 0\leq\theta,\theta\leq 2\pi}}$	(r)^(2) = 2(a)^(2) cos(2*theta)	(r)^(2) == 2(a)^(2) Cos[2*\[Theta]]	Failure	Failure	Failed [108 / 108] Result: 6.704966234 Test Values: {a = -3/2, r = -3/2, theta = 3/2} Result: -.181360376 Test Values: {a = -3/2, r = -3/2, theta = 1/2} ... skip entries to safe data	Failed [108 / 108] Result: 6.704966234702004 Test Values: {Rule[a, -1.5], Rule[r, -1.5], Rule[θ, 1.5]} Result: -0.18136037640662916 Test Values: {Rule[a, -1.5], Rule[r, -1.5], Rule[θ, 0.5]} ... skip entries to safe data
19.30.E11	${\displaystyle{\displaystyle s=2a^{2}\int_{0}^{r}\frac{\mathrm{d}t}{\sqrt{4a^{% 4}-t^{4}}}}}$ `s = 2a^{2}\int_{0}^{r}\frac{\diff{t}}{\sqrt{4a^{4}-t^{4}}}`	${\displaystyle{\displaystyle q=2a^{2}/r^{2},2a^{2}/r^{2}=\sec\left(2\theta% \right)}}$	s = 2(a)^(2) int((1)/(sqrt(4*(a)^(4)- (t)^(4))), t = 0..r)	s == 2(a)^(2) Integrate[Divide[1,Sqrt[4*(a)^(4)- (t)^(4)]], {t, 0, r}, GenerateConditions->None]	Error	Failure	-	Failed [208 / 216] Result: 0.042085201578189846 Test Values: {Rule[a, -1.5], Rule[r, -1.5], Rule[s, -1.5]} Result: 3.04208520157819 Test Values: {Rule[a, -1.5], Rule[r, -1.5], Rule[s, 1.5]} ... skip entries to safe data
19.30.E11	${\displaystyle{\displaystyle 2a^{2}\int_{0}^{r}\frac{\mathrm{d}t}{\sqrt{4a^{4}% -t^{4}}}=\sqrt{2a^{2}}R_{F}\left(q-1,q,q+1\right)}}$ `2a^{2}\int_{0}^{r}\frac{\diff{t}}{\sqrt{4a^{4}-t^{4}}} = \sqrt{2a^{2}}\CarlsonsymellintRF@{q-1}{q}{q+1}`	${\displaystyle{\displaystyle q=2a^{2}/r^{2},2a^{2}/r^{2}=\sec\left(2\theta% \right)}}$	2(a)^(2) int((1)/(sqrt(4(a)^(4)- (t)^(4))), t = 0..r) = sqrt(2(a)^(2))0.5int(1/(sqrt(t+q - 1)sqrt(t+q)sqrt(t+q + 1)), t = 0..infinity)	2(a)^(2) Integrate[Divide[1,Sqrt[4(a)^(4)- (t)^(4)]], {t, 0, r}, GenerateConditions->None] == Sqrt[2(a)^(2)]*EllipticF[ArcCos[Sqrt[q - 1/q + 1]],(q + 1-q)/(q + 1-q - 1)]/Sqrt[q + 1-q - 1]	Error	Failure	-	Failed [12 / 12] Result: Indeterminate Test Values: {Rule[a, -1.5], Rule[q, 2], Rule[r, -1.5]} Result: Indeterminate Test Values: {Rule[a, -1.5], Rule[q, 2], Rule[r, 1.5]} ... skip entries to safe data
19.30.E12	${\displaystyle{\displaystyle s=aF\left(\phi,1/\sqrt{2}\right)}}$ `s = a\incellintFk@{\phi}{1/\sqrt{2}}`	${\displaystyle{\displaystyle\phi=\operatorname{arcsin}\sqrt{2/(q+1)},% \operatorname{arcsin}\sqrt{2/(q+1)}=\operatorname{arccos}\left(\tan\theta% \right)}}$	s = a*EllipticF(sin(phi), 1/(sqrt(2)))	s == a*EllipticF[\[Phi], (1/(Sqrt[2]))^2]	Failure	Failure	Failed [300 / 300] Result: -.201379324+.8785912788I Test Values: {a = -3/2, phi = 1/23^(1/2)+1/2I, s = -3/2} Result: 2.798620676+.8785912788I Test Values: {a = -3/2, phi = 1/23^(1/2)+1/2I, s = 3/2} ... skip entries to safe data	Failed [300 / 300] Result: Complex[-0.8505476575870029, 0.390685462269601] Test Values: {Rule[a, -1.5], Rule[s, -1.5], Rule[ϕ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]} Result: Complex[-1.859414812385125, 0.6494166239344216] Test Values: {Rule[a, -1.5], Rule[s, -1.5], Rule[ϕ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]]} ... skip entries to safe data
19.30.E13	${\displaystyle{\displaystyle P=4\sqrt{2a^{2}}R_{F}\left(0,1,2\right)}}$ `P = 4\sqrt{2a^{2}}\CarlsonsymellintRF@{0}{1}{2}`		P = 4sqrt(2(a)^(2))0.5int(1/(sqrt(t+0)sqrt(t+1)sqrt(t+2)), t = 0..infinity)	P == 4Sqrt[2(a)^(2)]*EllipticF[ArcCos[Sqrt[0/2]],(2-1)/(2-0)]/Sqrt[2-0]	Failure	Failure	Failed [60 / 60] Result: -10.25842266+.5000000000I Test Values: {P = 1/23^(1/2)+1/2I, a = -3/2} Result: -10.25842266+.5000000000I Test Values: {P = 1/23^(1/2)+1/2I, a = 3/2} ... skip entries to safe data	Failed [60 / 60] Result: Complex[-10.691435361916012, 0.24999999999999997] Test Values: {Rule[a, -1.5], Rule[P, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]} Result: Complex[-11.37444806380823, 0.43301270189221935] Test Values: {Rule[a, -1.5], Rule[P, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]]} ... skip entries to safe data
19.30.E13	${\displaystyle{\displaystyle 4\sqrt{2a^{2}}R_{F}\left(0,1,2\right)=\sqrt{2a^{2% }}\times 5.24411\;51\ldots}}$ `4\sqrt{2a^{2}}\CarlsonsymellintRF@{0}{1}{2} = \sqrt{2a^{2}}\times 5.24411\;51\ldots`		4sqrt(2(a)^(2))0.5int(1/(sqrt(t+0)sqrt(t+1)sqrt(t+2)), t = 0..infinity) = sqrt(2(a)^(2)) 5.2441151	4Sqrt[2(a)^(2)]EllipticF[ArcCos[Sqrt[0/2]],(2-1)/(2-0)]/Sqrt[2-0] == Sqrt[2(a)^(2)] * 5.2441151	Translation Error	Translation Error	Skip - symbolical successful subtest	Skip - symbolical successful subtest
19.30.E13	${\displaystyle{\displaystyle\sqrt{2a^{2}}\times 5.24411\;51\ldots=4aK\left(1/% \sqrt{2}\right)}}$ `\sqrt{2a^{2}}\times 5.24411\;51\ldots = 4a\compellintKk@{1/\sqrt{2}}`		sqrt(2(a)^(2)) 5.2441151 = 4aEllipticK(1/(sqrt(2)))	Sqrt[2(a)^(2)] 5.2441151 == 4aEllipticK[(1/(Sqrt[2]))^2]	Translation Error	Translation Error	Skip - symbolical successful subtest	Skip - symbolical successful subtest
