3.8: Difference between revisions

Latest revision as of 11:03, 28 June 2021

DLMF	Formula	Constraints	Maple	Mathematica	Symbolic Maple	Symbolic Mathematica	Numeric Maple	Numeric Mathematica
3.8.E2	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle z = \phi(z)} `z = \phi(z)`	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle }	z = phi(z)	z == \[Phi][z]	Skipped - no semantic math	Skipped - no semantic math	-	-
3.8.E3	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \abs{z_{n+1}-\zeta} < A\abs{z_{n}-\zeta}^{p}} `\abs{z_{n+1}-\zeta} < A\abs{z_{n}-\zeta}^{p}`	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle }	abs(z[n + 1]- zeta) < A*(abs(z[n]- zeta))^(p)	Abs[Subscript[z, n + 1]- \[Zeta]] < A*(Abs[Subscript[z, n]- \[Zeta]])^(p)	Failure	Failure	Failed [30 / 300] Result: 0. < 0. Test Values: {A = 1/23^(1/2)+1/2I, p = 1/23^(1/2)+1/2I, zeta = 1/23^(1/2)+1/2I, z[n] = 1/23^(1/2)+1/2I, z[n+1] = 1/23^(1/2)+1/2I, n = 1} Result: 0. < 0. Test Values: {A = 1/23^(1/2)+1/2I, p = 1/23^(1/2)+1/2I, zeta = 1/23^(1/2)+1/2I, z[n] = 1/23^(1/2)+1/2I, z[n+1] = 1/23^(1/2)+1/2I, n = 2} Result: 0. < 0. Test Values: {A = 1/23^(1/2)+1/2I, p = 1/23^(1/2)+1/2I, zeta = 1/23^(1/2)+1/2I, z[n] = 1/23^(1/2)+1/2I, z[n+1] = 1/23^(1/2)+1/2I, n = 3} Result: 1.414213562 < 0. Test Values: {A = 1/23^(1/2)+1/2I, p = 1/23^(1/2)+1/2I, zeta = 1/23^(1/2)+1/2I, z[n] = 1/23^(1/2)+1/2I, z[n+1] = -1/2+1/2I3^(1/2), n = 1} ... skip entries to safe data	Failed [300 / 300] Result: False Test Values: {Rule[A, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[n, 1], Rule[p, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ζ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[z, n], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[z, Plus[1, n]], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} Result: False Test Values: {Rule[A, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[n, 2], Rule[p, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ζ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[z, n], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[z, Plus[1, n]], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} ... skip entries to safe data
3.8#Ex1	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle x_{n+1} = \phi(x_{n})} `x_{n+1} = \phi(x_{n})`	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle }	x[n + 1] = phi(x[n])	Subscript[x, n + 1] == \[Phi][Subscript[x, n]]	Skipped - no semantic math	Skipped - no semantic math	-	-
3.8#Ex2	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \phi(x) = x+x\cot^{2}@@{x}-\cot@@{x}} `\phi(x) = x+x\cot^{2}@@{x}-\cot@@{x}`	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle }	phi(x) = x + x*(cot(x))^(2)- cot(x)	\[Phi][x] == x + x*(Cot[x])^(2)- Cot[x]	Failure	Failure	Failed [30 / 30] Result: -.137590423+.7500000000I Test Values: {phi = 1/23^(1/2)+1/2I, x = 1.5} Result: .881577740e-1+.2500000000I Test Values: {phi = 1/23^(1/2)+1/2I, x = .5} Result: -1.144507621+1.I Test Values: {phi = 1/23^(1/2)+1/2I, x = 2} Result: -2.186628529+1.299038106I Test Values: {phi = -1/2+1/2I3^(1/2), x = 1.5} ... skip entries to safe data	Failed [30 / 30] Result: Complex[-0.1375904227343937, 0.7499999999999999] Test Values: {Rule[x, 1.5], Rule[ϕ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} Result: Complex[-2.186628528411051, 1.299038105676658] Test Values: {Rule[x, 1.5], Rule[ϕ, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]} ... skip entries to safe data
