Results of Algebraic and Analytic Methods: Difference between revisions

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; Notation : [[1.1|1.1 Special Notation]]<br>
! DLMF !! Formula !! Constraints !! Maple !! Mathematica !! Symbolic<br>Maple !! Symbolic<br>Mathematica !! Numeric<br>Maple !! Numeric<br>Mathematica
; Areas : [[1.2|1.2 Elementary Algebra]]<br>[[1.3|1.3 Determinants]]<br>[[1.4|1.4 Calculus of One Variable]]<br>[[1.5|1.5 Calculus of Two or More Variables]]<br>[[1.6|1.6 Vectors and Vector-Valued Functions]]<br>[[1.7|1.7 Inequalities]]<br>[[1.8|1.8 Fourier Series]]<br>[[1.9|1.9 Calculus of a Complex Variable]]<br>[[1.10|1.10 Functions of a Complex Variable]]<br>[[1.11|1.11 Zeros of Polynomials]]<br>[[1.12|1.12 Continued Fractions]]<br>[[1.13|1.13 Differential Equations]]<br>[[1.14|1.14 Integral Transforms]]<br>[[1.15|1.15 Summability Methods]]<br>[[1.16|1.16 Distributions]]<br>[[1.17|1.17 Integral and Series Representations of the Dirac Delta]]<br>
|-
</div>
| [https://dlmf.nist.gov/1.2.E1 1.2.E1] || [[Item:Q30|<math>\binom{n}{k} = \frac{n!}{(n-k)!k!}</math>]]<br><code>\binom{n}{k} = \frac{n!}{(n-k)!k!}</code> || <math></math> || <code>binomial(n,k) = (factorial(n))/(factorial(n - k)*factorial(k))</code> || <code>Binomial[n,k] == Divide[(n)!,(n - k)!*(k)!]</code> || Successful || Successful || - || Successful [Tested: 9]
|-
| [https://dlmf.nist.gov/1.2.E1 1.2.E1] || [[Item:Q30|<math>\frac{n!}{(n-k)!k!} = \binom{n}{n-k}</math>]]<br><code>\frac{n!}{(n-k)!k!} = \binom{n}{n-k}</code> || <math></math> || <code>(factorial(n))/(factorial(n - k)*factorial(k)) = binomial(n,n - k)</code> || <code>Divide[(n)!,(n - k)!*(k)!] == Binomial[n,n - k]</code> || Successful || Successful || - || Successful [Tested: 9]
|-
| [https://dlmf.nist.gov/1.2.E6 1.2.E6] || [[Item:Q35|<math>\frac{(-1)^{k}\Pochhammersym{-z}{k}}{k!} = (-1)^{k}\binom{k-z-1}{k}</math>]]<br><code>\frac{(-1)^{k}\Pochhammersym{-z}{k}}{k!} = (-1)^{k}\binom{k-z-1}{k}</code> || <math></math> || <code>((- 1)^(k)* pochhammer(- z, k))/(factorial(k)) = (- 1)^(k)*binomial(k - z - 1,k)</code> || <code>Divide[(- 1)^(k)* Pochhammer[- z, k],(k)!] == (- 1)^(k)*Binomial[k - z - 1,k]</code> || Successful || Successful || - || Successful [Tested: 21]
|-
| [https://dlmf.nist.gov/1.2.E7 1.2.E7] || [[Item:Q36|<math>\binom{z+1}{k} = \binom{z}{k}+\binom{z}{k-1}</math>]]<br><code>\binom{z+1}{k} = \binom{z}{k}+\binom{z}{k-1}</code> || <math></math> || <code>binomial(z + 1,k) = binomial(z,k)+binomial(z,k - 1)</code> || <code>Binomial[z + 1,k] == Binomial[z,k]+Binomial[z,k - 1]</code> || Successful || Successful || - || Successful [Tested: 21]
|-
| [https://dlmf.nist.gov/1.2.E8 1.2.E8] || [[Item:Q37|<math>\sum^{m}_{k=0}\binom{z+k}{k} = \binom{z+m+1}{m}</math>]]<br><code>\sum^{m}_{k=0}\binom{z+k}{k} = \binom{z+m+1}{m}</code> || <math></math> || <code>sum(binomial(z + k,k), k = 0..m) = binomial(z + m + 1,m)</code> || <code>Sum[Binomial[z + k,k], {k, 0, m}, GenerateConditions->None] == Binomial[z + m + 1,m]</code> || Successful || Successful || - || Successful [Tested: 21]
|-
| [https://dlmf.nist.gov/1.2.E10 1.2.E10] || [[Item:Q39|<math>na+\tfrac{1}{2}n(n-1)d = \tfrac{1}{2}n(a+\ell)</math>]]<br><code>na+\tfrac{1}{2}n(n-1)d = \tfrac{1}{2}n(a+\ell)</code> || <math></math> || <code>n*a +(1)/(2)*n*(n - 1)*d = (1)/(2)*n*(a + ell)</code> || <code>n*a +Divide[1,2]*n*(n - 1)*d == Divide[1,2]*n*(a + \[ScriptL])</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
|-
| [https://dlmf.nist.gov/1.2.E22 1.2.E22] || [[Item:Q51|<math>M(r) = 0</math>]]<br><code>M(r) = 0</code> || <math></math> || <code>M(r) = 0</code> || <code>M[r] == 0</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
|-
| [https://dlmf.nist.gov/1.2#Ex1 1.2#Ex1] || [[Item:Q54|<math>M(1) = A</math>]]<br><code>M(1) = A</code> || <math></math> || <code>M(1) = A</code> || <code>M[1] == A</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
|-
| [https://dlmf.nist.gov/1.2#Ex2 1.2#Ex2] || [[Item:Q55|<math>M(-1) = H</math>]]<br><code>M(-1) = H</code> || <math></math> || <code>M(- 1) = H</code> || <code>M[- 1] == H</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
|-
| [https://dlmf.nist.gov/1.2.E26 1.2.E26] || [[Item:Q56|<math>\lim_{r\to 0}M(r) = G</math>]]<br><code>\lim_{r\to 0}M(r) = G</code> || <math></math> || <code>limit(M(r), r = 0) = G</code> || <code>Limit[M[r], r -> 0, GenerateConditions->None] == G</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
|-
| [https://dlmf.nist.gov/1.4.E8 1.4.E8] || [[Item:Q87|<math>f^{(2)}(x) = \deriv[2]{f}{x}</math>]]<br><code>f^{(2)}(x) = \deriv[2]{f}{x}</code> || <math></math> || <code>(f(x))^(2) = diff(f, [x$(2)])</code> || <code>(f[x])^(2) == D[f, {x, 2}]</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [30 / 30]<div class="mw-collapsible-content"><code>30/30]: [[.7500000006+1.299038106*I <- {f = 1/2*3^(1/2)+1/2*I, x = 1.5}</code><br><code>.2500000002+.4330127020*I <- {f = 1/2*3^(1/2)+1/2*I, x = .5}</code><br><code>1.000000001+1.732050808*I <- {f = 1/2*3^(1/2)+1/2*I, x = 2}</code><br><code>-.7500000006-1.299038106*I <- {f = -1/2+1/2*I*3^(1/2), x = 1.5}</code><br>... skip entries to safe data<br></div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [30 / 30]<div class="mw-collapsible-content"><code>{Complex[0.7500000000000002, 1.299038105676658] <- {Rule[f, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[x, 1.5]}</code><br><code>Complex[0.25000000000000006, 0.4330127018922193] <- {Rule[f, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[x, 0.5]}</code><br></div></div>
|-
| [https://dlmf.nist.gov/1.4.E8 1.4.E8] || [[Item:Q87|<math>\deriv[2]{f}{x} = \deriv{}{x}\left(\deriv{f}{x}\right)</math>]]<br><code>\deriv[2]{f}{x} = \deriv{}{x}\left(\deriv{f}{x}\right)</code> || <math></math> || <code>diff(f, [x$(2)]) = diff(diff(f, x), x)</code> || <code>D[f, {x, 2}] == D[D[f, x], x]</code> || Successful || Successful || Skip - symbolical successful subtest || Successful [Tested: 30]
|-
| [https://dlmf.nist.gov/1.4.E9 1.4.E9] || [[Item:Q88|<math>f^{(n)}(x) = \deriv{}{x}f^{(n-1)}(x)</math>]]<br><code>f^{(n)}(x) = \deriv{}{x}f^{(n-1)}(x)</code> || <math></math> || <code>(f(x))^(n) = diff((f(x))^(n - 1), x)</code> || <code>(f[x])^(n) == D[(f[x])^(n - 1), x]</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [84 / 90]<div class="mw-collapsible-content"><code>84/90]: [[.299038106+.7500000000*I <- {f = 1/2*3^(1/2)+1/2*I, x = 1.5, n = 1}</code><br><code>-.1160254034+.7990381060*I <- {f = 1/2*3^(1/2)+1/2*I, x = 1.5, n = 2}</code><br><code>-.4999999999+.6339745980*I <- {f = 1/2*3^(1/2)+1/2*I, x = 1.5, n = 3}</code><br><code>-.5669872980+.2500000000*I <- {f = 1/2*3^(1/2)+1/2*I, x = .5, n = 1}</code><br>... skip entries to safe data<br></div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [84 / 90]<div class="mw-collapsible-content"><code>{Complex[0.299038105676658, 0.7499999999999999] <- {Rule[f, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[n, 1], Rule[x, 1.5]}</code><br><code>Complex[-0.11602540378443849, 0.799038105676658] <- {Rule[f, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[n, 2], Rule[x, 1.5]}</code><br></div></div>
|-
| [https://dlmf.nist.gov/1.4.E16 1.4.E16] || [[Item:Q95|<math>\int fg\diff{x} = \left(\int f\diff{x}\right)g-\int\left(\int f\diff{x}\right)\deriv{g}{x}\diff{x}</math>]]<br><code>\int fg\diff{x} = \left(\int f\diff{x}\right)g-\int\left(\int f\diff{x}\right)\deriv{g}{x}\diff{x}</code> || <math></math> || <code>int(f*g, x) = (int(f, x))*g - int((int(f, x))*diff(g, x), x)</code> || <code>Integrate[f*g, x, GenerateConditions->None] == (Integrate[f, x, GenerateConditions->None])*g - Integrate[(Integrate[f, x, GenerateConditions->None])*D[g, x], x, GenerateConditions->None]</code> || Successful || Successful || - || Successful [Tested: 100]
|-