19.30.E13	${\displaystyle{\displaystyle 4aK\left(1/\sqrt{2}\right)=a\times 7.41629\;87% \dots}}$ `4a\compellintKk@{1/\sqrt{2}} = a\times 7.41629\;87\dots`		4aEllipticK(1/(sqrt(2))) = a * 7.4162987	4aEllipticK[(1/(Sqrt[2]))^2] == a * 7.4162987	Translation Error	Translation Error	Skip - symbolical successful subtest	Skip - symbolical successful subtest
19.32.E1	${\displaystyle{\displaystyle z(p)=R_{F}\left(p-x_{1},p-x_{2},p-x_{3}\right)}}$ `z(p) = \CarlsonsymellintRF@{p-x_{1}}{p-x_{2}}{p-x_{3}}`		(x + yI)(p) = 0.5int(1/(sqrt(t+p - x[1])sqrt(t+p - x[2])*sqrt(t+p - x[3])), t = 0..infinity)	(x + yI)(p) == EllipticF[ArcCos[Sqrt[p - Subscript[x, 1]/p - Subscript[x, 3]]],(p - Subscript[x, 3]-p - Subscript[x, 2])/(p - Subscript[x, 3]-p - Subscript[x, 1])]/Sqrt[p - Subscript[x, 3]-p - Subscript[x, 1]]	Aborted	Failure	Skipped - Because timed out	Failed [300 / 300] Result: Complex[-0.7208699572238464, -0.7193085577979393] Test Values: {Rule[p, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[x, 1.5], Rule[y, -1.5], Rule[Subscript[x, 1], Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[Subscript[x, 2], Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[Subscript[x, 3], Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]} Result: Complex[1.3758216901446034, -2.446030868401005] Test Values: {Rule[p, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[x, 1.5], Rule[y, -1.5], Rule[Subscript[x, 1], Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[Subscript[x, 2], Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[Subscript[x, 3], Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]]} ... skip entries to safe data
19.32.E3	${\displaystyle{\displaystyle x_{1}>x_{2}}}$ `x_{1} > x_{2}`		x[1] > x[2]	Subscript[x, 1] > Subscript[x, 2]	Skipped - no semantic math	Skipped - no semantic math	-	-
19.32#Ex1	${\displaystyle{\displaystyle z(\infty)=0}}$ `z(\infty) = 0`		z(infinity) = 0	z[Infinity] == 0	Skipped - no semantic math	Skipped - no semantic math	-	-
19.32#Ex3	${\displaystyle{\displaystyle z(x_{2})=z(x_{1})+z(x_{3})}}$ `z(x_{2}) = z(x_{1})+z(x_{3})`		(x + yI)(x[2]) = (x + yI)(x[1])+(x + yI)(x[3])	(x + yI)(Subscript[x, 2]) == (x + yI)(Subscript[x, 1])+(x + yI)(Subscript[x, 3])	Skipped - no semantic math	Skipped - no semantic math	-	-
19.32#Ex4	${\displaystyle{\displaystyle z(x_{3})=R_{F}\left(x_{3}-x_{1},x_{3}-x_{2},0% \right)}}$ `z(x_{3}) = \CarlsonsymellintRF@{x_{3}-x_{1}}{x_{3}-x_{2}}{0}`		(x + yI)(x[3]) = 0.5int(1/(sqrt(t+x[3]- x[1])sqrt(t+x[3]- x[2])*sqrt(t+0)), t = 0..infinity)	(x + yI)(Subscript[x, 3]) == EllipticF[ArcCos[Sqrt[Subscript[x, 3]- Subscript[x, 1]/0]],(0-Subscript[x, 3]- Subscript[x, 2])/(0-Subscript[x, 3]- Subscript[x, 1])]/Sqrt[0-Subscript[x, 3]- Subscript[x, 1]]	Aborted	Failure	Skipped - Because timed out	Failed [300 / 300] Result: Plus[Complex[1.024519052838329, -0.27451905283832906], Times[Complex[-0.25881904510252074, -0.9659258262890683], EllipticF[DirectedInfinity[], 1.0]]] Test Values: {Rule[x, 1.5], Rule[y, -1.5], Rule[Subscript[x, 1], Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[Subscript[x, 2], Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[Subscript[x, 3], Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]} Result: Plus[Complex[0.27451905283832917, 1.0245190528383288], Times[Complex[-0.7239434227163943, -0.9434614369855119], EllipticF[DirectedInfinity[], 1.0]]] Test Values: {Rule[x, 1.5], Rule[y, -1.5], Rule[Subscript[x, 1], Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[Subscript[x, 2], Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[Subscript[x, 3], Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]]} ... skip entries to safe data
19.32#Ex4	${\displaystyle{\displaystyle R_{F}\left(x_{3}-x_{1},x_{3}-x_{2},0\right)=-iR_{% F}\left(0,x_{1}-x_{3},x_{2}-x_{3}\right)}}$ `\CarlsonsymellintRF@{x_{3}-x_{1}}{x_{3}-x_{2}}{0} = -i\CarlsonsymellintRF@{0}{x_{1}-x_{3}}{x_{2}-x_{3}}`		0.5int(1/(sqrt(t+x[3]- x[1])sqrt(t+x[3]- x[2])sqrt(t+0)), t = 0..infinity) = - I0.5int(1/(sqrt(t+0)sqrt(t+x[1]- x[3])*sqrt(t+x[2]- x[3])), t = 0..infinity)	EllipticF[ArcCos[Sqrt[Subscript[x, 3]- Subscript[x, 1]/0]],(0-Subscript[x, 3]- Subscript[x, 2])/(0-Subscript[x, 3]- Subscript[x, 1])]/Sqrt[0-Subscript[x, 3]- Subscript[x, 1]] == - I*EllipticF[ArcCos[Sqrt[0/Subscript[x, 2]- Subscript[x, 3]]],(Subscript[x, 2]- Subscript[x, 3]-Subscript[x, 1]- Subscript[x, 3])/(Subscript[x, 2]- Subscript[x, 3]-0)]/Sqrt[Subscript[x, 2]- Subscript[x, 3]-0]	Aborted	Failure	Skipped - Because timed out	Failed [300 / 300] Result: Indeterminate Test Values: {Rule[Subscript[x, 1], Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[Subscript[x, 2], Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[Subscript[x, 3], Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]} Result: Plus[Complex[-0.4754994064110389, 1.6461555153586378], Times[Complex[0.7239434227163943, 0.9434614369855119], EllipticF[DirectedInfinity[], 1.0]]] Test Values: {Rule[Subscript[x, 1], Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[Subscript[x, 2], Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[Subscript[x, 3], Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]]} ... skip entries to safe data