3.8.E6	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle x_{2} = x_{1}-\frac{x_{1}-x_{0}}{f_{1}-f_{0}}f_{1}} `x_{2} = x_{1}-\frac{x_{1}-x_{0}}{f_{1}-f_{0}}f_{1}`	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle }	x[2] = x[1]-(x[1]- x[0])/(f[1]- f[0])*f[1]	Subscript[x, 2] == Subscript[x, 1]-Divide[Subscript[x, 1]- Subscript[x, 0],Subscript[f, 1]- Subscript[f, 0]]*Subscript[f, 1]	Skipped - no semantic math	Skipped - no semantic math	-	-
3.8.E7	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle z_{n+1} = z_{n}-\frac{(\phi(z_{n})-z_{n})^{2}}{\phi(\phi(z_{n}))-2\phi(z_{n})+z_{n}}} `z_{n+1} = z_{n}-\frac{(\phi(z_{n})-z_{n})^{2}}{\phi(\phi(z_{n}))-2\phi(z_{n})+z_{n}}`	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle }	z[n + 1] = z[n]-((phi(z[n])- z[n])^(2))/(phi(phi(z[n]))- 2*phi(z[n])+ z[n])	Subscript[z, n + 1] == Subscript[z, n]-Divide[(\[Phi][Subscript[z, n]]- Subscript[z, n])^(2),\[Phi][\[Phi][Subscript[z, n]]]- 2*\[Phi][Subscript[z, n]]+ Subscript[z, n]]	Skipped - no semantic math	Skipped - no semantic math	-	-
3.8#Ex3	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle z_{n+1} = \phi(z_{n})} `z_{n+1} = \phi(z_{n})`	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle }	z[n + 1] = phi(z[n])	Subscript[z, n + 1] == \[Phi][Subscript[z, n]]	Skipped - no semantic math	Skipped - no semantic math	-	-
3.8#Ex4	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \phi(z) = \frac{3z^{4}+1}{4z^{3}}} `\phi(z) = \frac{3z^{4}+1}{4z^{3}}`	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle }	phi(z) = (3(z)^(4)+ 1)/(4(z)^(3))	\[Phi][z] == Divide[3(z)^(4)+ 1,4(z)^(3)]	Skipped - no semantic math	Skipped - no semantic math	-	-
3.8#Ex7	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Delta s = \frac{r_{3}q_{0}-r_{2}q_{1}}{r_{2}^{2}-\ell r_{3}}} `\Delta s = \frac{r_{3}q_{0}-r_{2}q_{1}}{r_{2}^{2}-\ell r_{3}}`	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle }	Deltas = (r[3]q[0]- r[2]q[1])/((r[2])^(2)- ellr[3])	\[CapitalDelta]s == Divide[Subscript[r, 3]Subscript[q, 0]- Subscript[r, 2]Subscript[q, 1],(Subscript[r, 2])^(2)- \[ScriptL]Subscript[r, 3]]	Skipped - no semantic math	Skipped - no semantic math	-	-
3.8#Ex8	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Delta t = \frac{\ell q_{1}-r_{2}q_{0}}{r_{2}^{2}-\ell r_{3}}} `\Delta t = \frac{\ell q_{1}-r_{2}q_{0}}{r_{2}^{2}-\ell r_{3}}`	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle }	Deltat = (ellq[1]- r[2]q[0])/((r[2])^(2)- ellr[3])	\[CapitalDelta]t == Divide[\[ScriptL]Subscript[q, 1]- Subscript[r, 2]Subscript[q, 0],(Subscript[r, 2])^(2)- \[ScriptL]Subscript[r, 3]]	Skipped - no semantic math	Skipped - no semantic math	-	-
3.8#Ex9	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \ell = sr_{2}+tr_{3}} `\ell = sr_{2}+tr_{3}`	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle }	ell = sr[2]+ tr[3]	\[ScriptL] == sSubscript[r, 2]+ tSubscript[r, 3]	Skipped - no semantic math	Skipped - no semantic math	-	-
3.8.E13	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \deriv{z}{\alpha} = -\ifrac{\pderiv{f}{\alpha}}{\pderiv{f}{z}}} `\deriv{z}{\alpha} = -\ifrac{\pderiv{f}{\alpha}}{\pderiv{f}{z}}`	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle }	diff(z, alpha) = -(diff(f, alpha))/(diff(f, z))	D[z, \[Alpha]] == -Divide[D[f, \[Alpha]],D[f, z]]	Error	Failure	-	Failed [210 / 210] Result: Indeterminate Test Values: {Rule[f, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[α, 1.5]} Result: Indeterminate Test Values: {Rule[f, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[α, 0.5]} ... skip entries to safe data