| [https://dlmf.nist.gov/1.4.E36 1.4.E36] || [[Item:Q115|<math>R_{n} = \frac{f^{(n+1)}(c)}{(n+1)!}(x-a)^{n+1}</math>]]<br><code>R_{n} = \frac{f^{(n+1)}(c)}{(n+1)!}(x-a)^{n+1}</code> || <math>a < c, c < x</math> || <code>R[n] = ((f(c))^(n + 1))/(factorial(n + 1))*(x - a)^(n + 1)</code> || <code>Subscript[R, n] == Divide[(f[c])^(n + 1),(n + 1)!]*(x - a)^(n + 1)</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
|-
| [https://dlmf.nist.gov/1.4.E37 1.4.E37] || [[Item:Q116|<math>R_{n} = \frac{1}{n!}\int^{x}_{a}(x-t)^{n}f^{(n+1)}(t)\diff{t}</math>]]<br><code>R_{n} = \frac{1}{n!}\int^{x}_{a}(x-t)^{n}f^{(n+1)}(t)\diff{t}</code> || <math></math> || <code>R[n] = (1)/(factorial(n))*int((x - t)^(n)* (f(t))^(n + 1), t = a..x)</code> || <code>Subscript[R, n] == Divide[1,(n)!]*Integrate[(x - t)^(n)* (f[t])^(n + 1), {t, a, x}, GenerateConditions->None]</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><code>300/300]: [[1.991025404+2.448557159*I <- {a = -1.5, f = 1/2*3^(1/2)+1/2*I, x = 1.5, R[n] = 1/2*3^(1/2)+1/2*I, n = 1}</code><br><code>.8660254040+3.875000000*I <- {a = -1.5, f = 1/2*3^(1/2)+1/2*I, x = 1.5, R[n] = 1/2*3^(1/2)+1/2*I, n = 2}</code><br><code>-.6527245960+3.130552164*I <- {a = -1.5, f = 1/2*3^(1/2)+1/2*I, x = 1.5, R[n] = 1/2*3^(1/2)+1/2*I, n = 3}</code><br><code>.6250000000+2.814582563*I <- {a = -1.5, f = 1/2*3^(1/2)+1/2*I, x = 1.5, R[n] = -1/2+1/2*I*3^(1/2), n = 1}</code><br>... skip entries to safe data<br></div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><code>{Complex[1.9910254037844388, 2.4485571585149866] <- {Rule[a, -1.5], Rule[f, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[n, 1], Rule[x, 1.5], Rule[Subscript[R, n], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br><code>Complex[0.8660254037844387, 3.875] <- {Rule[a, -1.5], Rule[f, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[n, 2], Rule[x, 1.5], Rule[Subscript[R, n], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br></div></div>
|-
| [https://dlmf.nist.gov/1.5.E4 1.5.E4] || [[Item:Q121|<math>\pderiv{f}{y} = D_{y}f</math>]]<br><code>\pderiv{f}{y} = D_{y}f</code> || <math></math> || <code>diff(f, y) = D[y]*f</code> || <code>D[f, y] == Subscript[D, y]*f</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><code>300/300]: [[-.5000000004-.8660254040*I <- {f = 1/2*3^(1/2)+1/2*I, y = -1.5, D[y] = 1/2*3^(1/2)+1/2*I}</code><br><code>.8660254040-.5000000004*I <- {f = 1/2*3^(1/2)+1/2*I, y = -1.5, D[y] = -1/2+1/2*I*3^(1/2)}</code><br><code>-.8660254040+.5000000004*I <- {f = 1/2*3^(1/2)+1/2*I, y = -1.5, D[y] = 1/2-1/2*I*3^(1/2)}</code><br><code>.5000000004+.8660254040*I <- {f = 1/2*3^(1/2)+1/2*I, y = -1.5, D[y] = -1/2*3^(1/2)-1/2*I}</code><br>... skip entries to safe data<br></div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><code>{Complex[-0.5000000000000001, -0.8660254037844386] <- {Rule[f, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[y, -1.5], Rule[Subscript[D, y], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br><code>Complex[0.8660254037844387, -0.49999999999999994] <- {Rule[f, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[y, -1.5], Rule[Subscript[D, y], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</code><br></div></div>
|-
| [https://dlmf.nist.gov/1.5.E4 1.5.E4] || [[Item:Q121|<math>D_{y}f = f_{y}</math>]]<br><code>D_{y}f = f_{y}</code> || <math></math> || <code>D[y]*f = f[y]</code> || <code>Subscript[D, y]*f == Subscript[f, y]</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><code>300/300]: [[-.3660254036+.3660254040*I <- {f = 1/2*3^(1/2)+1/2*I, y = -1.5, D[y] = 1/2*3^(1/2)+1/2*I, f[y] = 1/2*3^(1/2)+1/2*I}</code><br><code>1.000000000+0.*I <- {f = 1/2*3^(1/2)+1/2*I, y = -1.5, D[y] = 1/2*3^(1/2)+1/2*I, f[y] = -1/2+1/2*I*3^(1/2)}</code><br><code>.4e-9+1.732050808*I <- {f = 1/2*3^(1/2)+1/2*I, y = -1.5, D[y] = 1/2*3^(1/2)+1/2*I, f[y] = 1/2-1/2*I*3^(1/2)}</code><br><code>1.366025404+1.366025404*I <- {f = 1/2*3^(1/2)+1/2*I, y = -1.5, D[y] = 1/2*3^(1/2)+1/2*I, f[y] = -1/2*3^(1/2)-1/2*I}</code><br>... skip entries to safe data<br></div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><code>{Complex[-0.3660254037844386, 0.36602540378443865] <- {Rule[f, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[y, -1.5], Rule[Subscript[D, y], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[f, y], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br><code>Complex[0.9999999999999999, -1.1102230246251565*^-16] <- {Rule[f, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[y, -1.5], Rule[Subscript[D, y], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[f, y], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</code><br></div></div>
|-
| [https://dlmf.nist.gov/1.5#Ex3 1.5#Ex3] || [[Item:Q128|<math>x = r\cos@@{\phi}</math>]]<br><code>x = r\cos@@{\phi}</code> || <math></math> || <code>x = r*cos(phi)</code> || <code>x == r*Cos[\[Phi]]</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [180 / 180]<div class="mw-collapsible-content"><code>180/180]: [[2.595814528-.5954243254*I <- {phi = 1/2*3^(1/2)+1/2*I, r = -1.5, x = 1.5}</code><br><code>1.595814528-.5954243254*I <- {phi = 1/2*3^(1/2)+1/2*I, r = -1.5, x = .5}</code><br><code>3.095814528-.5954243254*I <- {phi = 1/2*3^(1/2)+1/2*I, r = -1.5, x = 2}</code><br><code>.404185472+.5954243254*I <- {phi = 1/2*3^(1/2)+1/2*I, r = 1.5, x = 1.5}</code><br>... skip entries to safe data<br></div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [180 / 180]<div class="mw-collapsible-content"><code>{Complex[2.595814528585838, -0.5954243253435487] <- {Rule[r, -1.5], Rule[x, 1.5], Rule[ϕ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br><code>Complex[3.3416482752961656, 0.7036130644027555] <- {Rule[r, -1.5], Rule[x, 1.5], Rule[ϕ, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</code><br></div></div>
|-
| [https://dlmf.nist.gov/1.5#Ex4 1.5#Ex4] || [[Item:Q129|<math>y = r\sin@@{\phi}</math>]]<br><code>y = r\sin@@{\phi}</code> || <math></math> || <code>y = r*sin(phi)</code> || <code>y == r*Sin[\[Phi]]</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><code>300/300]: [[-.211529498+.5063946946*I <- {phi = 1/2*3^(1/2)+1/2*I, r = -1.5, y = -1.5}</code><br><code>2.788470502+.5063946946*I <- {phi = 1/2*3^(1/2)+1/2*I, r = -1.5, y = 1.5}</code><br><code>.788470502+.5063946946*I <- {phi = 1/2*3^(1/2)+1/2*I, r = -1.5, y = -.5}</code><br><code>1.788470502+.5063946946*I <- {phi = 1/2*3^(1/2)+1/2*I, r = -1.5, y = .5}</code><br>... skip entries to safe data<br></div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><code>{Complex[-0.21152949854979308, 0.506394694834305] <- {Rule[r, -1.5], Rule[y, -1.5], Rule[ϕ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br><code>Complex[-2.506097038210817, 1.2879550752257174] <- {Rule[r, -1.5], Rule[y, -1.5], Rule[ϕ, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</code><br></div></div>
|-
| [https://dlmf.nist.gov/1.5.E13 1.5.E13] || [[Item:Q132|<math>\pderiv[2]{f}{x}+\pderiv[2]{f}{y} = \pderiv[2]{f}{r}+\frac{1}{r}\pderiv{f}{r}+\frac{1}{r^{2}}\pderiv[2]{f}{\phi}</math>]]<br><code>\pderiv[2]{f}{x}+\pderiv[2]{f}{y} = \pderiv[2]{f}{r}+\frac{1}{r}\pderiv{f}{r}+\frac{1}{r^{2}}\pderiv[2]{f}{\phi}</code> || <math></math> || <code>diff(f, [x$(2)])+ diff(f, [y$(2)]) = diff(f, [r$(2)])+(1)/(r)*diff(f, r)+(1)/((r)^(2))*diff(f, [phi$(2)])</code> || <code>D[f, {x, 2}]+ D[f, {y, 2}] == D[f, {r, 2}]+Divide[1,r]*D[f, r]+Divide[1,(r)^(2)]*D[f, {\[Phi], 2}]</code> || Successful || Successful || - || Successful [Tested: 300]
|-
| [https://dlmf.nist.gov/1.5#Ex5 1.5#Ex5] || [[Item:Q133|<math>x = r\cos@@{\phi}</math>]]<br><code>x = r\cos@@{\phi}</code> || <math></math> || <code>x = r*cos(phi)</code> || <code>x == r*Cos[\[Phi]]</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [180 / 180]<div class="mw-collapsible-content"><code>180/180]: [[2.595814528-.5954243254*I <- {phi = 1/2*3^(1/2)+1/2*I, r = -1.5, x = 1.5}</code><br><code>1.595814528-.5954243254*I <- {phi = 1/2*3^(1/2)+1/2*I, r = -1.5, x = .5}</code><br><code>3.095814528-.5954243254*I <- {phi = 1/2*3^(1/2)+1/2*I, r = -1.5, x = 2}</code><br><code>.404185472+.5954243254*I <- {phi = 1/2*3^(1/2)+1/2*I, r = 1.5, x = 1.5}</code><br>... skip entries to safe data<br></div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [180 / 180]<div class="mw-collapsible-content"><code>{Complex[2.595814528585838, -0.5954243253435487] <- {Rule[r, -1.5], Rule[x, 1.5], Rule[ϕ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br><code>Complex[3.3416482752961656, 0.7036130644027555] <- {Rule[r, -1.5], Rule[x, 1.5], Rule[ϕ, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</code><br></div></div>