19.33.E1	${\displaystyle{\displaystyle S=3VR_{G}\left(a^{-2},b^{-2},c^{-2}\right)}}$ `S = 3V\CarlsonsymellintRG@{a^{-2}}{b^{-2}}{c^{-2}}`		Error	S == 3VSqrt[(c)^(- 2)-(a)^(- 2)](EllipticE[ArcCos[Sqrt[(a)^(- 2)/(c)^(- 2)]],((c)^(- 2)-(b)^(- 2))/((c)^(- 2)-(a)^(- 2))]+(Cot[ArcCos[Sqrt[(a)^(- 2)/(c)^(- 2)]]])^2EllipticF[ArcCos[Sqrt[(a)^(- 2)/(c)^(- 2)]],((c)^(- 2)-(b)^(- 2))/((c)^(- 2)-(a)^(- 2))]+Cot[ArcCos[Sqrt[(a)^(- 2)/(c)^(- 2)]]]Sqrt[1-k^2Sin[ArcCos[Sqrt[(a)^(- 2)/(c)^(- 2)]]]^2])	Missing Macro Error	Failure	-	Failed [300 / 300] Result: Indeterminate Test Values: {Rule[a, -1.5], Rule[b, -1.5], Rule[c, -1.5], Rule[S, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[V, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]} Result: Indeterminate Test Values: {Rule[a, -1.5], Rule[b, -1.5], Rule[c, -1.5], Rule[S, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[V, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]]} ... skip entries to safe data
19.33.E2	${\displaystyle{\displaystyle\frac{S}{2\pi}=c^{2}+\frac{ab}{\sin\phi}\left(E% \left(\phi,k\right){\sin^{2}}\phi+F\left(\phi,k\right){\cos^{2}}\phi\right)}}$ `\frac{S}{2\pi} = c^{2}+\frac{ab}{\sin@@{\phi}}\left(\incellintEk@{\phi}{k}\sin^{2}@@{\phi}+\incellintFk@{\phi}{k}\cos^{2}@@{\phi}\right)`	${\displaystyle{\displaystyle a\geq b,b\geq c}}$	(S)/(2Pi) = (c)^(2)+(ab)/(sin(phi))(EllipticE(sin(phi), k)(sin(phi))^(2)+ EllipticF(sin(phi), k)*(cos(phi))^(2))	Divide[S,2Pi] == (c)^(2)+Divide[ab,Sin[\[Phi]]](EllipticE[\[Phi], (k)^2](Sin[\[Phi]])^(2)+ EllipticF[\[Phi], (k)^2]*(Cos[\[Phi]])^(2))	Failure	Failure	Failed [300 / 300] Result: -4.910443424-.9759333290e-1I Test Values: {S = 1/23^(1/2)+1/2I, a = -3/2, b = -3/2, c = -3/2, phi = 1/23^(1/2)+1/2I, k = 1} Result: -5.505002077-.4622644670e-1I Test Values: {S = 1/23^(1/2)+1/2I, a = -3/2, b = -3/2, c = -3/2, phi = 1/23^(1/2)+1/2I, k = 2} ... skip entries to safe data	Failed [300 / 300] Result: Complex[-4.54039506540302, -0.09283854764917886] Test Values: {Rule[a, -1.5], Rule[b, -1.5], Rule[c, -1.5], Rule[k, 1], Rule[S, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[ϕ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]} Result: Complex[-4.634568996487559, -0.31545051747139075] Test Values: {Rule[a, -1.5], Rule[b, -1.5], Rule[c, -1.5], Rule[k, 2], Rule[S, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[ϕ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]} ... skip entries to safe data
19.33#Ex1	${\displaystyle{\displaystyle\cos\phi=\frac{c}{a}}}$ `\cos@@{\phi} = \frac{c}{a}`		cos(phi) = (c)/(a)	Cos[\[Phi]] == Divide[c,a]	Failure	Failure	Failed [300 / 300] Result: -.2694569811-.3969495503I Test Values: {a = -3/2, c = -3/2, phi = 1/23^(1/2)+1/2I} Result: .227765517+.4690753764I Test Values: {a = -3/2, c = -3/2, phi = -1/2+1/2I3^(1/2)} ... skip entries to safe data	Failed [300 / 300] Result: Complex[-0.06378043051909243, -0.10599798465255418] Test Values: {Rule[a, -1.5], Rule[c, -1.5], Rule[ϕ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]} Result: Complex[0.061176166972244816, 0.11050836582743673] Test Values: {Rule[a, -1.5], Rule[c, -1.5], Rule[ϕ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]]} ... skip entries to safe data
19.33#Ex2	${\displaystyle{\displaystyle k^{2}=\frac{a^{2}(b^{2}-c^{2})}{b^{2}(a^{2}-c^{2}% )}}}$ `k^{2} = \frac{a^{2}(b^{2}-c^{2})}{b^{2}(a^{2}-c^{2})}`		(k)^(2) = ((a)^(2)((b)^(2)- (c)^(2)))/((b)^(2)((a)^(2)- (c)^(2)))	(k)^(2) == Divide[(a)^(2)((b)^(2)- (c)^(2)),(b)^(2)((a)^(2)- (c)^(2))]	Skipped - no semantic math	Skipped - no semantic math	-	-
19.33.E4	${\displaystyle{\displaystyle\frac{x^{2}}{a^{2}+\lambda}+\frac{y^{2}}{b^{2}+% \lambda}+\frac{z^{2}}{c^{2}+\lambda}=1}}$ `\frac{x^{2}}{a^{2}+\lambda}+\frac{y^{2}}{b^{2}+\lambda}+\frac{z^{2}}{c^{2}+\lambda} = 1`		((x)^(2))/((a)^(2)+ lambda)+((y)^(2))/((b)^(2)+ lambda)+((x + y*I)^(2))/((c)^(2)+ lambda) = 1	Divide[(x)^(2),(a)^(2)+ \[Lambda]]+Divide[(y)^(2),(b)^(2)+ \[Lambda]]+Divide[(x + y*I)^(2),(c)^(2)+ \[Lambda]] == 1	Skipped - no semantic math	Skipped - no semantic math	-	-
19.33.E5	${\displaystyle{\displaystyle V(\lambda)=QR_{F}\left(a^{2}+\lambda,b^{2}+% \lambda,c^{2}+\lambda\right)}}$ `V(\lambda) = Q\CarlsonsymellintRF@{a^{2}+\lambda}{b^{2}+\lambda}{c^{2}+\lambda}`		V(lambda) = Q0.5int(1/(sqrt(t+(a)^(2)+ lambda)sqrt(t+(b)^(2)+ lambda)sqrt(t+(c)^(2)+ lambda)), t = 0..infinity)	V[\[Lambda]] == Q*EllipticF[ArcCos[Sqrt[(a)^(2)+ \[Lambda]/(c)^(2)+ \[Lambda]]],((c)^(2)+ \[Lambda]-(b)^(2)+ \[Lambda])/((c)^(2)+ \[Lambda]-(a)^(2)+ \[Lambda])]/Sqrt[(c)^(2)+ \[Lambda]-(a)^(2)+ \[Lambda]]	Aborted	Failure	Skipped - Because timed out	Failed [300 / 300] Result: Complex[-0.01914487900157147, 0.6670953471925876] Test Values: {Rule[a, -1.5], Rule[b, -1.5], Rule[c, -1.5], Rule[Q, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[V, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[λ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]} Result: Complex[-0.08207662518407155, 0.5134467292285442] Test Values: {Rule[a, -1.5], Rule[b, -1.5], Rule[c, -1.5], Rule[Q, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[V, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[λ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]]} ... skip entries to safe data
