36.4

DLMF	Formula	Constraints	Maple	Mathematica	Symbolic Maple	Symbolic Mathematica	Numeric Maple	Numeric Mathematica
36.4.E5	${\displaystyle{\displaystyle x=0}}$ x = 0		x = 0	x == 0	Skipped - no semantic math	Skipped - no semantic math	-	-
36.4.E6	${\displaystyle{\displaystyle 27x^{2}=-8y^{3}}}$ 27x^{2} = -8y^{3}		27*(x)^(2) = - 8*(y)^(3)	27*(x)^(2) == - 8*(y)^(3)	Skipped - no semantic math	Skipped - no semantic math	-	-
36.4#Ex3	${\displaystyle{\displaystyle x=3t^{2}(z+5t^{2})}}$ x = 3t^{2}(z+5t^{2})		x = 3*(t)^(2)*((x + y*I)+ 5*(t)^(2))	x == 3*(t)^(2)*((x + y*I)+ 5*(t)^(2))	Skipped - no semantic math	Skipped - no semantic math	-	-
36.4#Ex4	${\displaystyle{\displaystyle y=-t(3z+10t^{2})}}$ y = -t(3z+10t^{2})	${\displaystyle{\displaystyle-\infty<t,t<\infty}}$	y = - t*(3*(x + y*I)+ 10*(t)^(2))	y == - t*(3*(x + y*I)+ 10*(t)^(2))	Skipped - no semantic math	Skipped - no semantic math	-	-
36.4#Ex5	${\displaystyle{\displaystyle y=0}}$ y = 0		y = 0	y == 0	Skipped - no semantic math	Skipped - no semantic math	-	-
36.4#Ex6	${\displaystyle{\displaystyle z\leq 0}}$ z \leq 0		z <= 0	z <= 0	Skipped - no semantic math	Skipped - no semantic math	-	-
36.4#Ex7	${\displaystyle{\displaystyle x=\tfrac{9}{20}z^{2}}}$ x = \tfrac{9}{20}z^{2}		x = (9)/(20)*(x + y*I)^(2)	x == Divide[9,20]*(x + y*I)^(2)	Skipped - no semantic math	Skipped - no semantic math	-	-
36.4#Ex8	${\displaystyle{\displaystyle z\leq 0}}$ z \leq 0		z <= 0	z <= 0	Skipped - no semantic math	Skipped - no semantic math	-	-
36.4#Ex9	${\displaystyle{\displaystyle x=-\tfrac{3}{20}z^{2}}}$ x = -\tfrac{3}{20}z^{2}		x = -(3)/(20)*(x + y*I)^(2)	x == -Divide[3,20]*(x + y*I)^(2)	Skipped - no semantic math	Skipped - no semantic math	-	-
36.4#Ex10	${\displaystyle{\displaystyle 10y^{2}=-4z^{3}}}$ 10y^{2} = -4z^{3}		10*(y)^(2) = - 4*(x + y*I)^(3)	10*(y)^(2) == - 4*(x + y*I)^(3)	Skipped - no semantic math	Skipped - no semantic math	-	-
36.4#Ex11	${\displaystyle{\displaystyle x=\tfrac{1}{3}z^{2}(-\cos\left(2\phi\right)-2\cos\phi)}}$ x = \tfrac{1}{3}z^{2}(-\cos@{2\phi}-2\cos@@{\phi})		x = (1)/(3)*(x + y*I)^(2)*(- cos(2*phi)- 2*cos(phi))	x == Divide[1,3]*(x + y*I)^(2)*(- Cos[2*\[Phi]]- 2*Cos[\[Phi]])	Failure	Failure	Failed [180 / 180] Result: -1.430780988-1.820001528*I Test Values: {phi = 1/2*3^(1/2)+1/2*I, x = 3/2, y = -3/2} Result: 4.430780988+1.820001528*I Test Values: {phi = 1/2*3^(1/2)+1/2*I, x = 3/2, y = 3/2} ... skip entries to safe data	Failed [180 / 180] Result: Complex[-1.4307809877134479, -1.8200015289703178] Test Values: {Rule[x, 1.5], Rule[y, -1.5], Rule[ϕ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} Result: Complex[6.36271355956067, -6.045425917929804] Test Values: {Rule[x, 1.5], Rule[y, -1.5], Rule[ϕ, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]} ... skip entries to safe data
36.4#Ex12	${\displaystyle{\displaystyle y=\tfrac{1}{3}z^{2}(\sin\left(2\phi\right)-2\sin\phi)}}$ y = \tfrac{1}{3}z^{2}(\sin@{2\phi}-2\sin@@{\phi})	${\displaystyle{\displaystyle 0\leq\phi,\phi\leq 2\pi}}$	y = (1)/(3)*(x + y*I)^(2)*(sin(2*phi)- 2*sin(phi))	y == Divide[1,3]*(x + y*I)^(2)*(Sin[2*\[Phi]]- 2*Sin[\[Phi]])	Failure	Failure	Failed [54 / 54] Result: -1.500000000-2.780804948*I Test Values: {phi = 3/2, x = 3/2, y = -3/2} Result: 1.500000000+2.780804948*I Test Values: {phi = 3/2, x = 3/2, y = 3/2} ... skip entries to safe data	Failed [54 / 54] Result: Complex[-1.5, -2.7808049477223626] Test Values: {Rule[x, 1.5], Rule[y, -1.5], Rule[ϕ, 1.5]} Result: Complex[-1.5, -0.17607013860076426] Test Values: {Rule[x, 1.5], Rule[y, -1.5], Rule[ϕ, 0.5]} ... skip entries to safe data
36.4.E11	${\displaystyle{\displaystyle x+iy=-z^{2}\exp\left(\tfrac{2}{3}i\pi m\right)}}$ x+iy = -z^{2}\exp@{\tfrac{2}{3}i\pi m}		x + I*y = -(x + y*I)^(2)* exp((2)/(3)*I*Pi*m)	x + I*y == -(x + y*I)^(2)* Exp[Divide[2,3]*I*Pi*m]	Error	Failure	-	Skip - No test values generated