|-
| [https://dlmf.nist.gov/1.5#Ex6 1.5#Ex6] || [[Item:Q134|<math>y = r\sin@@{\phi}</math>]]<br><code>y = r\sin@@{\phi}</code> || <math></math> || <code>y = r*sin(phi)</code> || <code>y == r*Sin[\[Phi]]</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><code>300/300]: [[-.211529498+.5063946946*I <- {phi = 1/2*3^(1/2)+1/2*I, r = -1.5, y = -1.5}</code><br><code>2.788470502+.5063946946*I <- {phi = 1/2*3^(1/2)+1/2*I, r = -1.5, y = 1.5}</code><br><code>.788470502+.5063946946*I <- {phi = 1/2*3^(1/2)+1/2*I, r = -1.5, y = -.5}</code><br><code>1.788470502+.5063946946*I <- {phi = 1/2*3^(1/2)+1/2*I, r = -1.5, y = .5}</code><br>... skip entries to safe data<br></div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><code>{Complex[-0.21152949854979308, 0.506394694834305] <- {Rule[r, -1.5], Rule[y, -1.5], Rule[ϕ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br><code>Complex[-2.506097038210817, 1.2879550752257174] <- {Rule[r, -1.5], Rule[y, -1.5], Rule[ϕ, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</code><br></div></div>
|-
| [https://dlmf.nist.gov/1.5#Ex7 1.5#Ex7] || [[Item:Q135|<math>z = z</math>]]<br><code>z = z</code> || <math></math> || <code>z = z</code> || <code>z == z</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
|-
| [https://dlmf.nist.gov/1.5.E15 1.5.E15] || [[Item:Q136|<math>\pderiv[2]{f}{x}+\pderiv[2]{f}{y}+\pderiv[2]{f}{z} = \pderiv[2]{f}{r}+\frac{1}{r}\pderiv{f}{r}+\frac{1}{r^{2}}\pderiv[2]{f}{\phi}+\pderiv[2]{f}{z}</math>]]<br><code>\pderiv[2]{f}{x}+\pderiv[2]{f}{y}+\pderiv[2]{f}{z} = \pderiv[2]{f}{r}+\frac{1}{r}\pderiv{f}{r}+\frac{1}{r^{2}}\pderiv[2]{f}{\phi}+\pderiv[2]{f}{z}</code> || <math></math> || <code>diff(f, [x$(2)])+ diff(f, [y$(2)])+ subs( temp=(x + y*I), diff( f, temp$(2) ) ) = diff(f, [r$(2)])+(1)/(r)*diff(f, r)+(1)/((r)^(2))*diff(f, [phi$(2)])+ subs( temp=(x + y*I), diff( f, temp$(2) ) )</code> || <code>D[f, {x, 2}]+ D[f, {y, 2}]+ (D[f, {temp, 2}]/.temp-> (x + y*I)) == D[f, {r, 2}]+Divide[1,r]*D[f, r]+Divide[1,(r)^(2)]*D[f, {\[Phi], 2}]+ (D[f, {temp, 2}]/.temp-> (x + y*I))</code> || Successful || Successful || - || Successful [Tested: 300]
|-
| [https://dlmf.nist.gov/1.5#Ex8 1.5#Ex8] || [[Item:Q137|<math>x = \rho\sin@@{\theta}\cos@@{\phi}</math>]]<br><code>x = \rho\sin@@{\theta}\cos@@{\phi}</code> || <math></math> || <code>x = rho*sin(theta)*cos(phi)</code> || <code>x == \[Rho]*Sin[\[Theta]]*Cos[\[Phi]]</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><code>300/300]: [[.7933233780-.2990618885*I <- {phi = 1/2*3^(1/2)+1/2*I, rho = 1/2*3^(1/2)+1/2*I, theta = 1/2*3^(1/2)+1/2*I, x = 1.5}</code><br><code>-.2066766220-.2990618885*I <- {phi = 1/2*3^(1/2)+1/2*I, rho = 1/2*3^(1/2)+1/2*I, theta = 1/2*3^(1/2)+1/2*I, x = .5}</code><br><code>1.293323378-.2990618885*I <- {phi = 1/2*3^(1/2)+1/2*I, rho = 1/2*3^(1/2)+1/2*I, theta = 1/2*3^(1/2)+1/2*I, x = 2}</code><br><code>2.075937432-.6992275886*I <- {phi = 1/2*3^(1/2)+1/2*I, rho = 1/2*3^(1/2)+1/2*I, theta = -1/2+1/2*I*3^(1/2), x = 1.5}</code><br>... skip entries to safe data<br></div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><code>{Complex[0.7933233783531031, -0.29906188871772155] <- {Rule[x, 1.5], Rule[θ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ρ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ϕ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br><code>Complex[1.1325168401075085, -1.15603698835011] <- {Rule[x, 1.5], Rule[θ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ρ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ϕ, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</code><br></div></div>
|-
| [https://dlmf.nist.gov/1.5#Ex9 1.5#Ex9] || [[Item:Q138|<math>y = \rho\sin@@{\theta}\sin@@{\phi}</math>]]<br><code>y = \rho\sin@@{\theta}\sin@@{\phi}</code> || <math></math> || <code>y = rho*sin(theta)*sin(phi)</code> || <code>y == \[Rho]*Sin[\[Theta]]*Sin[\[Phi]]</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><code>300/300]: [[-1.750303606-.8142131232*I <- {phi = 1/2*3^(1/2)+1/2*I, rho = 1/2*3^(1/2)+1/2*I, theta = 1/2*3^(1/2)+1/2*I, y = -1.5}</code><br><code>1.249696394-.8142131232*I <- {phi = 1/2*3^(1/2)+1/2*I, rho = 1/2*3^(1/2)+1/2*I, theta = 1/2*3^(1/2)+1/2*I, y = 1.5}</code><br><code>-.7503036064-.8142131232*I <- {phi = 1/2*3^(1/2)+1/2*I, rho = 1/2*3^(1/2)+1/2*I, theta = 1/2*3^(1/2)+1/2*I, y = -.5}</code><br><code>.2496963936-.8142131232*I <- {phi = 1/2*3^(1/2)+1/2*I, rho = 1/2*3^(1/2)+1/2*I, theta = 1/2*3^(1/2)+1/2*I, y = .5}</code><br>... skip entries to safe data<br></div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><code>{Complex[-1.750303605777159, -0.8142131229438421] <- {Rule[y, -1.5], Rule[θ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ρ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ϕ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br><code>Complex[-0.49444885508381575, -0.009630141394747549] <- {Rule[y, -1.5], Rule[θ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ρ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ϕ, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</code><br></div></div>
|-
| [https://dlmf.nist.gov/1.5#Ex10 1.5#Ex10] || [[Item:Q139|<math>z = \rho\cos@@{\theta}</math>]]<br><code>z = \rho\cos@@{\theta}</code> || <math></math> || <code>z = rho*cos(theta)</code> || <code>z == \[Rho]*Cos[\[Theta]]</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><code>300/300]: [[.348818158e-1+.4784968852*I <- {rho = 1/2*3^(1/2)+1/2*I, theta = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I}</code><br><code>-1.331143588+.8445222892*I <- {rho = 1/2*3^(1/2)+1/2*I, theta = 1/2*3^(1/2)+1/2*I, z = -1/2+1/2*I*3^(1/2)}</code><br><code>-.3311435882-.8875285188*I <- {rho = 1/2*3^(1/2)+1/2*I, theta = 1/2*3^(1/2)+1/2*I, z = 1/2-1/2*I*3^(1/2)}</code><br><code>-1.697168992-.5215031148*I <- {rho = 1/2*3^(1/2)+1/2*I, theta = 1/2*3^(1/2)+1/2*I, z = -1/2*3^(1/2)-1/2*I}</code><br>... skip entries to safe data<br></div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><code>{Complex[0.03488181560898618, 0.4784968849905366] <- {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[θ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ρ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br><code>Complex[0.8875285187939019, -0.3311435881754526] <- {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[θ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ρ, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</code><br></div></div>
|-
| [https://dlmf.nist.gov/1.5.E17 1.5.E17] || [[Item:Q140|<math>\pderiv[2]{f}{x}+\pderiv[2]{f}{y}+\pderiv[2]{f}{z} = {\frac{1}{\rho^{2}}\pderiv{}{\rho}\left(\rho^{2}\pderiv{f}{\rho}\right)+\frac{1}{\rho^{2}\sin^{2}@@{\theta}}\pderiv[2]{f}{\phi}}+\frac{1}{\rho^{2}\sin@@{\theta}}\pderiv{}{\theta}\left(\sin@@{\theta}\pderiv{f}{\theta}\right)</math>]]<br><code>\pderiv[2]{f}{x}+\pderiv[2]{f}{y}+\pderiv[2]{f}{z} = {\frac{1}{\rho^{2}}\pderiv{}{\rho}\left(\rho^{2}\pderiv{f}{\rho}\right)+\frac{1}{\rho^{2}\sin^{2}@@{\theta}}\pderiv[2]{f}{\phi}}+\frac{1}{\rho^{2}\sin@@{\theta}}\pderiv{}{\theta}\left(\sin@@{\theta}\pderiv{f}{\theta}\right)</code> || <math></math> || <code>diff(f, [x$(2)])+ diff(f, [y$(2)])+ subs( temp=(x + y*I), diff( f, temp$(2) ) ) = (1)/((rho)^(2))*diff(((rho)^(2)* diff(f, rho))+(1)/((rho)^(2)* (sin(theta))^(2))*diff(f, [phi$(2)]), rho)+(1)/((rho)^(2)* sin(theta))*diff(sin(theta)*diff(f, theta), theta)</code> || <code>D[f, {x, 2}]+ D[f, {y, 2}]+ (D[f, {temp, 2}]/.temp-> (x + y*I)) == Divide[1,\[Rho]^(2)]*D[(\[Rho]^(2)* D[f, \[Rho]])+Divide[1,\[Rho]^(2)* (Sin[\[Theta]])^(2)]*D[f, {\[Phi], 2}], \[Rho]]+Divide[1,\[Rho]^(2)* Sin[\[Theta]]]*D[Sin[\[Theta]]*D[f, \[Theta]], \[Theta]]</code> || Successful || Successful || - || Successful [Tested: 300]