19.33.E6	${\displaystyle{\displaystyle 1/C=R_{F}\left(a^{2},b^{2},c^{2}\right)}}$ `1/C = \CarlsonsymellintRF@{a^{2}}{b^{2}}{c^{2}}`		1/C = 0.5int(1/(sqrt(t+(a)^(2))sqrt(t+(b)^(2))*sqrt(t+(c)^(2))), t = 0..infinity)	1/C == EllipticF[ArcCos[Sqrt[(a)^(2)/(c)^(2)]],((c)^(2)-(b)^(2))/((c)^(2)-(a)^(2))]/Sqrt[(c)^(2)-(a)^(2)]	Aborted	Failure	Skipped - Because timed out	Failed [300 / 300] Result: Indeterminate Test Values: {Rule[a, -1.5], Rule[b, -1.5], Rule[c, -1.5], Rule[C, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]} Result: Indeterminate Test Values: {Rule[a, -1.5], Rule[b, -1.5], Rule[c, -1.5], Rule[C, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]]} ... skip entries to safe data
19.33.E7	${\displaystyle{\displaystyle L_{c}=2\pi abc\int_{0}^{\infty}\frac{\mathrm{d}% \lambda}{\sqrt{(a^{2}+\lambda)(b^{2}+\lambda)(c^{2}+\lambda)^{3}}}}}$ `L_{c} = 2\pi abc\int_{0}^{\infty}\frac{\diff{\lambda}}{\sqrt{(a^{2}+\lambda)(b^{2}+\lambda)(c^{2}+\lambda)^{3}}}`		L[c] = 2Piabcint((1)/(sqrt(((a)^(2)+ lambda)((b)^(2)+ lambda)*((c)^(2)+ lambda)^(3))), lambda = 0..infinity)	Subscript[L, c] == 2PiabcIntegrate[Divide[1,Sqrt[((a)^(2)+ \[Lambda])((b)^(2)+ \[Lambda])*((c)^(2)+ \[Lambda])^(3)]], {\[Lambda], 0, Infinity}, GenerateConditions->None]	Aborted	Aborted	Skipped - Because timed out	Skipped - Because timed out
19.33.E7	${\displaystyle{\displaystyle 2\pi abc\int_{0}^{\infty}\frac{\mathrm{d}\lambda}% {\sqrt{(a^{2}+\lambda)(b^{2}+\lambda)(c^{2}+\lambda)^{3}}}=VR_{D}\left(a^{2},b% ^{2},c^{2}\right)}}$ `2\pi abc\int_{0}^{\infty}\frac{\diff{\lambda}}{\sqrt{(a^{2}+\lambda)(b^{2}+\lambda)(c^{2}+\lambda)^{3}}} = V\CarlsonsymellintRD@{a^{2}}{b^{2}}{c^{2}}`		Error	2PiabcIntegrate[Divide[1,Sqrt[((a)^(2)+ \[Lambda])((b)^(2)+ \[Lambda])((c)^(2)+ \[Lambda])^(3)]], {\[Lambda], 0, Infinity}, GenerateConditions->None] == V3(EllipticF[ArcCos[Sqrt[(a)^(2)/(c)^(2)]],((c)^(2)-(b)^(2))/((c)^(2)-(a)^(2))]-EllipticE[ArcCos[Sqrt[(a)^(2)/(c)^(2)]],((c)^(2)-(b)^(2))/((c)^(2)-(a)^(2))])/(((c)^(2)-(b)^(2))((c)^(2)-(a)^(2))^(1/2))	Missing Macro Error	Aborted	Skip - symbolical successful subtest	Skipped - Because timed out
19.33.E8	${\displaystyle{\displaystyle L_{a}+L_{b}+L_{c}=4\pi}}$ `L_{a}+L_{b}+L_{c} = 4\pi`		L[a]+ L[b]+ L[c] = 4*Pi	Subscript[L, a]+ Subscript[L, b]+ Subscript[L, c] == 4*Pi	Skipped - no semantic math	Skipped - no semantic math	-	-
19.34.E1	${\displaystyle{\displaystyle ab\int_{0}^{2\pi}(h^{2}+a^{2}+b^{2}-2ab\cos\theta% )^{-1/2}\cos\theta\mathrm{d}\theta=2ab\int_{-1}^{1}\frac{t\mathrm{d}t}{\sqrt{(% 1+t)(1-t)(a_{3}-2abt)}}}}$ `ab\int_{0}^{2\pi}(h^{2}+a^{2}+b^{2}-2ab\cos@@{\theta})^{-1/2}\cos@@{\theta}\diff{\theta} = 2ab\int_{-1}^{1}\frac{t\diff{t}}{\sqrt{(1+t)(1-t)(a_{3}-2abt)}}`		abint(((h)^(2)+ (a)^(2)+ (b)^(2)- 2abcos(theta))^(- 1/2) cos(theta), theta = 0..2Pi) = 2abint((t)/(sqrt((1 + t)(1 - t)(a[3]- 2ab*t))), t = - 1..1)	abIntegrate[((h)^(2)+ (a)^(2)+ (b)^(2)- 2abCos[\[Theta]])^(- 1/2) Cos[\[Theta]], {\[Theta], 0, 2Pi}, GenerateConditions->None] == 2abIntegrate[Divide[t,Sqrt[(1 + t)(1 - t)(Subscript[a, 3]- 2ab*t)]], {t, - 1, 1}, GenerateConditions->None]	Aborted	Aborted	Skipped - Because timed out	Skipped - Because timed out
19.34.E1	${\displaystyle{\displaystyle 2ab\int_{-1}^{1}\frac{t\mathrm{d}t}{\sqrt{(1+t)(1% -t)(a_{3}-2abt)}}=2abI(\mathbf{e}_{5})}}$ `2ab\int_{-1}^{1}\frac{t\diff{t}}{\sqrt{(1+t)(1-t)(a_{3}-2abt)}} = 2abI(\mathbf{e}_{5})`		2abint((t)/(sqrt((1 + t)(1 - t)(a[3]- 2abt))), t = - 1..1) = 2*abI(e[5])	2abIntegrate[Divide[t,Sqrt[(1 + t)(1 - t)(Subscript[a, 3]- 2abt)]], {t, - 1, 1}, GenerateConditions->None] == 2*abI[Subscript[e, 5]]	Failure	Aborted	Failed [300 / 300] Result: -3.959693187-6.593729744I Test Values: {I = 1/23^(1/2)+1/2I, a = -3/2, b = -3/2, a[3] = 1/23^(1/2)+1/2I, e[5] = 1/23^(1/2)+1/2I} Result: 2.187421133-4.946615428I Test Values: {I = 1/23^(1/2)+1/2I, a = -3/2, b = -3/2, a[3] = 1/23^(1/2)+1/2I, e[5] = -1/2+1/2I3^(1/2)} ... skip entries to safe data	Skipped - Because timed out
19.34#Ex1	${\displaystyle{\displaystyle a_{3}=h^{2}+a^{2}+b^{2}}}$ `a_{3} = h^{2}+a^{2}+b^{2}`		a[3] = (h)^(2)+ (a)^(2)+ (b)^(2)	Subscript[a, 3] == (h)^(2)+ (a)^(2)+ (b)^(2)	Skipped - no semantic math	Skipped - no semantic math	-	-
19.34#Ex2	${\displaystyle{\displaystyle a_{5}=0}}$ `a_{5} = 0`		a[5] = 0	Subscript[a, 5] == 0	Skipped - no semantic math	Skipped - no semantic math	-	-
19.34#Ex3	${\displaystyle{\displaystyle b_{5}=1}}$ `b_{5} = 1`		b[5] = 1	Subscript[b, 5] == 1	Skipped - no semantic math	Skipped - no semantic math	-	-