3.8.E16	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \deriv{x}{a_{19}} = -\frac{20^{19}}{19!}} `\deriv{x}{a_{19}} = -\frac{20^{19}}{19!}`	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle }	subs( temp=a[19], diff( x, temp$(1) ) ) = -((20)^(19))/(factorial(19))	(D[x, {temp, 1}]/.temp-> Subscript[a, 19]) == -Divide[(20)^(19),(19)!]	Failure	Failure	Skip - No test values generated	Failed [30 / 30] Result: 4.309980412182177^7 Test Values: {Rule[x, 1.5], Rule[Subscript[a, 19], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} Result: 4.309980412182177^7 Test Values: {Rule[x, 1.5], Rule[Subscript[a, 19], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]} ... skip entries to safe data
3.8.E16	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle -\frac{20^{19}}{19!} = (-4.30\dots)\times 10^{7}} `-\frac{20^{19}}{19!} = (-4.30\dots)\times 10^{7}`	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle }	-((20)^(19))/(factorial(19)) = (- 4.30) * (10)^(7)	-Divide[(20)^(19),(19)!] == (- 4.30) * (10)^(7)	Translation Error	Translation Error	Skip - symbolical successful subtest	Skip - symbolical successful subtest
3.8.E17	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle z_{n+1} = \phi(z_{n})} `z_{n+1} = \phi(z_{n})`	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle }	z[n + 1] = phi(z[n])	Subscript[z, n + 1] == \[Phi][Subscript[z, n]]	Skipped - no semantic math	Skipped - no semantic math	-	-

@@ Line 14: / Line 14: @@
 ! scope="col" style="position: sticky; top: 0;" | Numeric<br>Mathematica
 |- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/3.8.E2 3.8.E2] || [[Item:Q1365|<math>z = \phi(z)</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>z = \phi(z)</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">z = phi(z)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">z == \[Phi][z]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
+| [https://dlmf.nist.gov/3.8.E2 3.8.E2] || <math qid="Q1365">z = \phi(z)</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>z = \phi(z)</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">z = phi(z)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">z == \[Phi][z]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
 |-
-| [https://dlmf.nist.gov/3.8.E3 3.8.E3] || [[Item:Q1366|<math>\abs{z_{n+1}-\zeta} < A\abs{z_{n}-\zeta}^{p}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\abs{z_{n+1}-\zeta} < A\abs{z_{n}-\zeta}^{p}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>abs(z[n + 1]- zeta) < A*(abs(z[n]- zeta))^(p)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Abs[Subscript[z, n + 1]- \[Zeta]] < A*(Abs[Subscript[z, n]- \[Zeta]])^(p)</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [30 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: 0. < 0.
+| [https://dlmf.nist.gov/3.8.E3 3.8.E3] || <math qid="Q1366">\abs{z_{n+1}-\zeta} < A\abs{z_{n}-\zeta}^{p}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\abs{z_{n+1}-\zeta} < A\abs{z_{n}-\zeta}^{p}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>abs(z[n + 1]- zeta) < A*(abs(z[n]- zeta))^(p)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Abs[Subscript[z, n + 1]- \[Zeta]] < A*(Abs[Subscript[z, n]- \[Zeta]])^(p)</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [30 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: 0. < 0.
 Test Values: {A = 1/2*3^(1/2)+1/2*I, p = 1/2*3^(1/2)+1/2*I, zeta = 1/2*3^(1/2)+1/2*I, z[n] = 1/2*3^(1/2)+1/2*I, z[n+1] = 1/2*3^(1/2)+1/2*I, n = 1}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: 0. < 0.