|-
| [https://dlmf.nist.gov/1.5.E19 1.5.E19] || [[Item:Q142|<math>\pderiv{f}{x} = \pderiv{f}{y}</math>]]<br><code>\pderiv{f}{x} = \pderiv{f}{y}</code> || <math></math> || <code>diff(f, x) = diff(f, y)</code> || <code>D[f, x] == D[f, y]</code> || Successful || Successful || - || Successful [Tested: 180]
|-
| [https://dlmf.nist.gov/1.5.E23 1.5.E23] || [[Item:Q146|<math>\abs{\int_{c_{1}}^{d}(\ipderiv{f}{x})\diff{y}} < \epsilon</math>]]<br><code>\abs{\int_{c_{1}}^{d}(\ipderiv{f}{x})\diff{y}} < \epsilon</code> || <math></math> || <code>abs(int(diff(f, x), y = c[1]..d)) < epsilon</code> || <code>Abs[Integrate[D[f, x], {y, Subscript[c, 1], d}, GenerateConditions->None]] < \[Epsilon]</code> || Failure || Failure || Successful [Tested: 300] || Successful [Tested: 300]
|-
| [https://dlmf.nist.gov/1.5.E25 1.5.E25] || [[Item:Q148|<math>a = x_{0}</math>]]<br><code>a = x_{0}</code> || <math></math> || <code>a = x[0]</code> || <code>a == Subscript[x, 0]</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
|-
| [https://dlmf.nist.gov/1.5.E26 1.5.E26] || [[Item:Q149|<math>c = y_{0}</math>]]<br><code>c = y_{0}</code> || <math></math> || <code>c = y[0]</code> || <code>c == Subscript[y, 0]</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
|-
| [https://dlmf.nist.gov/1.5#Ex11 1.5#Ex11] || [[Item:Q153|<math>a \leq x</math>]]<br><code>a \leq x</code> || <math></math> || <code>a <= x</code> || <code>a <= x</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
|-
| [https://dlmf.nist.gov/1.5#Ex12 1.5#Ex12] || [[Item:Q154|<math>\phi_{1}(x) \leq y</math>]]<br><code>\phi_{1}(x) \leq y</code> || <math></math> || <code>phi[1](x) <= y</code> || <code>Subscript[\[Phi], 1][x] <= y</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
|-
| [https://dlmf.nist.gov/1.5#Ex13 1.5#Ex13] || [[Item:Q157|<math>c \leq y</math>]]<br><code>c \leq y</code> || <math></math> || <code>c <= y</code> || <code>c <= y</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
|-
| [https://dlmf.nist.gov/1.5#Ex14 1.5#Ex14] || [[Item:Q158|<math>\psi_{1}(y) \leq x</math>]]<br><code>\psi_{1}(y) \leq x</code> || <math></math> || <code>psi[1](y) <= x</code> || <code>Subscript[\[Psi], 1][y] <= x</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
|-
| [https://dlmf.nist.gov/1.5#Ex15 1.5#Ex15] || [[Item:Q162|<math>a \leq x</math>]]<br><code>a \leq x</code> || <math></math> || <code>a <= x</code> || <code>a <= x</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
|-
| [https://dlmf.nist.gov/1.5#Ex16 1.5#Ex16] || [[Item:Q163|<math>\phi_{1}(x) \leq y</math>]]<br><code>\phi_{1}(x) \leq y</code> || <math></math> || <code>phi[1](x) <= y</code> || <code>Subscript[\[Phi], 1][x] <= y</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
|-
| [https://dlmf.nist.gov/1.5#Ex17 1.5#Ex17] || [[Item:Q164|<math>\psi_{1}(x,y) \leq z</math>]]<br><code>\psi_{1}(x,y) \leq z</code> || <math></math> || <code>psi[1](x , y) <= (x + y*I)</code> || <code>Subscript[\[Psi], 1][x , y] <= (x + y*I)</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
|-
| [https://dlmf.nist.gov/1.6#Ex1 1.6#Ex1] || [[Item:Q171|<math>\mathbf{a} = (a_{1},a_{2},a_{3})</math>]]<br><code>\mathbf{a} = (a_{1},a_{2},a_{3})</code> || <math></math> || <code>a = (a[1], a[2], a[3])</code> || <code>a == (Subscript[a, 1], Subscript[a, 2], Subscript[a, 3])</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
|-
| [https://dlmf.nist.gov/1.6#Ex2 1.6#Ex2] || [[Item:Q172|<math>\mathbf{b} = (b_{1},b_{2},b_{3})</math>]]<br><code>\mathbf{b} = (b_{1},b_{2},b_{3})</code> || <math></math> || <code>b = (b[1], b[2], b[3])</code> || <code>b == (Subscript[b, 1], Subscript[b, 2], Subscript[b, 3])</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
|-
| [https://dlmf.nist.gov/1.6.E2 1.6.E2] || [[Item:Q173|<math>\mathbf{a}\cdot\mathbf{b} = a_{1}b_{1}+a_{2}b_{2}+a_{3}b_{3}</math>]]<br><code>\mathbf{a}\cdot\mathbf{b} = a_{1}b_{1}+a_{2}b_{2}+a_{3}b_{3}</code> || <math></math> || <code>a * b = a[1]*b[1]+ a[2]*b[2]+ a[3]*b[3]</code> || <code>a * b == Subscript[a, 1]*Subscript[b, 1]+ Subscript[a, 2]*Subscript[b, 2]+ Subscript[a, 3]*Subscript[b, 3]</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
|-
| [https://dlmf.nist.gov/1.6.E3 1.6.E3] || [[Item:Q174|<math>\|\mathbf{a}\| = \sqrt{\mathbf{a}\cdot\mathbf{a}}</math>]]<br><code>\|\mathbf{a}\| = \sqrt{\mathbf{a}\cdot\mathbf{a}}</code> || <math></math> || <code>Error</code> || <code>Norm[a] == Sqrt[a * a]</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
|-
| [https://dlmf.nist.gov/1.6.E4 1.6.E4] || [[Item:Q175|<math>\cos@@{\theta} = \frac{\mathbf{a}\cdot\mathbf{b}}{\|\mathbf{a}\|\;\|\mathbf{b}\|}</math>]]<br><code>\cos@@{\theta} = \frac{\mathbf{a}\cdot\mathbf{b}}{\|\mathbf{a}\|\;\|\mathbf{b}\|}</code> || <math></math> || <code>Error</code> || <code>Cos[\[Theta]] == Divide[a * b,Norm[a]*Norm[b]]</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><code>300/300]: [[-.2694569811-.3969495503*I <- {a = -1.5, b = -1.5, theta = 1/2*3^(1/2)+1/2*I}</code><br><code>.227765517+.4690753764*I <- {a = -1.5, b = -1.5, theta = -1/2+1/2*I*3^(1/2)}</code><br><code>.227765517+.4690753764*I <- {a = -1.5, b = -1.5, theta = 1/2-1/2*I*3^(1/2)}</code><br><code>-.2694569811-.3969495503*I <- {a = -1.5, b = -1.5, theta = -1/2*3^(1/2)-1/2*I}</code><br>... skip entries to safe data<br></div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><code>{Complex[-0.2694569809427748, -0.3969495502290325] <- {Rule[a, -1.5], Rule[b, -1.5], Rule[θ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br><code>Complex[0.2277655168641104, 0.46907537626850365] <- {Rule[a, -1.5], Rule[b, -1.5], Rule[θ, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</code><br></div></div>
|-
| [https://dlmf.nist.gov/1.6.E6 1.6.E6] || [[Item:Q179|<math>\mathbf{a} = a_{1}\mathbf{i}+a_{2}\mathbf{j}+a_{3}\mathbf{k}</math>]]<br><code>\mathbf{a} = a_{1}\mathbf{i}+a_{2}\mathbf{j}+a_{3}\mathbf{k}</code> || <math></math> || <code>a = a[1]*I + a[2]*j + a[3]*k</code> || <code>a == Subscript[a, 1]*I + Subscript[a, 2]*j + Subscript[a, 3]*k</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
|-
| [https://dlmf.nist.gov/1.6#Ex6 1.6#Ex6] || [[Item:Q180|<math>\mathbf{i}\times\mathbf{j} = \mathbf{k}</math>]]<br><code>\mathbf{i}\times\mathbf{j} = \mathbf{k}</code> || <math></math> || <code>I * j = k</code> || <code>I * j == k</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
|-
| [https://dlmf.nist.gov/1.6#Ex7 1.6#Ex7] || [[Item:Q181|<math>\mathbf{j}\times\mathbf{k} = \mathbf{i}</math>]]<br><code>\mathbf{j}\times\mathbf{k} = \mathbf{i}</code> || <math></math> || <code>j * k = I</code> || <code>j * k == I</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
|-
| [https://dlmf.nist.gov/1.6#Ex8 1.6#Ex8] || [[Item:Q182|<math>\mathbf{k}\times\mathbf{i} = \mathbf{j}</math>]]<br><code>\mathbf{k}\times\mathbf{i} = \mathbf{j}</code> || <math></math> || <code>k * I = j</code> || <code>k * I == j</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
|-
| [https://dlmf.nist.gov/1.6#Ex9 1.6#Ex9] || [[Item:Q183|<math>\mathbf{j}\times\mathbf{i} = -\mathbf{k}</math>]]<br><code>\mathbf{j}\times\mathbf{i} = -\mathbf{k}</code> || <math></math> || <code>j * I = - k</code> || <code>j * I == - k</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
|-
| [https://dlmf.nist.gov/1.6#Ex10 1.6#Ex10] || [[Item:Q184|<math>\mathbf{k}\times\mathbf{j} = -\mathbf{i}</math>]]<br><code>\mathbf{k}\times\mathbf{j} = -\mathbf{i}</code> || <math></math> || <code>k * j = - I</code> || <code>k * j == - I</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
|-
| [https://dlmf.nist.gov/1.6#Ex11 1.6#Ex11] || [[Item:Q185|<math>\mathbf{i}\times\mathbf{k} = -\mathbf{j}</math>]]<br><code>\mathbf{i}\times\mathbf{k} = -\mathbf{j}</code> || <math></math> || <code>I * k = - j</code> || <code>I * k == - j</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