19.34.E3	${\displaystyle{\displaystyle 2abI(\mathbf{e}_{5})=a_{3}I(\boldsymbol{{0}})-I(% \mathbf{e}_{3})}}$ `2abI(\mathbf{e}_{5}) = a_{3}I(\boldsymbol{{0}})-I(\mathbf{e}_{3})`		2abI(e[5]) = a[3]I(0)- I(e[3])	2abI[Subscript[e, 5]] == Subscript[a, 3]I[0]- I[Subscript[e, 3]]	Skipped - no semantic math	Skipped - no semantic math	-	-
19.34.E4	${\displaystyle{\displaystyle r_{+}^{2}=a_{3}+2ab}}$ `r_{+}^{2} = a_{3}+ 2ab`		(r[+])^(2) = a[3]+ 2ab	(Subscript[r, +])^(2) == Subscript[a, 3]+ 2ab	Skipped - no semantic math	Skipped - no semantic math	-	-
19.36.E3	${\displaystyle{\displaystyle R_{F}\left(1,2,4\right)=R_{F}\left(z_{1},z_{2},z_% {3}\right)}}$ `\CarlsonsymellintRF@{1}{2}{4} = \CarlsonsymellintRF@{z_{1}}{z_{2}}{z_{3}}`		0.5int(1/(sqrt(t+1)sqrt(t+2)sqrt(t+4)), t = 0..infinity) = 0.5int(1/(sqrt(t+z[1])sqrt(t+z[2])sqrt(t+z[3])), t = 0..infinity)	EllipticF[ArcCos[Sqrt[1/4]],(4-2)/(4-1)]/Sqrt[4-1] == EllipticF[ArcCos[Sqrt[Subscript[z, 1]/Subscript[z, 3]]],(Subscript[z, 3]-Subscript[z, 2])/(Subscript[z, 3]-Subscript[z, 1])]/Sqrt[Subscript[z, 3]-Subscript[z, 1]]	Aborted	Failure	Skipped - Because timed out	Failed [300 / 300] Result: Indeterminate Test Values: {Rule[Subscript[z, 1], Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[Subscript[z, 2], Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[Subscript[z, 3], Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]} Result: Complex[-0.6113291272616378, 0.7460602493090597] Test Values: {Rule[Subscript[z, 1], Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[Subscript[z, 2], Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[Subscript[z, 3], Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]]} ... skip entries to safe data
19.36.E4	`\begin{aligned} \displaystyle z_{1}&\displaystyle = 2.10985\;99098\;8,\\ \displaystyle z_{3}&\displaystyle`				Skipped - no semantic math	Skipped - no semantic math	-	-
19.36.E5	${\displaystyle{\displaystyle R_{F}\left(1,2,4\right)=0.68508\;58166\dots}}$ `\CarlsonsymellintRF@{1}{2}{4} = 0.68508\;58166\dots`		0.5int(1/(sqrt(t+1)sqrt(t+2)*sqrt(t+4)), t = 0..infinity) = 0.6850858166	EllipticF[ArcCos[Sqrt[1/4]],(4-2)/(4-1)]/Sqrt[4-1] == 0.6850858166	Failure	Failure	Successful [Tested: 0]	Successful [Tested: 1]
19.36#Ex1	${\displaystyle{\displaystyle 2a_{n+1}=a_{n}+\sqrt{a_{n}^{2}-c_{n}^{2}}}}$ `2a_{n+1} = a_{n}+\sqrt{a_{n}^{2}-c_{n}^{2}}`		2*a[n + 1] = a[n]+sqrt((a[n])^(2)- (c[n])^(2))	2*Subscript[a, n + 1] == Subscript[a, n]+Sqrt[(Subscript[a, n])^(2)- (Subscript[c, n])^(2)]	Skipped - no semantic math	Skipped - no semantic math	-	-
19.36#Ex2	${\displaystyle{\displaystyle 2c_{n+1}=a_{n}-\sqrt{a_{n}^{2}-c_{n}^{2}}}}$ `2c_{n+1} = a_{n}-\sqrt{a_{n}^{2}-c_{n}^{2}}`		2*c[n + 1] = a[n]-sqrt((a[n])^(2)- (c[n])^(2))	2*Subscript[c, n + 1] == Subscript[a, n]-Sqrt[(Subscript[a, n])^(2)- (Subscript[c, n])^(2)]	Skipped - no semantic math	Skipped - no semantic math	-	-
19.36#Ex3	${\displaystyle{\displaystyle 2t_{n+1}=t_{n}+\sqrt{t_{n}^{2}+\theta c_{n}^{2}}}}$ `2t_{n+1} = t_{n}+\sqrt{t_{n}^{2}+\theta c_{n}^{2}}`		2t[n + 1] = t[n]+sqrt((t[n])^(2)+ theta(c[n])^(2))	2Subscript[t, n + 1] == Subscript[t, n]+Sqrt[(Subscript[t, n])^(2)+ \[Theta](Subscript[c, n])^(2)]	Skipped - no semantic math	Skipped - no semantic math	-	-
19.36#Ex4	${\displaystyle{\displaystyle 0<c_{0}}}$ `0 < c_{0}`		0 < c[0]	0 < Subscript[c, 0]	Skipped - no semantic math	Skipped - no semantic math	-	-
19.36#Ex5	${\displaystyle{\displaystyle t_{0}\geq 0}}$ `t_{0} \geq 0`		t[0] >= 0	Subscript[t, 0] >= 0	Skipped - no semantic math	Skipped - no semantic math	-	-
19.36#Ex6	${\displaystyle{\displaystyle t_{0}^{2}+\theta a_{0}^{2}\geq 0}}$ `t_{0}^{2}+\theta a_{0}^{2} \geq 0`		(t[0])^(2)+ theta*(a[0])^(2) >= 0	(Subscript[t, 0])^(2)+ \[Theta]*(Subscript[a, 0])^(2) >= 0	Skipped - no semantic math	Skipped - no semantic math	-	-
19.36#Ex7	${\displaystyle{\displaystyle\theta=+1}}$ `\theta = + 1`		theta = + 1	\[Theta] == + 1	Skipped - no semantic math	Skipped - no semantic math	-	-
19.36.E9	${\displaystyle{\displaystyle R_{F}\left(t_{0}^{2},t_{0}^{2}+\theta c_{0}^{2},t% _{0}^{2}+\theta a_{0}^{2}\right)=R_{F}\left(T^{2},T^{2},T^{2}+\theta M^{2}% \right)}}$ `\CarlsonsymellintRF@{t_{0}^{2}}{t_{0}^{2}+\theta c_{0}^{2}}{t_{0}^{2}+\theta a_{0}^{2}} = \CarlsonsymellintRF@{T^{2}}{T^{2}}{T^{2}+\theta M^{2}}`		0.5int(1/(sqrt(t+(t[0])^(2))sqrt(t+(t[0])^(2)+ theta(c[0])^(2))sqrt(t+(t[0])^(2)+ theta(a[0])^(2))), t = 0..infinity) = 0.5int(1/(sqrt(t+(T)^(2))sqrt(t+(T)^(2))sqrt(t+(T)^(2)+ theta*(M)^(2))), t = 0..infinity)	EllipticF[ArcCos[Sqrt[(Subscript[t, 0])^(2)/(Subscript[t, 0])^(2)+ \[Theta](Subscript[a, 0])^(2)]],((Subscript[t, 0])^(2)+ \[Theta](Subscript[a, 0])^(2)-(Subscript[t, 0])^(2)+ \[Theta](Subscript[c, 0])^(2))/((Subscript[t, 0])^(2)+ \[Theta](Subscript[a, 0])^(2)-(Subscript[t, 0])^(2))]/Sqrt[(Subscript[t, 0])^(2)+ \[Theta](Subscript[a, 0])^(2)-(Subscript[t, 0])^(2)] == EllipticF[ArcCos[Sqrt[(T)^(2)/(T)^(2)+ \[Theta](M)^(2)]],((T)^(2)+ \[Theta](M)^(2)-(T)^(2))/((T)^(2)+ \[Theta](M)^(2)-(T)^(2))]/Sqrt[(T)^(2)+ \[Theta]*(M)^(2)-(T)^(2)]	