 Test Values: {A = 1/2*3^(1/2)+1/2*I, p = 1/2*3^(1/2)+1/2*I, zeta = 1/2*3^(1/2)+1/2*I, z[n] = 1/2*3^(1/2)+1/2*I, z[n+1] = 1/2*3^(1/2)+1/2*I, n = 2}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: 0. < 0.
@@ Line 24: / Line 24: @@
 Test Values: {Rule[A, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[n, 2], Rule[p, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ζ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[z, n], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[z, Plus[1, n]], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
 |- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/3.8#Ex1 3.8#Ex1] || [[Item:Q1368|<math>x_{n+1} = \phi(x_{n})</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>x_{n+1} = \phi(x_{n})</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">x[n + 1] = phi(x[n])</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[x, n + 1] == \[Phi][Subscript[x, n]]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
+| [https://dlmf.nist.gov/3.8#Ex1 3.8#Ex1] || <math qid="Q1368">x_{n+1} = \phi(x_{n})</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>x_{n+1} = \phi(x_{n})</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">x[n + 1] = phi(x[n])</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[x, n + 1] == \[Phi][Subscript[x, n]]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
 |-
-| [https://dlmf.nist.gov/3.8#Ex2 3.8#Ex2] || [[Item:Q1369|<math>\phi(x) = x+x\cot^{2}@@{x}-\cot@@{x}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\phi(x) = x+x\cot^{2}@@{x}-\cot@@{x}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>phi(x) = x + x*(cot(x))^(2)- cot(x)</syntaxhighlight> || <syntaxhighlight lang=mathematica>\[Phi][x] == x + x*(Cot[x])^(2)- Cot[x]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [30 / 30]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -.137590423+.7500000000*I
+| [https://dlmf.nist.gov/3.8#Ex2 3.8#Ex2] || <math qid="Q1369">\phi(x) = x+x\cot^{2}@@{x}-\cot@@{x}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\phi(x) = x+x\cot^{2}@@{x}-\cot@@{x}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>phi(x) = x + x*(cot(x))^(2)- cot(x)</syntaxhighlight> || <syntaxhighlight lang=mathematica>\[Phi][x] == x + x*(Cot[x])^(2)- Cot[x]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [30 / 30]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -.137590423+.7500000000*I
 Test Values: {phi = 1/2*3^(1/2)+1/2*I, x = 1.5}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: .881577740e-1+.2500000000*I
 Test Values: {phi = 1/2*3^(1/2)+1/2*I, x = .5}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -1.144507621+1.*I
@@ Line 34: / Line 34: @@
 Test Values: {Rule[x, 1.5], Rule[ϕ, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
 |- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/3.8.E6 3.8.E6] || [[Item:Q1370|<math>x_{2} = x_{1}-\frac{x_{1}-x_{0}}{f_{1}-f_{0}}f_{1}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>x_{2} = x_{1}-\frac{x_{1}-x_{0}}{f_{1}-f_{0}}f_{1}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">x[2] = x[1]-(x[1]- x[0])/(f[1]- f[0])*f[1]</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[x, 2] == Subscript[x, 1]-Divide[Subscript[x, 1]- Subscript[x, 0],Subscript[f, 1]- Subscript[f, 0]]*Subscript[f, 1]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
+| [https://dlmf.nist.gov/3.8.E6 3.8.E6] || <math qid="Q1370">x_{2} = x_{1}-\frac{x_{1}-x_{0}}{f_{1}-f_{0}}f_{1}</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>x_{2} = x_{1}-\frac{x_{1}-x_{0}}{f_{1}-f_{0}}f_{1}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">x[2] = x[1]-(x[1]- x[0])/(f[1]- f[0])*f[1]</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[x, 2] == Subscript[x, 1]-Divide[Subscript[x, 1]- Subscript[x, 0],Subscript[f, 1]- Subscript[f, 0]]*Subscript[f, 1]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