|-
| [https://dlmf.nist.gov/1.6.E12 1.6.E12] || [[Item:Q189|<math>a_{j}b_{j} = \sum_{j=1}^{3}a_{j}b_{j}</math>]]<br><code>a_{j}b_{j} = \sum_{j=1}^{3}a_{j}b_{j}</code> || <math></math> || <code>a[j]*b[j] = sum(a[j]*b[j], j = 1..3)</code> || <code>Subscript[a, j]*Subscript[b, j] == Sum[Subscript[a, j]*Subscript[b, j], {j, 1, 3}, GenerateConditions->None]</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
|-
| [https://dlmf.nist.gov/1.6#Ex15 1.6#Ex15] || [[Item:Q194|<math>\LeviCivitasym{1}{2}{3} = \LeviCivitasym{3}{1}{2}</math>]]<br><code>\LeviCivitasym{1}{2}{3} = \LeviCivitasym{3}{1}{2}</code> || <math></math> || <code>LeviCivita[1, 2, 3] = LeviCivita[3, 1, 2]</code> || <code>Part[LeviCivitaTensor[3,List], 1, 2, 3] == Part[LeviCivitaTensor[3,List], 3, 1, 2]</code> || Successful || Successful || - || Successful [Tested: 1]
|-
| [https://dlmf.nist.gov/1.6#Ex15 1.6#Ex15] || [[Item:Q194|<math>\LeviCivitasym{3}{1}{2} = 1</math>]]<br><code>\LeviCivitasym{3}{1}{2} = 1</code> || <math></math> || <code>LeviCivita[3, 1, 2] = 1</code> || <code>Part[LeviCivitaTensor[3,List], 3, 1, 2] == 1</code> || Successful || Successful || - || Successful [Tested: 1]
|-
| [https://dlmf.nist.gov/1.6#Ex16 1.6#Ex16] || [[Item:Q195|<math>\LeviCivitasym{2}{1}{3} = \LeviCivitasym{3}{2}{1}</math>]]<br><code>\LeviCivitasym{2}{1}{3} = \LeviCivitasym{3}{2}{1}</code> || <math></math> || <code>LeviCivita[2, 1, 3] = LeviCivita[3, 2, 1]</code> || <code>Part[LeviCivitaTensor[3,List], 2, 1, 3] == Part[LeviCivitaTensor[3,List], 3, 2, 1]</code> || Successful || Successful || - || Successful [Tested: 1]
|-
| [https://dlmf.nist.gov/1.6#Ex16 1.6#Ex16] || [[Item:Q195|<math>\LeviCivitasym{3}{2}{1} = -1</math>]]<br><code>\LeviCivitasym{3}{2}{1} = -1</code> || <math></math> || <code>LeviCivita[3, 2, 1] = - 1</code> || <code>Part[LeviCivitaTensor[3,List], 3, 2, 1] == - 1</code> || Successful || Successful || - || Successful [Tested: 1]
|-
| [https://dlmf.nist.gov/1.6#Ex17 1.6#Ex17] || [[Item:Q196|<math>\LeviCivitasym{2}{2}{1} = 0</math>]]<br><code>\LeviCivitasym{2}{2}{1} = 0</code> || <math></math> || <code>LeviCivita[2, 2, 1] = 0</code> || <code>Part[LeviCivitaTensor[3,List], 2, 2, 1] == 0</code> || Successful || Successful || - || Successful [Tested: 1]
|-
| [https://dlmf.nist.gov/1.6.E16 1.6.E16] || [[Item:Q197|<math>\LeviCivitasym{j}{k}{\ell}\LeviCivitasym{\ell}{m}{n} = \Kroneckerdelta{j}{m}\Kroneckerdelta{k}{n}-\Kroneckerdelta{j}{n}\Kroneckerdelta{k}{m}</math>]]<br><code>\LeviCivitasym{j}{k}{\ell}\LeviCivitasym{\ell}{m}{n} = \Kroneckerdelta{j}{m}\Kroneckerdelta{k}{n}-\Kroneckerdelta{j}{n}\Kroneckerdelta{k}{m}</code> || <math></math> || <code>LeviCivita[j, k, ell]*LeviCivita[ell, m, n] = KroneckerDelta[j, m]*KroneckerDelta[k, n]- KroneckerDelta[j, n]*KroneckerDelta[k, m]</code> || <code>Part[LeviCivitaTensor[3,List], j, k, \[ScriptL]]*Part[LeviCivitaTensor[3,List], \[ScriptL], m, n] == KroneckerDelta[j, m]*KroneckerDelta[k, n]- KroneckerDelta[j, n]*KroneckerDelta[k, m]</code> || Failure || Failure || Error || Error
|-
| [https://dlmf.nist.gov/1.6.E17 1.6.E17] || [[Item:Q198|<math>\mathbf{e}_{j}\times\mathbf{e}_{k} = \LeviCivitasym{j}{k}{\ell}\mathbf{e}_{\ell}</math>]]<br><code>\mathbf{e}_{j}\times\mathbf{e}_{k} = \LeviCivitasym{j}{k}{\ell}\mathbf{e}_{\ell}</code> || <math></math> || <code>exp(1)[j] * exp(1)[k] = LeviCivita[j, k, ell]*exp(1)[ell]</code> || <code>Subscript[E, j] * Subscript[E, k] == Part[LeviCivitaTensor[3,List], j, k, \[ScriptL]]*Subscript[E, \[ScriptL]]</code> || Translation Error || Translation Error || - || -
|-
| [https://dlmf.nist.gov/1.6.E18 1.6.E18] || [[Item:Q199|<math>a_{j}\mathbf{e}_{j}\times b_{k}\mathbf{e}_{k} = \LeviCivitasym{j}{k}{\ell}a_{j}b_{k}\mathbf{e}_{\ell}</math>]]<br><code>a_{j}\mathbf{e}_{j}\times b_{k}\mathbf{e}_{k} = \LeviCivitasym{j}{k}{\ell}a_{j}b_{k}\mathbf{e}_{\ell}</code> || <math></math> || <code>a[j]*exp(1)[j] * b[k]*exp(1)[k] = LeviCivita[j, k, ell]*a[j]*b[k]*exp(1)[ell]</code> || <code>Subscript[a, j]*Subscript[E, j] * Subscript[b, k]*Subscript[E, k] == Part[LeviCivitaTensor[3,List], j, k, \[ScriptL]]*Subscript[a, j]*Subscript[b, k]*Subscript[E, \[ScriptL]]</code> || Translation Error || Translation Error || - || -
|-
| [https://dlmf.nist.gov/1.6.E43 1.6.E43] || [[Item:Q224|<math>\mathbf{F}(x,y) = F_{1}(x,y)\mathbf{i}+F_{2}(x,y)\mathbf{j}</math>]]<br><code>\mathbf{F}(x,y) = F_{1}(x,y)\mathbf{i}+F_{2}(x,y)\mathbf{j}</code> || <math></math> || <code>F(x , y) = F[1](x , y)* I + F[2](x , y)* j</code> || <code>F[x , y] == Subscript[F, 1][x , y]* I + Subscript[F, 2][x , y]* j</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
|-
| [https://dlmf.nist.gov/1.6.E46 1.6.E46] || [[Item:Q227|<math>\mathbf{T}_{u} = \pderiv{x}{u}(u_{0},v_{0})\mathbf{i}+\pderiv{y}{u}(u_{0},v_{0})\mathbf{j}+\pderiv{z}{u}(u_{0},v_{0})\mathbf{k}</math>]]<br><code>\mathbf{T}_{u} = \pderiv{x}{u}(u_{0},v_{0})\mathbf{i}+\pderiv{y}{u}(u_{0},v_{0})\mathbf{j}+\pderiv{z}{u}(u_{0},v_{0})\mathbf{k}</code> || <math></math> || <code>T[u] = diff(x, u)*(u[0], v[0])*I + diff(y, u)*(u[0], v[0])*j + diff(x + y*I, u)*(u[0], v[0])*k</code> || <code>Subscript[T, u] == D[x, u]*(Subscript[u, 0], Subscript[v, 0])*I + D[y, u]*(Subscript[u, 0], Subscript[v, 0])*j + D[x + y*I, u]*(Subscript[u, 0], Subscript[v, 0])*k</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><code>300/300]: [[.8660254040+.5000000000*I <- {u = 1/2*3^(1/2)+1/2*I, x = 1.5, y = -1.5, T[u] = 1/2*3^(1/2)+1/2*I, u[0] = 1/2*3^(1/2)+1/2*I, v[0] = 1/2*3^(1/2)+1/2*I, j = 1, k = 1}</code><br><code>.8660254040+.5000000000*I <- {u = 1/2*3^(1/2)+1/2*I, x = 1.5, y = -1.5, T[u] = 1/2*3^(1/2)+1/2*I, u[0] = 1/2*3^(1/2)+1/2*I, v[0] = 1/2*3^(1/2)+1/2*I, j = 1, k = 2}</code><br><code>.8660254040+.5000000000*I <- {u = 1/2*3^(1/2)+1/2*I, x = 1.5, y = -1.5, T[u] = 1/2*3^(1/2)+1/2*I, u[0] = 1/2*3^(1/2)+1/2*I, v[0] = 1/2*3^(1/2)+1/2*I, j = 1, k = 3}</code><br><code>.8660254040+.5000000000*I <- {u = 1/2*3^(1/2)+1/2*I, x = 1.5, y = -1.5, T[u] = 1/2*3^(1/2)+1/2*I, u[0] = 1/2*3^(1/2)+1/2*I, v[0] = 1/2*3^(1/2)+1/2*I, j = 2, k = 1}</code><br>... skip entries to safe data<br></div></div> || -
|-
| [https://dlmf.nist.gov/1.6.E47 1.6.E47] || [[Item:Q228|<math>\mathbf{T}_{v} = \pderiv{x}{v}(u_{0},v_{0})\mathbf{i}+\pderiv{y}{v}(u_{0},v_{0})\mathbf{j}+\pderiv{z}{v}(u_{0},v_{0})\mathbf{k}</math>]]<br><code>\mathbf{T}_{v} = \pderiv{x}{v}(u_{0},v_{0})\mathbf{i}+\pderiv{y}{v}(u_{0},v_{0})\mathbf{j}+\pderiv{z}{v}(u_{0},v_{0})\mathbf{k}</code> || <math></math> || <code>T[v] = diff(x, v)*(u[0], v[0])*I + diff(y, v)*(u[0], v[0])*j + diff(x + y*I, v)*(u[0], v[0])*k</code> || <code>Subscript[T, v] == D[x, v]*(Subscript[u, 0], Subscript[v, 0])*I + D[y, v]*(Subscript[u, 0], Subscript[v, 0])*j + D[x + y*I, v]*(Subscript[u, 0], Subscript[v, 0])*k</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><code>300/300]: [[.8660254040+.5000000000*I <- {v = 1/2*3^(1/2)+1/2*I, x = 1.5, y = -1.5, T[v] = 1/2*3^(1/2)+1/2*I, u[0] = 1/2*3^(1/2)+1/2*I, v[0] = 1/2*3^(1/2)+1/2*I, j = 1, k = 1}</code><br><code>.8660254040+.5000000000*I <- {v = 1/2*3^(1/2)+1/2*I, x = 1.5, y = -1.5, T[v] = 1/2*3^(1/2)+1/2*I, u[0] = 1/2*3^(1/2)+1/2*I, v[0] = 1/2*3^(1/2)+1/2*I, j = 1, k = 2}</code><br><code>.8660254040+.5000000000*I <- {v = 1/2*3^(1/2)+1/2*I, x = 1.5, y = -1.5, T[v] = 1/2*3^(1/2)+1/2*I, u[0] = 1/2*3^(1/2)+1/2*I, v[0] = 1/2*3^(1/2)+1/2*I, j = 1, k = 3}</code><br><code>.8660254040+.5000000000*I <- {v = 1/2*3^(1/2)+1/2*I, x = 1.5, y = -1.5, T[v] = 1/2*3^(1/2)+1/2*I, u[0] = 1/2*3^(1/2)+1/2*I, v[0] = 1/2*3^(1/2)+1/2*I, j = 2, k = 1}</code><br>... skip entries to safe data<br></div></div> || Error
|-