36.4#Ex13	${\displaystyle{\displaystyle x=-\tfrac{1}{12}z^{2}(\exp\left(2\tau\right)+2\exp\left(-\tau\right))}}$ x = -\tfrac{1}{12}z^{2}(\exp@{2\tau}+ 2\exp@{-\tau})		x = -(1)/(12)*(x + y*I)^(2)*(exp(2*tau)+ 2*exp(- tau))	x == -Divide[1,12]*(x + y*I)^(2)*(Exp[2*\[Tau]]+ 2*Exp[- \[Tau]])	Failure	Failure	Failed [180 / 180] Result: 3.132329502-1.422064683*I Test Values: {tau = 1/2*3^(1/2)+1/2*I, x = 3/2, y = -3/2} Result: -.132329502+1.422064683*I Test Values: {tau = 1/2*3^(1/2)+1/2*I, x = 3/2, y = 3/2} ... skip entries to safe data	Failed [180 / 180] Result: Complex[3.1323295016161525, -1.4220646828050367] Test Values: {Rule[x, 1.5], Rule[y, -1.5], Rule[τ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} Result: Complex[0.694217640570763, -0.7789550680773418] Test Values: {Rule[x, 1.5], Rule[y, -1.5], Rule[τ, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]} ... skip entries to safe data
36.4#Ex13	${\displaystyle{\displaystyle x=-\tfrac{1}{12}z^{2}(\exp\left(2\tau\right)-2\exp\left(-\tau\right))}}$ x = -\tfrac{1}{12}z^{2}(\exp@{2\tau}- 2\exp@{-\tau})		x = -(1)/(12)*(x + y*I)^(2)*(exp(2*tau)- 2*exp(- tau))	x == -Divide[1,12]*(x + y*I)^(2)*(Exp[2*\[Tau]]- 2*Exp[- \[Tau]])	Failure	Failure	Failed [180 / 180] Result: 3.434813476-.8683714834*I Test Values: {tau = 1/2*3^(1/2)+1/2*I, x = 3/2, y = -3/2} Result: -.434813476+.8683714834*I Test Values: {tau = 1/2*3^(1/2)+1/2*I, x = 3/2, y = 3/2} ... skip entries to safe data	Failed [180 / 180] Result: Complex[3.4348134754242143, -0.8683714827345889] Test Values: {Rule[x, 1.5], Rule[y, -1.5], Rule[τ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} Result: Complex[2.578112467364518, 0.8232541553428006] Test Values: {Rule[x, 1.5], Rule[y, -1.5], Rule[τ, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]} ... skip entries to safe data
36.4#Ex14	${\displaystyle{\displaystyle y=-\tfrac{1}{12}z^{2}(\exp\left(-2\tau\right)+2\exp\left(\tau\right))}}$ y = -\tfrac{1}{12}z^{2}(\exp@{-2\tau}+ 2\exp@{\tau})	${\displaystyle{\displaystyle-\infty\leq\tau,\tau<\infty.}}$	y = -(1)/(12)*(x + y*I)^(2)*(exp(- 2*tau)+ 2*exp(tau))	y == -Divide[1,12]*(x + y*I)^(2)*(Exp[- 2*\[Tau]]+ 2*Exp[\[Tau]])	Failure	Failure	Failed [108 / 108] Result: -1.500000000-7.699423965*I Test Values: {tau = -3/2, x = 3/2, y = -3/2} Result: 1.500000000+7.699423965*I Test Values: {tau = -3/2, x = 3/2, y = 3/2} ... skip entries to safe data	Failed [108 / 108] Result: Complex[-1.5, -7.699423966306697] Test Values: {Rule[x, 1.5], Rule[y, -1.5], Rule[τ, -1.5]} Result: Complex[-1.5, -3.3799369533914976] Test Values: {Rule[x, 1.5], Rule[y, -1.5], Rule[τ, 1.5]} ... skip entries to safe data
36.4#Ex14	${\displaystyle{\displaystyle y=-\tfrac{1}{12}z^{2}(\exp\left(-2\tau\right)-2\exp\left(\tau\right))}}$ y = -\tfrac{1}{12}z^{2}(\exp@{-2\tau}- 2\exp@{\tau})	${\displaystyle{\displaystyle-\infty\leq\tau,\tau<\infty.}}$	y = -(1)/(12)*(x + y*I)^(2)*(exp(- 2*tau)- 2*exp(tau))	y == -Divide[1,12]*(x + y*I)^(2)*(Exp[- 2*\[Tau]]- 2*Exp[\[Tau]])	Failure	Failure	Failed [108 / 108] Result: -1.500000000-7.364728725*I Test Values: {tau = -3/2, x = 3/2, y = -3/2} Result: 1.500000000+7.364728725*I Test Values: {tau = -3/2, x = 3/2, y = 3/2} ... skip entries to safe data	Failed [108 / 108] Result: Complex[-1.5, -7.364728726084054] Test Values: {Rule[x, 1.5], Rule[y, -1.5], Rule[τ, -1.5]} Result: Complex[-1.5, 3.3425966521155988] Test Values: {Rule[x, 1.5], Rule[y, -1.5], Rule[τ, 1.5]} ... skip entries to safe data
36.4.E13	${\displaystyle{\displaystyle x=y}}$ x = y		x = y	x == y	Skipped - no semantic math	Skipped - no semantic math	-	-