 |- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/3.8.E7 3.8.E7] || [[Item:Q1371|<math>z_{n+1} = z_{n}-\frac{(\phi(z_{n})-z_{n})^{2}}{\phi(\phi(z_{n}))-2\phi(z_{n})+z_{n}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>z_{n+1} = z_{n}-\frac{(\phi(z_{n})-z_{n})^{2}}{\phi(\phi(z_{n}))-2\phi(z_{n})+z_{n}}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">z[n + 1] = z[n]-((phi(z[n])- z[n])^(2))/(phi(phi(z[n]))- 2*phi(z[n])+ z[n])</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[z, n + 1] == Subscript[z, n]-Divide[(\[Phi][Subscript[z, n]]- Subscript[z, n])^(2),\[Phi][\[Phi][Subscript[z, n]]]- 2*\[Phi][Subscript[z, n]]+ Subscript[z, n]]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
+| [https://dlmf.nist.gov/3.8.E7 3.8.E7] || <math qid="Q1371">z_{n+1} = z_{n}-\frac{(\phi(z_{n})-z_{n})^{2}}{\phi(\phi(z_{n}))-2\phi(z_{n})+z_{n}}</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>z_{n+1} = z_{n}-\frac{(\phi(z_{n})-z_{n})^{2}}{\phi(\phi(z_{n}))-2\phi(z_{n})+z_{n}}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">z[n + 1] = z[n]-((phi(z[n])- z[n])^(2))/(phi(phi(z[n]))- 2*phi(z[n])+ z[n])</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[z, n + 1] == Subscript[z, n]-Divide[(\[Phi][Subscript[z, n]]- Subscript[z, n])^(2),\[Phi][\[Phi][Subscript[z, n]]]- 2*\[Phi][Subscript[z, n]]+ Subscript[z, n]]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
 |- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/3.8#Ex3 3.8#Ex3] || [[Item:Q1373|<math>z_{n+1} = \phi(z_{n})</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>z_{n+1} = \phi(z_{n})</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">z[n + 1] = phi(z[n])</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[z, n + 1] == \[Phi][Subscript[z, n]]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
+| [https://dlmf.nist.gov/3.8#Ex3 3.8#Ex3] || <math qid="Q1373">z_{n+1} = \phi(z_{n})</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>z_{n+1} = \phi(z_{n})</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">z[n + 1] = phi(z[n])</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[z, n + 1] == \[Phi][Subscript[z, n]]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
 |- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/3.8#Ex4 3.8#Ex4] || [[Item:Q1374|<math>\phi(z) = \frac{3z^{4}+1}{4z^{3}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\phi(z) = \frac{3z^{4}+1}{4z^{3}}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">phi(z) = (3*(z)^(4)+ 1)/(4*(z)^(3))</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">\[Phi][z] == Divide[3*(z)^(4)+ 1,4*(z)^(3)]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
+| [https://dlmf.nist.gov/3.8#Ex4 3.8#Ex4] || <math qid="Q1374">\phi(z) = \frac{3z^{4}+1}{4z^{3}}</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\phi(z) = \frac{3z^{4}+1}{4z^{3}}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">phi(z) = (3*(z)^(4)+ 1)/(4*(z)^(3))</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">\[Phi][z] == Divide[3*(z)^(4)+ 1,4*(z)^(3)]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
 |- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/3.8#Ex7 3.8#Ex7] || [[Item:Q1377|<math>\Delta s = \frac{r_{3}q_{0}-r_{2}q_{1}}{r_{2}^{2}-\ell r_{3}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\Delta s = \frac{r_{3}q_{0}-r_{2}q_{1}}{r_{2}^{2}-\ell r_{3}}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Delta*s = (r[3]*q[0]- r[2]*q[1])/((r[2])^(2)- ell*r[3])</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">\[CapitalDelta]*s == Divide[Subscript[r, 3]*Subscript[q, 0]- Subscript[r, 2]*Subscript[q, 1],(Subscript[r, 2])^(2)- \[ScriptL]*Subscript[r, 3]]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