| [https://dlmf.nist.gov/1.6.E49 1.6.E49] || [[Item:Q230|<math>\|\mathbf{T}_{u}\times\mathbf{T}_{v}\| = \sqrt{\left(\pderiv{(x,y)}{(u,v)}\right)^{2}+\left(\pderiv{(y,z)}{(u,v)}\right)^{2}+\left(\pderiv{(x,z)}{(u,v)}\right)^{2}}</math>]]<br><code>\|\mathbf{T}_{u}\times\mathbf{T}_{v}\| = \sqrt{\left(\pderiv{(x,y)}{(u,v)}\right)^{2}+\left(\pderiv{(y,z)}{(u,v)}\right)^{2}+\left(\pderiv{(x,z)}{(u,v)}\right)^{2}}</code> || <math></math> || <code>Error</code> || <code>Norm[Subscript[T, u] * Subscript[T, v]] == Sqrt[(((D[(x , y), {temp, 1}]/.temp-> (u , v))))^(2)+(((D[(y ,(x + y*I)), {temp, 1}]/.temp-> (u , v))))^(2)+(((D[(x ,(x + y*I)), {temp, 1}]/.temp-> (u , v))))^(2)]</code> || Translation Error || Translation Error || - || -
|-
| [https://dlmf.nist.gov/1.6.E50 1.6.E50] || [[Item:Q231|<math>\|\mathbf{T}_{\theta}\times\mathbf{T}_{\phi}\| = \rho^{2}\abs{\sin@@{\theta}}</math>]]<br><code>\|\mathbf{T}_{\theta}\times\mathbf{T}_{\phi}\| = \rho^{2}\abs{\sin@@{\theta}}</code> || <math></math> || <code>Error</code> || <code>Norm[Subscript[T, \[Theta]] * Subscript[T, \[Phi]]] == \[Rho]^(2)* Abs[Sin[\[Theta]]]</code> || Translation Error || Translation Error || - || -
|-
| [https://dlmf.nist.gov/1.7.E1 1.7.E1] || [[Item:Q242|<math>\left(\sum^{n}_{j=1}a_{j}b_{j}\right)^{2} \leq \left(\sum^{n}_{j=1}a_{j}^{2}\right)\left(\sum^{n}_{j=1}b_{j}^{2}\right)</math>]]<br><code>\left(\sum^{n}_{j=1}a_{j}b_{j}\right)^{2} \leq \left(\sum^{n}_{j=1}a_{j}^{2}\right)\left(\sum^{n}_{j=1}b_{j}^{2}\right)</code> || <math></math> || <code>(sum(a[j]*b[j], j = 1..n))^(2) <= (sum((a[j])^(2), j = 1..n))*(sum((b[j])^(2), j = 1..n))</code> || <code>((Sum[Subscript[a, j]*Subscript[b, j], {j, 1, n}, GenerateConditions->None]))^(2) <= (Sum[(Subscript[a, j])^(2), {j, 1, n}, GenerateConditions->None])*(Sum[(Subscript[b, j])^(2), {j, 1, n}, GenerateConditions->None])</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
|-
| [https://dlmf.nist.gov/1.7.E2 1.7.E2] || [[Item:Q243|<math>\sum^{n}_{j=1}a_{j}b_{j} \leq \left(\sum^{n}_{j=1}a_{j}^{p}\right)^{1/p}\left(\sum^{n}_{j=1}b_{j}^{q}\right)^{1/q}</math>]]<br><code>\sum^{n}_{j=1}a_{j}b_{j} \leq \left(\sum^{n}_{j=1}a_{j}^{p}\right)^{1/p}\left(\sum^{n}_{j=1}b_{j}^{q}\right)^{1/q}</code> || <math></math> || <code>sum(a[j]*b[j], j = 1..n) <= (sum((a[j])^(p), j = 1..n))^(1/p)*(sum((b[j])^(q), j = 1..n))^(1/q)</code> || <code>Sum[Subscript[a, j]*Subscript[b, j], {j, 1, n}, GenerateConditions->None] <= ((Sum[(Subscript[a, j])^(p), {j, 1, n}, GenerateConditions->None]))^(1/p)*((Sum[(Subscript[b, j])^(q), {j, 1, n}, GenerateConditions->None]))^(1/q)</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
|-
| [https://dlmf.nist.gov/1.7.E3 1.7.E3] || [[Item:Q244|<math>\left(\sum^{n}_{j=1}(a_{j}+b_{j})^{p}\right)^{1/p} \leq \left(\sum^{n}_{j=1}a_{j}^{p}\right)^{1/p}+\left(\sum^{n}_{j=1}b_{j}^{p}\right)^{1/p}</math>]]<br><code>\left(\sum^{n}_{j=1}(a_{j}+b_{j})^{p}\right)^{1/p} \leq \left(\sum^{n}_{j=1}a_{j}^{p}\right)^{1/p}+\left(\sum^{n}_{j=1}b_{j}^{p}\right)^{1/p}</code> || <math></math> || <code>(sum((a[j]+ b[j])^(p), j = 1..n))^(1/p) <= (sum((a[j])^(p), j = 1..n))^(1/p)+(sum((b[j])^(p), j = 1..n))^(1/p)</code> || <code>((Sum[(Subscript[a, j]+ Subscript[b, j])^(p), {j, 1, n}, GenerateConditions->None]))^(1/p) <= ((Sum[(Subscript[a, j])^(p), {j, 1, n}, GenerateConditions->None]))^(1/p)+((Sum[(Subscript[b, j])^(p), {j, 1, n}, GenerateConditions->None]))^(1/p)</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
|-
| [https://dlmf.nist.gov/1.7.E7 1.7.E7] || [[Item:Q248|<math>H \leq G</math>]]<br><code>H \leq G</code> || <math></math> || <code>H <= G</code> || <code>H <= G</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
|-
| [https://dlmf.nist.gov/1.7.E9 1.7.E9] || [[Item:Q250|<math>M(r) \leq M(s)</math>]]<br><code>M(r) \leq M(s)</code> || <math>r < s</math> || <code>M(r) <= M(s)</code> || <code>M[r] <= M[s]</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
|-
| [https://dlmf.nist.gov/1.8.E16 1.8.E16] || [[Item:Q270|<math>\sum_{n=-\infty}^{\infty}e^{-(n+x)^{2}\omega} = {\sqrt{\frac{\pi}{\omega}}\*\left(1+2\sum_{n=1}^{\infty}e^{-n^{2}\pi^{2}/\omega}\cos@{2n\pi x}\right)}</math>]]<br><code>\sum_{n=-\infty}^{\infty}e^{-(n+x)^{2}\omega} = {\sqrt{\frac{\pi}{\omega}}\*\left(1+2\sum_{n=1}^{\infty}e^{-n^{2}\pi^{2}/\omega}\cos@{2n\pi x}\right)}</code> || <math>\realpart@@{\omega} > 0</math> || <code>sum(exp(-(n + x)^(2)* omega), n = - infinity..infinity) = sqrt((Pi)/(omega))*(1 + 2*sum(exp(- (n)^(2)* (Pi)^(2)/omega)*cos(2*n*Pi*x), n = 1..infinity))</code> || <code>Sum[Exp[-(n + x)^(2)* \[Omega]], {n, - Infinity, Infinity}, GenerateConditions->None] == Sqrt[Divide[Pi,\[Omega]]]*(1 + 2*Sum[Exp[- (n)^(2)* (Pi)^(2)/\[Omega]]*Cos[2*n*Pi*x], {n, 1, Infinity}, GenerateConditions->None])</code> || Failure || Successful || Successful [Tested: 15] || Successful [Tested: 15]
|-
| [https://dlmf.nist.gov/1.9.E1 1.9.E1] || [[Item:Q271|<math>z = x+iy</math>]]<br><code>z = x+iy</code> || <math></math> || <code>(x + y*I) = x + I*y</code> || <code>(x + y*I) == x + I*y</code> || Successful || Successful || - || Successful [Tested: 1]
|-
| [https://dlmf.nist.gov/1.9#Ex1 1.9#Ex1] || [[Item:Q272|<math>\realpart@@{z} = x</math>]]<br><code>\realpart@@{z} = x</code> || <math></math> || <code>Re(x + y*I) = x</code> || <code>Re[x + y*I] == x</code> || Failure || Failure || Successful [Tested: 18] || Successful [Tested: 18]
|-
| [https://dlmf.nist.gov/1.9#Ex2 1.9#Ex2] || [[Item:Q273|<math>\imagpart@@{z} = y</math>]]<br><code>\imagpart@@{z} = y</code> || <math></math> || <code>Im(x + y*I) = y</code> || <code>Im[x + y*I] == y</code> || Failure || Failure || Successful [Tested: 18] || Successful [Tested: 18]
|-
| [https://dlmf.nist.gov/1.9#Ex3 1.9#Ex3] || [[Item:Q274|<math>x = r\cos@@{\theta}</math>]]<br><code>x = r\cos@@{\theta}</code> || <math></math> || <code>x = r*cos(theta)</code> || <code>x == r*Cos[\[Theta]]</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [180 / 180]<div class="mw-collapsible-content"><code>180/180]: [[2.595814528-.5954243254*I <- {r = -1.5, theta = 1/2*3^(1/2)+1/2*I, x = 1.5}</code><br><code>1.595814528-.5954243254*I <- {r = -1.5, theta = 1/2*3^(1/2)+1/2*I, x = .5}</code><br><code>3.095814528-.5954243254*I <- {r = -1.5, theta = 1/2*3^(1/2)+1/2*I, x = 2}</code><br><code>3.341648276+.7036130646*I <- {r = -1.5, theta = -1/2+1/2*I*3^(1/2), x = 1.5}</code><br>... skip entries to safe data<br></div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [180 / 180]<div class="mw-collapsible-content"><code>{Complex[2.595814528585838, -0.5954243253435487] <- {Rule[r, -1.5], Rule[x, 1.5], Rule[θ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br><code>Complex[3.3416482752961656, 0.7036130644027555] <- {Rule[r, -1.5], Rule[x, 1.5], Rule[θ, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</code><br></div></div>
|-
| [https://dlmf.nist.gov/1.9#Ex4 1.9#Ex4] || [[Item:Q275|<math>y = r\sin@@{\theta}</math>]]<br><code>y = r\sin@@{\theta}</code> || <math></math> || <code>y = r*sin(theta)</code> || <code>y == r*Sin[\[Theta]]</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><code>300/300]: [[-.211529498+.5063946946*I <- {r = -1.5, theta = 1/2*3^(1/2)+1/2*I, y = -1.5}</code><br><code>2.788470502+.5063946946*I <- {r = -1.5, theta = 1/2*3^(1/2)+1/2*I, y = 1.5}</code><br><code>.788470502+.5063946946*I <- {r = -1.5, theta = 1/2*3^(1/2)+1/2*I, y = -.5}</code><br><code>1.788470502+.5063946946*I <- {r = -1.5, theta = 1/2*3^(1/2)+1/2*I, y = .5}</code><br>... skip entries to safe data<br></div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><code>{Complex[-0.21152949854979308, 0.506394694834305] <- {Rule[r, -1.5], Rule[y, -1.5], Rule[θ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br><code>Complex[-2.506097038210817, 1.2879550752257174] <- {Rule[r, -1.5], Rule[y, -1.5], Rule[θ, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</code><br></div></div>
|-
| [https://dlmf.nist.gov/1.9.E4 1.9.E4] || [[Item:Q276|<math>r = (x^{2}+y^{2})^{1/2}</math>]]<br><code>r = (x^{2}+y^{2})^{1/2}</code> || <math></math> || <code>r = ((x)^(2)+ (y)^(2))^(1/2)</code> || <code>r == ((x)^(2)+ (y)^(2))^(1/2)</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
|-