Error	Failure	-	Failed [300 / 300] Result: Plus[Complex[0.041390391732804066, 0.9969018367602411], Times[2.8284271247461903, Power[Times[Complex[0.0, 1.0], a], Rational[-1, 2]], EllipticF[ArcCos[Power[Plus[Complex[-0.031249999999999986, 0.05412658773652742], Times[Complex[0.0, 0.125], a]], Rational[1, 2]]], Times[Complex[0.0, -8.0], Power[a, -1], Plus[Times[Complex[0.0, 0.125], a], Times[Complex[0.0, 0.125], c]]]]]] Test Values: {Rule[M, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[T, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[θ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[Subscript[a, 0], Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[Subscript[c, 0], Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[Subscript[t, 0], Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]} Result: Plus[Complex[0.041390391732804066, 0.9969018367602411], Times[2.8284271247461903, Power[Times[Complex[0.0, 1.0], a], Rational[-1, 2]], EllipticF[ArcCos[Power[Plus[Complex[-0.031249999999999986, 0.05412658773652742], Times[Complex[0.0, 0.125], a]], Rational[1, 2]]], Times[Complex[0.0, -8.0], Power[a, -1], Plus[Times[Complex[0.0, 0.125], a], Times[Complex[0.0, 0.125], c]]]]]] Test Values: {Rule[M, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[T, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[θ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[Subscript[a, 0], Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[Subscript[c, 0], Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[Subscript[t, 0], Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]]} ... skip entries to safe data
19.36.E9	${\displaystyle{\displaystyle R_{F}\left(T^{2},T^{2},T^{2}+\theta M^{2}\right)=% R_{C}\left(T^{2}+\theta M^{2},T^{2}\right)}}$ `\CarlsonsymellintRF@{T^{2}}{T^{2}}{T^{2}+\theta M^{2}} = \CarlsonellintRC@{T^{2}+\theta M^{2}}{T^{2}}`		Error	EllipticF[ArcCos[Sqrt[(T)^(2)/(T)^(2)+ \[Theta](M)^(2)]],((T)^(2)+ \[Theta](M)^(2)-(T)^(2))/((T)^(2)+ \[Theta](M)^(2)-(T)^(2))]/Sqrt[(T)^(2)+ \[Theta](M)^(2)-(T)^(2)] == 1/Sqrt[(T)^(2)]Hypergeometric2F1[1/2,1/2,3/2,1-((T)^(2)+ \[Theta](M)^(2))/((T)^(2))]	Missing Macro Error	Failure	-	Failed [300 / 300] Result: Complex[-1.634056915706757, -0.008820605997006181] Test Values: {Rule[M, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[T, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[θ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]} Result: Complex[-1.6914869520542948, 0.13073697514602478] Test Values: {Rule[M, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[T, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[θ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]]} ... skip entries to safe data
19.36#Ex9	${\displaystyle{\displaystyle a_{3}^{2}=2.46209\;30206\;0}}$ `a_{3}^{2} = 2.46209\;30206\;0`		(a[3])^(2) = 2.46209302060	(Subscript[a, 3])^(2) == 2.46209302060	Skipped - no semantic math	Skipped - no semantic math	-	-
19.36#Ex10	${\displaystyle{\displaystyle t_{3}^{2}=1.46971\;53173\;1}}$ `t_{3}^{2} = 1.46971\;53173\;1`		(t[3])^(2) = 1.46971531731	(Subscript[t, 3])^(2) == 1.46971531731	Skipped - no semantic math	Skipped - no semantic math	-	-
19.36.E11	${\displaystyle{\displaystyle R_{F}\left(1,2,4\right)=R_{C}\left(T^{2}+M^{2},T^% {2}\right)}}$ `\CarlsonsymellintRF@{1}{2}{4} = \CarlsonellintRC@{T^{2}+M^{2}}{T^{2}}`		Error	EllipticF[ArcCos[Sqrt[1/4]],(4-2)/(4-1)]/Sqrt[4-1] == 1/Sqrt[(T)^(2)]*Hypergeometric2F1[1/2,1/2,3/2,1-((T)^(2)+ (M)^(2))/((T)^(2))]	Missing Macro Error	Failure	-	Failed [100 / 100] Result: Complex[-0.841498016533642, 0.8813735870195429] Test Values: {Rule[M, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[T, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]} Result: Complex[-0.8857105197615976, -2.720699010523131] Test Values: {Rule[M, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[T, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]]} ... skip entries to safe data
19.36.E11	${\displaystyle{\displaystyle R_{C}\left(T^{2}+M^{2},T^{2}\right)=0.68508\;5816% 6}}$ `\CarlsonellintRC@{T^{2}+M^{2}}{T^{2}} = 0.68508\;58166`		Error	1/Sqrt[(T)^(2)]*Hypergeometric2F1[1/2,1/2,3/2,1-((T)^(2)+ (M)^(2))/((T)^(2))] == 0.6850858166	Missing Macro Error	Failure	-	Failed [100 / 100] Result: Complex[0.8414980165670778, -0.8813735870195429] Test Values: {Rule[M, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[T, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]} Result: Complex[0.8857105197950335, 2.720699010523131] Test Values: {Rule[M, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[T, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]]} ... skip entries to safe data
19.36#Ex11	${\displaystyle{\displaystyle h_{n}=\sqrt{t_{n}^{2}+\theta a_{n}^{2}}}}$ `h_{n} = \sqrt{t_{n}^{2}+\theta a_{n}^{2}}`		h[n] = sqrt((t[n])^(2)+ theta*(a[n])^(2))	Subscript[h, n] == Sqrt[(Subscript[t, n])^(2)+ \[Theta]*(Subscript[a, n])^(2)]	Skipped - no semantic math	Skipped - no semantic math	-	-