+| [https://dlmf.nist.gov/3.8#Ex7 3.8#Ex7] || <math qid="Q1377">\Delta s = \frac{r_{3}q_{0}-r_{2}q_{1}}{r_{2}^{2}-\ell r_{3}}</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\Delta s = \frac{r_{3}q_{0}-r_{2}q_{1}}{r_{2}^{2}-\ell r_{3}}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Delta*s = (r[3]*q[0]- r[2]*q[1])/((r[2])^(2)- ell*r[3])</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">\[CapitalDelta]*s == Divide[Subscript[r, 3]*Subscript[q, 0]- Subscript[r, 2]*Subscript[q, 1],(Subscript[r, 2])^(2)- \[ScriptL]*Subscript[r, 3]]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
 |- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/3.8#Ex8 3.8#Ex8] || [[Item:Q1378|<math>\Delta t = \frac{\ell q_{1}-r_{2}q_{0}}{r_{2}^{2}-\ell r_{3}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\Delta t = \frac{\ell q_{1}-r_{2}q_{0}}{r_{2}^{2}-\ell r_{3}}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Delta*t = (ell*q[1]- r[2]*q[0])/((r[2])^(2)- ell*r[3])</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">\[CapitalDelta]*t == Divide[\[ScriptL]*Subscript[q, 1]- Subscript[r, 2]*Subscript[q, 0],(Subscript[r, 2])^(2)- \[ScriptL]*Subscript[r, 3]]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
+| [https://dlmf.nist.gov/3.8#Ex8 3.8#Ex8] || <math qid="Q1378">\Delta t = \frac{\ell q_{1}-r_{2}q_{0}}{r_{2}^{2}-\ell r_{3}}</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\Delta t = \frac{\ell q_{1}-r_{2}q_{0}}{r_{2}^{2}-\ell r_{3}}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Delta*t = (ell*q[1]- r[2]*q[0])/((r[2])^(2)- ell*r[3])</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">\[CapitalDelta]*t == Divide[\[ScriptL]*Subscript[q, 1]- Subscript[r, 2]*Subscript[q, 0],(Subscript[r, 2])^(2)- \[ScriptL]*Subscript[r, 3]]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
 |- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/3.8#Ex9 3.8#Ex9] || [[Item:Q1379|<math>\ell = sr_{2}+tr_{3}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\ell = sr_{2}+tr_{3}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">ell = s*r[2]+ t*r[3]</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">\[ScriptL] == s*Subscript[r, 2]+ t*Subscript[r, 3]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
+| [https://dlmf.nist.gov/3.8#Ex9 3.8#Ex9] || <math qid="Q1379">\ell = sr_{2}+tr_{3}</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\ell = sr_{2}+tr_{3}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">ell = s*r[2]+ t*r[3]</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">\[ScriptL] == s*Subscript[r, 2]+ t*Subscript[r, 3]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
 |-
-| [https://dlmf.nist.gov/3.8.E13 3.8.E13] || [[Item:Q1381|<math>\deriv{z}{\alpha} = -\ifrac{\pderiv{f}{\alpha}}{\pderiv{f}{z}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\deriv{z}{\alpha} = -\ifrac{\pderiv{f}{\alpha}}{\pderiv{f}{z}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>diff(z, alpha) = -(diff(f, alpha))/(diff(f, z))</syntaxhighlight> || <syntaxhighlight lang=mathematica>D[z, \[Alpha]] == -Divide[D[f, \[Alpha]],D[f, z]]</syntaxhighlight> || Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [210 / 210]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Indeterminate
+| [https://dlmf.nist.gov/3.8.E13 3.8.E13] || <math qid="Q1381">\deriv{z}{\alpha} = -\ifrac{\pderiv{f}{\alpha}}{\pderiv{f}{z}}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\deriv{z}{\alpha} = -\ifrac{\pderiv{f}{\alpha}}{\pderiv{f}{z}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>diff(z, alpha) = -(diff(f, alpha))/(diff(f, z))</syntaxhighlight> || <syntaxhighlight lang=mathematica>D[z, \[Alpha]] == -Divide[D[f, \[Alpha]],D[f, z]]</syntaxhighlight> || Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [210 / 210]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Indeterminate
 Test Values: {Rule[f, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[α, 1.5]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Indeterminate