| [https://dlmf.nist.gov/1.9.E6 1.9.E6] || [[Item:Q278|<math>\omega = \atan@{|y/x|}\in\left[0,\tfrac{1}{2}\pi\right]</math>]]<br><code>\omega = \atan@{|y/x|}\in\left[0,\tfrac{1}{2}\pi\right]</code> || <math></math> || <code>omega 0 <= arctan(abs(y/x)) <= (1)/(2)*Pi</code> || <code>\[Omega] 0 <= ArcTan[Abs[y/x]] <= Divide[1,2]*Pi</code> || Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [180 / 180]<div class="mw-collapsible-content"><code>{Plus[Complex[0.8660254037844387, 0.49999999999999994], Times[-1.0, True]] <- {Rule[x, 1.5], Rule[y, -1.5], Rule[ω, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br><code>Plus[Complex[-0.4999999999999998, 0.8660254037844387], Times[-1.0, True]] <- {Rule[x, 1.5], Rule[y, -1.5], Rule[ω, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</code><br></div></div>
|-
| [https://dlmf.nist.gov/1.9#Ex5 1.9#Ex5] || [[Item:Q279|<math>|z| = r</math>]]<br><code>|z| = r</code> || <math></math> || <code>abs(z) = r</code> || <code>Abs[z] == r</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [39 / 42]<div class="mw-collapsible-content"><code>39/42]: [[2.5 <- {r = -1.5, z = 1/2*3^(1/2)+1/2*I}</code><br><code>2.5 <- {r = -1.5, z = -1/2+1/2*I*3^(1/2)}</code><br><code>2.5 <- {r = -1.5, z = 1/2-1/2*I*3^(1/2)}</code><br><code>2.5 <- {r = -1.5, z = -1/2*3^(1/2)-1/2*I}</code><br>... skip entries to safe data<br></div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [39 / 42]<div class="mw-collapsible-content"><code>{2.5 <- {Rule[r, -1.5], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br><code>2.5 <- {Rule[r, -1.5], Rule[z, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</code><br></div></div>
|-
| [https://dlmf.nist.gov/1.9#Ex6 1.9#Ex6] || [[Item:Q280|<math>\phase@@{z} = \theta+2n\pi</math>]]<br><code>\phase@@{z} = \theta+2n\pi</code> || <math></math> || <code>argument(z) = theta + 2*n*Pi</code> || <code>Arg[z] == \[Theta]+ 2*n*Pi</code> || Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [70 / 70]<div class="mw-collapsible-content"><code>{Complex[-19.191982549724898, -0.49999999999999994] <- {Rule[n, 3], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[θ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br><code>Complex[-17.82595714594046, -0.8660254037844387] <- {Rule[n, 3], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[θ, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</code><br></div></div>
|-
| [https://dlmf.nist.gov/1.9#Ex7 1.9#Ex7] || [[Item:Q281|<math>|\realpart@@{z}| \leq |z|</math>]]<br><code>|\realpart@@{z}| \leq |z|</code> || <math></math> || <code>abs(Re(z)) <= abs(z)</code> || <code>Abs[Re[z]] <= Abs[z]</code> || Failure || Failure || Successful [Tested: 7] || Successful [Tested: 7]
|-
| [https://dlmf.nist.gov/1.9#Ex8 1.9#Ex8] || [[Item:Q282|<math>|\imagpart@@{z}| \leq |z|</math>]]<br><code>|\imagpart@@{z}| \leq |z|</code> || <math></math> || <code>abs(Im(z)) <= abs(z)</code> || <code>Abs[Im[z]] <= Abs[z]</code> || Failure || Failure || Successful [Tested: 7] || Successful [Tested: 7]
|-
| [https://dlmf.nist.gov/1.9.E9 1.9.E9] || [[Item:Q283|<math>z = re^{i\theta}</math>]]<br><code>z = re^{i\theta}</code> || <math></math> || <code>z = r*exp(I*theta)</code> || <code>z == r*Exp[I*\[Theta]]</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
|-
| [https://dlmf.nist.gov/1.9.E10 1.9.E10] || [[Item:Q284|<math>e^{i\theta} = \cos@@{\theta}+i\sin@@{\theta}</math>]]<br><code>e^{i\theta} = \cos@@{\theta}+i\sin@@{\theta}</code> || <math></math> || <code>exp(I*theta) = cos(theta)+ I*sin(theta)</code> || <code>Exp[I*\[Theta]] == Cos[\[Theta]]+ I*Sin[\[Theta]]</code> || Successful || Successful || - || Successful [Tested: 10]
|-
| [https://dlmf.nist.gov/1.9.E11 1.9.E11] || [[Item:Q285|<math>\conj{z} = x-iy</math>]]<br><code>\conj{z} = x-iy</code> || <math></math> || <code>conjugate(x + y*I) = x - I*y</code> || <code>Conjugate[x + y*I] == x - I*y</code> || Failure || Failure || Successful [Tested: 18] || Successful [Tested: 18]
|-
| [https://dlmf.nist.gov/1.9.E12 1.9.E12] || [[Item:Q286|<math>|\conj{z}| = |z|</math>]]<br><code>|\conj{z}| = |z|</code> || <math></math> || <code>abs(conjugate(z)) = abs(z)</code> || <code>Abs[Conjugate[z]] == Abs[z]</code> || Successful || Successful || - || Successful [Tested: 7]
|-
| [https://dlmf.nist.gov/1.9.E13 1.9.E13] || [[Item:Q287|<math>\phase@@{\conj{z}} = -\phase@@{z}</math>]]<br><code>\phase@@{\conj{z}} = -\phase@@{z}</code> || <math></math> || <code>argument(conjugate(z)) = - argument(z)</code> || <code>Arg[Conjugate[z]] == - Arg[z]</code> || Failure || Failure || Successful [Tested: 7] || Successful [Tested: 7]
|-
| [https://dlmf.nist.gov/1.9.E14 1.9.E14] || [[Item:Q288|<math>z_{1}+ z_{2} = x_{1}+ x_{2}+\iunit(y_{1}+ y_{2})</math>]]<br><code>z_{1}+ z_{2} = x_{1}+ x_{2}+\iunit(y_{1}+ y_{2})</code> || <math></math> || <code>x + y*I[1]+x + y*I[2] = x[1]+ x[2]+ I*(y[1]+ y[2])</code> || <code>Subscript[x + y*I, 1]+Subscript[x + y*I, 2] == Subscript[x, 1]+ Subscript[x, 2]+ I*(Subscript[y, 1]+ Subscript[y, 2])</code> || Failure || Failure || Error || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><code>{Plus[Complex[-0.7320508075688775, -2.732050807568877], Subscript[Complex[1.5, -1.5], 1], Subscript[Complex[1.5, -1.5], 2]] <- {Rule[x, 1.5], Rule[y, -1.5], Rule[Subscript[x, 1], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[x, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[y, 1], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[y, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br><code>Plus[Complex[-0.3660254037844388, -1.3660254037844388], Subscript[Complex[1.5, -1.5], 1], Subscript[Complex[1.5, -1.5], 2]] <- {Rule[x, 1.5], Rule[y, -1.5], Rule[Subscript[x, 1], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[x, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[y, 1], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[y, 2], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</code><br></div></div>
|-
| [https://dlmf.nist.gov/1.9.E14 1.9.E14] || [[Item:Q288|<math>z_{1}- z_{2} = x_{1}- x_{2}+\iunit(y_{1}- y_{2})</math>]]<br><code>z_{1}- z_{2} = x_{1}- x_{2}+\iunit(y_{1}- y_{2})</code> || <math></math> || <code>x + y*I[1]-x + y*I[2] = x[1]- x[2]+ I*(y[1]- y[2])</code> || <code>Subscript[x + y*I, 1]-Subscript[x + y*I, 2] == Subscript[x, 1]- Subscript[x, 2]+ I*(Subscript[y, 1]- Subscript[y, 2])</code> || Failure || Failure || Error || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><code>{Plus[Subscript[Complex[1.5, -1.5], 1], Times[-1.0, Subscript[Complex[1.5, -1.5], 2]]] <- {Rule[x, 1.5], Rule[y, -1.5], Rule[Subscript[x, 1], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[x, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[y, 1], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[y, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br><code>Plus[Complex[-0.36602540378443876, -1.3660254037844384], Subscript[Complex[1.5, -1.5], 1], Times[-1.0, Subscript[Complex[1.5, -1.5], 2]]] <- {Rule[x, 1.5], Rule[y, -1.5], Rule[Subscript[x, 1], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[x, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[y, 1], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[y, 2], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</code><br></div></div>
|-
| [https://dlmf.nist.gov/1.9.E15 1.9.E15] || [[Item:Q289|<math>z_{1}z_{2} = x_{1}x_{2}-y_{1}y_{2}+i(x_{1}y_{2}+x_{2}y_{1})</math>]]<br><code>z_{1}z_{2} = x_{1}x_{2}-y_{1}y_{2}+i(x_{1}y_{2}+x_{2}y_{1})</code> || <math></math> || <code>x + y*I[1]*x + y*I[2] = x[1]*x[2]- y[1]*y[2]+ I*(x[1]*y[2]+ x[2]*y[1])</code> || <code>Subscript[x + y*I, 1]*Subscript[x + y*I, 2] == Subscript[x, 1]*Subscript[x, 2]- Subscript[y, 1]*Subscript[y, 2]+ I*(Subscript[x, 1]*Subscript[y, 2]+ Subscript[x, 2]*Subscript[y, 1])</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
|-