19.36#Ex12	${\displaystyle{\displaystyle h_{n}=h_{n-1}\frac{t_{n}}{\sqrt{t_{n}^{2}+\theta c% _{n}^{2}}}}}$ `h_{n} = h_{n-1}\frac{t_{n}}{\sqrt{t_{n}^{2}+\theta c_{n}^{2}}}`		h[n] = h[n - 1](t[n])/(sqrt((t[n])^(2)+ theta(c[n])^(2)))	Subscript[h, n] == Subscript[h, n - 1]Divide[Subscript[t, n],Sqrt[(Subscript[t, n])^(2)+ \[Theta](Subscript[c, n])^(2)]]	Skipped - no semantic math	Skipped - no semantic math	-	-
19.36.E13	${\displaystyle{\displaystyle 2R_{G}\left(t_{0}^{2},t_{0}^{2}+\theta c_{0}^{2},% t_{0}^{2}+\theta a_{0}^{2}\right)=\left(t_{0}^{2}+\theta\sum_{m=0}^{\infty}2^{% m-1}c_{m}^{2}\right)R_{C}\left(T^{2}+\theta M^{2},T^{2}\right)+h_{0}+\sum_{m=1% }^{\infty}2^{m}(h_{m}-h_{m-1})}}$ `2\CarlsonsymellintRG@{t_{0}^{2}}{t_{0}^{2}+\theta c_{0}^{2}}{t_{0}^{2}+\theta a_{0}^{2}} = \left(t_{0}^{2}+\theta\sum_{m=0}^{\infty}2^{m-1}c_{m}^{2}\right)\CarlsonellintRC@{T^{2}+\theta M^{2}}{T^{2}}+h_{0}+\sum_{m=1}^{\infty}2^{m}(h_{m}-h_{m-1})`		Error	2Sqrt[(Subscript[t, 0])^(2)+ \[Theta](Subscript[a, 0])^(2)-(Subscript[t, 0])^(2)](EllipticE[ArcCos[Sqrt[(Subscript[t, 0])^(2)/(Subscript[t, 0])^(2)+ \[Theta](Subscript[a, 0])^(2)]],((Subscript[t, 0])^(2)+ \[Theta](Subscript[a, 0])^(2)-(Subscript[t, 0])^(2)+ \[Theta](Subscript[c, 0])^(2))/((Subscript[t, 0])^(2)+ \[Theta](Subscript[a, 0])^(2)-(Subscript[t, 0])^(2))]+(Cot[ArcCos[Sqrt[(Subscript[t, 0])^(2)/(Subscript[t, 0])^(2)+ \[Theta](Subscript[a, 0])^(2)]]])^2EllipticF[ArcCos[Sqrt[(Subscript[t, 0])^(2)/(Subscript[t, 0])^(2)+ \[Theta](Subscript[a, 0])^(2)]],((Subscript[t, 0])^(2)+ \[Theta](Subscript[a, 0])^(2)-(Subscript[t, 0])^(2)+ \[Theta](Subscript[c, 0])^(2))/((Subscript[t, 0])^(2)+ \[Theta](Subscript[a, 0])^(2)-(Subscript[t, 0])^(2))]+Cot[ArcCos[Sqrt[(Subscript[t, 0])^(2)/(Subscript[t, 0])^(2)+ \[Theta](Subscript[a, 0])^(2)]]]Sqrt[1-k^2Sin[ArcCos[Sqrt[(Subscript[t, 0])^(2)/(Subscript[t, 0])^(2)+ \[Theta](Subscript[a, 0])^(2)]]]^2]) == ((Subscript[t, 0])^(2)+ \[Theta]Sum[(2)^(m - 1)* (Subscript[c, m])^(2), {m, 0, Infinity}, GenerateConditions->None])1/Sqrt[(T)^(2)]Hypergeometric2F1[1/2,1/2,3/2,1-((T)^(2)+ \[Theta](M)^(2))/((T)^(2))]+ Subscript[h, 0]+ Sum[(2)^(m)(Subscript[h, m]- Subscript[h, m - 1]), {m, 1, Infinity}, GenerateConditions->None]	Missing Macro Error	Aborted	-	Failed [1 / 1]

@@ Line 439: / Line 439: @@
 | [https://dlmf.nist.gov/19.27#Ex6 19.27#Ex6] || [[Item:Q6593|<math>h = (yz)^{1/2}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>h = (yz)^{1/2}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">h = (y*(x + y*I))^(1/2)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">h == (y*(x + y*I))^(1/2)</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
 |-
-| [https://dlmf.nist.gov/19.28.E1 19.28.E1] || [[Item:Q6609|<math>\int_{0}^{1}t^{\sigma-1}\CarlsonsymellintRF@{0}{t}{1}\diff{t} = \tfrac{1}{2}\left(\EulerBeta@{\sigma}{\tfrac{1}{2}}\right)^{2}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\int_{0}^{1}t^{\sigma-1}\CarlsonsymellintRF@{0}{t}{1}\diff{t} = \tfrac{1}{2}\left(\EulerBeta@{\sigma}{\tfrac{1}{2}}\right)^{2}</syntaxhighlight> || <math>\realpart@@{(\sigma)} > 0, \realpart@@{(\tfrac{1}{2})} > 0, \realpart@@{((\sigma)+b)} > 0, \realpart@@{(a+(\tfrac{1}{2}))} > 0</math> || <syntaxhighlight lang=mathematica>int((t)^(sigma - 1)* 0.5*int(1/(sqrt(t+0)*sqrt(t+t)*sqrt(t+1)), t = 0..infinity), t = 0..1) = (1)/(2)*(Beta(sigma, (1)/(2)))^(2)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Integrate[(t)^(\[Sigma]- 1)* EllipticF[ArcCos[Sqrt[0/1]],(1-t)/(1-0)]/Sqrt[1-0], {t, 0, 1}, GenerateConditions->None] == Divide[1,2]*(Beta[\[Sigma], Divide[1,2]])^(2)</syntaxhighlight> || Failure || Aborted || <div class="toccolours mw-collapsible mw-collapsed">Failed [10 / 10]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Float(undefined)+1.162857938*I
+| [https://dlmf.nist.gov/19.28.E1 19.28.E1] || [[Item:Q6609|<math>\int_{0}^{1}t^{\sigma-1}\CarlsonsymellintRF@{0}{t}{1}\diff{t} = \tfrac{1}{2}\left(\EulerBeta@{\sigma}{\tfrac{1}{2}}\right)^{2}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\int_{0}^{1}t^{\sigma-1}\CarlsonsymellintRF@{0}{t}{1}\diff{t} = \tfrac{1}{2}\left(\EulerBeta@{\sigma}{\tfrac{1}{2}}\right)^{2}</syntaxhighlight> || <math>\realpart@@{(\sigma)} > 0, \realpart@@{((\sigma)+b)} > 0, \realpart@@{(a+(\tfrac{1}{2}))} > 0</math> || <syntaxhighlight lang=mathematica>int((t)^(sigma - 1)* 0.5*int(1/(sqrt(t+0)*sqrt(t+t)*sqrt(t+1)), t = 0..infinity), t = 0..1) = (1)/(2)*(Beta(sigma, (1)/(2)))^(2)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Integrate[(t)^(\[Sigma]- 1)* EllipticF[ArcCos[Sqrt[0/1]],(1-t)/(1-0)]/Sqrt[1-0], {t, 0, 1}, GenerateConditions->None] == Divide[1,2]*(Beta[\[Sigma], Divide[1,2]])^(2)</syntaxhighlight> || Failure || Aborted || <div class="toccolours mw-collapsible mw-collapsed">Failed [10 / 10]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Float(undefined)+1.162857938*I
 Test Values: {sigma = 1/2*3^(1/2)+1/2*I}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Float(undefined)+.9984297790*I