 Test Values: {Rule[f, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[α, 0.5]}</syntaxhighlight><br>... skip entries to safe data</div></div>
 |-
-| [https://dlmf.nist.gov/3.8.E16 3.8.E16] || [[Item:Q1384|<math>\deriv{x}{a_{19}} = -\frac{20^{19}}{19!}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\deriv{x}{a_{19}} = -\frac{20^{19}}{19!}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>subs( temp=a[19], diff( x, temp$(1) ) ) = -((20)^(19))/(factorial(19))</syntaxhighlight> || <syntaxhighlight lang=mathematica>(D[x, {temp, 1}]/.temp-> Subscript[a, 19]) == -Divide[(20)^(19),(19)!]</syntaxhighlight> || Failure || Failure || Skip - No test values generated || <div class="toccolours mw-collapsible mw-collapsed">Failed [30 / 30]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: 4.309980412182177*^7
+| [https://dlmf.nist.gov/3.8.E16 3.8.E16] || <math qid="Q1384">\deriv{x}{a_{19}} = -\frac{20^{19}}{19!}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\deriv{x}{a_{19}} = -\frac{20^{19}}{19!}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>subs( temp=a[19], diff( x, temp$(1) ) ) = -((20)^(19))/(factorial(19))</syntaxhighlight> || <syntaxhighlight lang=mathematica>(D[x, {temp, 1}]/.temp-> Subscript[a, 19]) == -Divide[(20)^(19),(19)!]</syntaxhighlight> || Failure || Failure || Skip - No test values generated || <div class="toccolours mw-collapsible mw-collapsed">Failed [30 / 30]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: 4.309980412182177*^7
 Test Values: {Rule[x, 1.5], Rule[Subscript[a, 19], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: 4.309980412182177*^7
 Test Values: {Rule[x, 1.5], Rule[Subscript[a, 19], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
 |-
-| [https://dlmf.nist.gov/3.8.E16 3.8.E16] || [[Item:Q1384|<math>-\frac{20^{19}}{19!} = (-4.30\dots)\times 10^{7}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>-\frac{20^{19}}{19!} = (-4.30\dots)\times 10^{7}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>-((20)^(19))/(factorial(19)) = (- 4.30) * (10)^(7)</syntaxhighlight> || <syntaxhighlight lang=mathematica>-Divide[(20)^(19),(19)!] == (- 4.30) * (10)^(7)</syntaxhighlight> || Translation Error || Translation Error || Skip - symbolical successful subtest || Skip - symbolical successful subtest
+| [https://dlmf.nist.gov/3.8.E16 3.8.E16] || <math qid="Q1384">-\frac{20^{19}}{19!} = (-4.30\dots)\times 10^{7}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>-\frac{20^{19}}{19!} = (-4.30\dots)\times 10^{7}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>-((20)^(19))/(factorial(19)) = (- 4.30) * (10)^(7)</syntaxhighlight> || <syntaxhighlight lang=mathematica>-Divide[(20)^(19),(19)!] == (- 4.30) * (10)^(7)</syntaxhighlight> || Translation Error || Translation Error || Skip - symbolical successful subtest || Skip - symbolical successful subtest
 |- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/3.8.E17 3.8.E17] || [[Item:Q1385|<math>z_{n+1} = \phi(z_{n})</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>z_{n+1} = \phi(z_{n})</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">z[n + 1] = phi(z[n])</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[z, n + 1] == \[Phi][Subscript[z, n]]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
+| [https://dlmf.nist.gov/3.8.E17 3.8.E17] || <math qid="Q1385">z_{n+1} = \phi(z_{n})</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>z_{n+1} = \phi(z_{n})</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">z[n + 1] = phi(z[n])</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[z, n + 1] == \[Phi][Subscript[z, n]]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
 |}
 </div>

3.8: Difference between revisions

Latest revision as of 11:03, 28 June 2021

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