 Test Values: {sigma = -1/2+1/2*I*3^(1/2)}</syntaxhighlight><br>... skip entries to safe data</div></div> || Skipped - Because timed out
 |-
-| [https://dlmf.nist.gov/19.28.E2 19.28.E2] || [[Item:Q6610|<math>\int_{0}^{1}t^{\sigma-1}\CarlsonsymellintRG@{0}{t}{1}\diff{t} = \frac{\sigma}{4\sigma+2}\left(\EulerBeta@{\sigma}{\tfrac{1}{2}}\right)^{2}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\int_{0}^{1}t^{\sigma-1}\CarlsonsymellintRG@{0}{t}{1}\diff{t} = \frac{\sigma}{4\sigma+2}\left(\EulerBeta@{\sigma}{\tfrac{1}{2}}\right)^{2}</syntaxhighlight> || <math>\realpart@@{(\sigma)} > 0, \realpart@@{(\tfrac{1}{2})} > 0, \realpart@@{((\sigma)+b)} > 0, \realpart@@{(a+(\tfrac{1}{2}))} > 0</math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>Integrate[(t)^(\[Sigma]- 1)* Sqrt[1-0]*(EllipticE[ArcCos[Sqrt[0/1]],(1-t)/(1-0)]+(Cot[ArcCos[Sqrt[0/1]]])^2*EllipticF[ArcCos[Sqrt[0/1]],(1-t)/(1-0)]+Cot[ArcCos[Sqrt[0/1]]]*Sqrt[1-k^2*Sin[ArcCos[Sqrt[0/1]]]^2]), {t, 0, 1}, GenerateConditions->None] == Divide[\[Sigma],4*\[Sigma]+ 2]*(Beta[\[Sigma], Divide[1,2]])^(2)</syntaxhighlight> || Missing Macro Error || Aborted || - || Skipped - Because timed out
+| [https://dlmf.nist.gov/19.28.E2 19.28.E2] || [[Item:Q6610|<math>\int_{0}^{1}t^{\sigma-1}\CarlsonsymellintRG@{0}{t}{1}\diff{t} = \frac{\sigma}{4\sigma+2}\left(\EulerBeta@{\sigma}{\tfrac{1}{2}}\right)^{2}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\int_{0}^{1}t^{\sigma-1}\CarlsonsymellintRG@{0}{t}{1}\diff{t} = \frac{\sigma}{4\sigma+2}\left(\EulerBeta@{\sigma}{\tfrac{1}{2}}\right)^{2}</syntaxhighlight> || <math>\realpart@@{(\sigma)} > 0, \realpart@@{((\sigma)+b)} > 0, \realpart@@{(a+(\tfrac{1}{2}))} > 0</math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>Integrate[(t)^(\[Sigma]- 1)* Sqrt[1-0]*(EllipticE[ArcCos[Sqrt[0/1]],(1-t)/(1-0)]+(Cot[ArcCos[Sqrt[0/1]]])^2*EllipticF[ArcCos[Sqrt[0/1]],(1-t)/(1-0)]+Cot[ArcCos[Sqrt[0/1]]]*Sqrt[1-k^2*Sin[ArcCos[Sqrt[0/1]]]^2]), {t, 0, 1}, GenerateConditions->None] == Divide[\[Sigma],4*\[Sigma]+ 2]*(Beta[\[Sigma], Divide[1,2]])^(2)</syntaxhighlight> || Missing Macro Error || Aborted || - || Skipped - Because timed out
 |-
-| [https://dlmf.nist.gov/19.28.E3 19.28.E3] || [[Item:Q6611|<math>\int_{0}^{1}t^{\sigma-1}(1-t)\CarlsonsymellintRD@{0}{t}{1}\diff{t} = \frac{3}{4\sigma+2}\left(\EulerBeta@{\sigma}{\tfrac{1}{2}}\right)^{2}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\int_{0}^{1}t^{\sigma-1}(1-t)\CarlsonsymellintRD@{0}{t}{1}\diff{t} = \frac{3}{4\sigma+2}\left(\EulerBeta@{\sigma}{\tfrac{1}{2}}\right)^{2}</syntaxhighlight> || <math>\realpart@@{(\sigma)} > 0, \realpart@@{(\tfrac{1}{2})} > 0, \realpart@@{((\sigma)+b)} > 0, \realpart@@{(a+(\tfrac{1}{2}))} > 0</math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>Integrate[(t)^(\[Sigma]- 1)*(1 - t)*3*(EllipticF[ArcCos[Sqrt[0/1]],(1-t)/(1-0)]-EllipticE[ArcCos[Sqrt[0/1]],(1-t)/(1-0)])/((1-t)*(1-0)^(1/2)), {t, 0, 1}, GenerateConditions->None] == Divide[3,4*\[Sigma]+ 2]*(Beta[\[Sigma], Divide[1,2]])^(2)</syntaxhighlight> || Missing Macro Error || Aborted || - || Skipped - Because timed out
+| [https://dlmf.nist.gov/19.28.E3 19.28.E3] || [[Item:Q6611|<math>\int_{0}^{1}t^{\sigma-1}(1-t)\CarlsonsymellintRD@{0}{t}{1}\diff{t} = \frac{3}{4\sigma+2}\left(\EulerBeta@{\sigma}{\tfrac{1}{2}}\right)^{2}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\int_{0}^{1}t^{\sigma-1}(1-t)\CarlsonsymellintRD@{0}{t}{1}\diff{t} = \frac{3}{4\sigma+2}\left(\EulerBeta@{\sigma}{\tfrac{1}{2}}\right)^{2}</syntaxhighlight> || <math>\realpart@@{(\sigma)} > 0, \realpart@@{((\sigma)+b)} > 0, \realpart@@{(a+(\tfrac{1}{2}))} > 0</math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>Integrate[(t)^(\[Sigma]- 1)*(1 - t)*3*(EllipticF[ArcCos[Sqrt[0/1]],(1-t)/(1-0)]-EllipticE[ArcCos[Sqrt[0/1]],(1-t)/(1-0)])/((1-t)*(1-0)^(1/2)), {t, 0, 1}, GenerateConditions->None] == Divide[3,4*\[Sigma]+ 2]*(Beta[\[Sigma], Divide[1,2]])^(2)</syntaxhighlight> || Missing Macro Error || Aborted || - || Skipped - Because timed out
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 | [https://dlmf.nist.gov/19.28.E5 19.28.E5] || [[Item:Q6613|<math>\int_{z}^{\infty}\CarlsonsymellintRD@{x}{y}{t}\diff{t} = 6\CarlsonsymellintRF@{x}{y}{z}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\int_{z}^{\infty}\CarlsonsymellintRD@{x}{y}{t}\diff{t} = 6\CarlsonsymellintRF@{x}{y}{z}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>Integrate[3*(EllipticF[ArcCos[Sqrt[x/t]],(t-y)/(t-x)]-EllipticE[ArcCos[Sqrt[x/t]],(t-y)/(t-x)])/((t-y)*(t-x)^(1/2)), {t, (x + y*I), Infinity}, GenerateConditions->None] == 6*EllipticF[ArcCos[Sqrt[x/x + y*I]],(x + y*I-y)/(x + y*I-x)]/Sqrt[x + y*I-x]</syntaxhighlight> || Missing Macro Error || Aborted || - || Skipped - Because timed out

Results of Elliptic Integrals II: Difference between revisions

Latest revision as of 07:16, 25 May 2021

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