| [https://dlmf.nist.gov/1.9.E16 1.9.E16] || [[Item:Q290|<math>\frac{z_{1}}{z_{2}} = \frac{z_{1}\conj{z}_{2}}{|z_{2}|^{2}}</math>]]<br><code>\frac{z_{1}}{z_{2}} = \frac{z_{1}\conj{z}_{2}}{|z_{2}|^{2}}</code> || <math></math> || <code>(z[1])/(z[2]) = (z[1]*conjugate(z)[2])/((abs(z[2]))^(2))</code> || <code>Divide[Subscript[z, 1],Subscript[z, 2]] == Divide[Subscript[z, 1]*Subscript[Conjugate[z], 2],(Abs[Subscript[z, 2]])^(2)]</code> || Failure || Failure || Error || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><code>{Plus[1.0, Times[Complex[-0.8660254037844387, -0.49999999999999994], Subscript[Complex[0.8660254037844387, -0.49999999999999994], 2]]] <- {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[z, 1], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[z, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br><code>Plus[Complex[0.0, -1.0], Times[Complex[-0.8660254037844387, -0.49999999999999994], Subscript[Complex[0.8660254037844387, -0.49999999999999994], 2]]] <- {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[z, 1], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[z, 2], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</code><br></div></div>
|-
| [https://dlmf.nist.gov/1.9.E16 1.9.E16] || [[Item:Q290|<math>\frac{z_{1}\conj{z}_{2}}{|z_{2}|^{2}} = \frac{x_{1}x_{2}+y_{1}y_{2}+i(x_{2}y_{1}-x_{1}y_{2})}{x_{2}^{2}+y_{2}^{2}}</math>]]<br><code>\frac{z_{1}\conj{z}_{2}}{|z_{2}|^{2}} = \frac{x_{1}x_{2}+y_{1}y_{2}+i(x_{2}y_{1}-x_{1}y_{2})}{x_{2}^{2}+y_{2}^{2}}</code> || <math></math> || <code>(x + y*I[1]*conjugate(x + y*I)[2])/((abs(x + y*I[2]))^(2)) = (x[1]*x[2]+ y[1]*y[2]+ I*(x[2]*y[1]- x[1]*y[2]))/((x[2])^(2)+ (y[2])^(2))</code> || <code>Divide[Subscript[x + y*I, 1]*Subscript[Conjugate[x + y*I], 2],(Abs[Subscript[x + y*I, 2]])^(2)] == Divide[Subscript[x, 1]*Subscript[x, 2]+ Subscript[y, 1]*Subscript[y, 2]+ I*(Subscript[x, 2]*Subscript[y, 1]- Subscript[x, 1]*Subscript[y, 2]),(Subscript[x, 2])^(2)+ (Subscript[y, 2])^(2)]</code> || Failure || Failure || Error || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><code>{DirectedInfinity[] <- {Rule[x, 1.5], Rule[y, -1.5], Rule[Subscript[x, 1], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[x, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[y, 1], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[y, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br><code>Plus[Complex[-0.6666666666666669, -0.6666666666666667], Times[Power[Abs[Subscript[Complex[1.5, -1.5], 2]], -2], Subscript[Complex[1.5, -1.5], 1], Subscript[Complex[1.5, 1.5], 2]]] <- {Rule[x, 1.5], Rule[y, -1.5], Rule[Subscript[x, 1], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[x, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[y, 1], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[y, 2], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</code><br></div></div>
|-
| [https://dlmf.nist.gov/1.9.E17 1.9.E17] || [[Item:Q291|<math>|z_{1}z_{2}| = |z_{1}|\;|z_{2}|</math>]]<br><code>|z_{1}z_{2}| = |z_{1}|\;|z_{2}|</code> || <math></math> || <code>abs(z[1]*z[2]) = abs(z[1])*abs(z[2])</code> || <code>Abs[Subscript[z, 1]*Subscript[z, 2]] == Abs[Subscript[z, 1]]*Abs[Subscript[z, 2]]</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
|-
| [https://dlmf.nist.gov/1.9.E18 1.9.E18] || [[Item:Q292|<math>\phase@{z_{1}z_{2}} = \phase@@{z_{1}}+\phase@@{z_{2}}</math>]]<br><code>\phase@{z_{1}z_{2}} = \phase@@{z_{1}}+\phase@@{z_{2}}</code> || <math></math> || <code>argument(z[1]*z[2]) = argument(z[1])+ argument(z[2])</code> || <code>Arg[Subscript[z, 1]*Subscript[z, 2]] == Arg[Subscript[z, 1]]+ Arg[Subscript[z, 2]]</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [25 / 100]<div class="mw-collapsible-content"><code>25/100]: [[-6.283185308 <- {z[1] = 1/2*3^(1/2)+1/2*I, z[2] = -1.5}</code><br><code>-6.283185308 <- {z[1] = 1/2*3^(1/2)+1/2*I, z[2] = -.5}</code><br><code>-6.283185308 <- {z[1] = 1/2*3^(1/2)+1/2*I, z[2] = -2}</code><br><code>-6.283185309 <- {z[1] = -1/2+1/2*I*3^(1/2), z[2] = -1/2+1/2*I*3^(1/2)}</code><br>... skip entries to safe data<br></div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [25 / 100]<div class="mw-collapsible-content"><code>{-6.283185307179587 <- {Rule[Subscript[z, 1], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[z, 2], -1.5]}</code><br><code>-6.283185307179587 <- {Rule[Subscript[z, 1], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[z, 2], -0.5]}</code><br></div></div>
|-
| [https://dlmf.nist.gov/1.9.E19 1.9.E19] || [[Item:Q293|<math>\abs{\frac{z_{1}}{z_{2}}} = \frac{|z_{1}|}{|z_{2}|}</math>]]<br><code>\abs{\frac{z_{1}}{z_{2}}} = \frac{|z_{1}|}{|z_{2}|}</code> || <math></math> || <code>abs((z[1])/(z[2])) = (abs(z[1]))/(abs(z[2]))</code> || <code>Abs[Divide[Subscript[z, 1],Subscript[z, 2]]] == Divide[Abs[Subscript[z, 1]],Abs[Subscript[z, 2]]]</code> || Successful || Successful || - || Successful [Tested: 100]
|-
| [https://dlmf.nist.gov/1.9.E20 1.9.E20] || [[Item:Q294|<math>\phase@@{\frac{z_{1}}{z_{2}}} = \phase@@{z_{1}}-\phase@@{z_{2}}</math>]]<br><code>\phase@@{\frac{z_{1}}{z_{2}}} = \phase@@{z_{1}}-\phase@@{z_{2}}</code> || <math></math> || <code>argument((z[1])/(z[2])) = argument(z[1])- argument(z[2])</code> || <code>Arg[Divide[Subscript[z, 1],Subscript[z, 2]]] == Arg[Subscript[z, 1]]- Arg[Subscript[z, 2]]</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [25 / 100]<div class="mw-collapsible-content"><code>25/100]: [[-6.283185308 <- {z[1] = -1/2+1/2*I*3^(1/2), z[2] = -1/2*3^(1/2)-1/2*I}</code><br><code>6.283185308 <- {z[1] = 1/2-1/2*I*3^(1/2), z[2] = -1/2+1/2*I*3^(1/2)}</code><br><code>6.283185307 <- {z[1] = 1/2-1/2*I*3^(1/2), z[2] = -1.5}</code><br><code>6.283185307 <- {z[1] = 1/2-1/2*I*3^(1/2), z[2] = -.5}</code><br>... skip entries to safe data<br></div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [25 / 100]<div class="mw-collapsible-content"><code>{-6.283185307179586 <- {Rule[Subscript[z, 1], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]], Rule[Subscript[z, 2], Power[E, Times[Complex[0, Rational[-5, 6]], Pi]]]}</code><br><code>6.283185307179586 <- {Rule[Subscript[z, 1], Power[E, Times[Complex[0, Rational[-1, 3]], Pi]]], Rule[Subscript[z, 2], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</code><br></div></div>
|-
| [https://dlmf.nist.gov/1.9.E22 1.9.E22] || [[Item:Q296|<math>\cos@@{n\theta}+i\sin@@{n\theta} = (\cos@@{\theta}+i\sin@@{\theta})^{n}</math>]]<br><code>\cos@@{n\theta}+i\sin@@{n\theta} = (\cos@@{\theta}+i\sin@@{\theta})^{n}</code> || <math></math> || <code>cos(n*theta)+ I*sin(n*theta) = (cos(theta)+ I*sin(theta))^(n)</code> || <code>Cos[n*\[Theta]]+ I*Sin[n*\[Theta]] == (Cos[\[Theta]]+ I*Sin[\[Theta]])^(n)</code> || Error || Successful || - || Successful [Tested: 10]
|-
| [https://dlmf.nist.gov/1.9.E23 1.9.E23] || [[Item:Q297|<math>\abs{\abs{z_{1}}-\abs{z_{2}}} \leq \abs{z_{1}+z_{2}}</math>]]<br><code>\abs{\abs{z_{1}}-\abs{z_{2}}} \leq \abs{z_{1}+z_{2}}</code> || <math></math> || <code>abs(abs(z[1])- abs(z[2])) <= abs(z[1]+ z[2])</code> || <code>Abs[Abs[Subscript[z, 1]]- Abs[Subscript[z, 2]]] <= Abs[Subscript[z, 1]+ Subscript[z, 2]]</code> || Failure || Failure || Successful [Tested: 100] || Successful [Tested: 100]
|-
| [https://dlmf.nist.gov/1.9.E23 1.9.E23] || [[Item:Q297|<math>\abs{z_{1}+z_{2}} \leq \abs{z_{1}}+\abs{z_{2}}</math>]]<br><code>\abs{z_{1}+z_{2}} \leq \abs{z_{1}}+\abs{z_{2}}</code> || <math></math> || <code>abs(z[1]+ z[2]) <= abs(z[1])+ abs(z[2])</code> || <code>Abs[Subscript[z, 1]+ Subscript[z, 2]] <= Abs[Subscript[z, 1]]+ Abs[Subscript[z, 2]]</code> || Failure || Failure || Successful [Tested: 100] || Successful [Tested: 100]
|-
| [https://dlmf.nist.gov/1.9#Ex9 1.9#Ex9] || [[Item:Q299|<math>\pderiv{u}{x} = \pderiv{v}{y}</math>]]<br><code>\pderiv{u}{x} = \pderiv{v}{y}</code> || <math></math> || <code>diff(u, x) = diff(v, y)</code> || <code>D[u, x] == D[v, y]</code> || Successful || Successful || - || Successful [Tested: 300]
|-
| [https://dlmf.nist.gov/1.9#Ex10 1.9#Ex10] || [[Item:Q300|<math>\pderiv{u}{y} = -\pderiv{v}{x}</math>]]<br><code>\pderiv{u}{y} = -\pderiv{v}{x}</code> || <math></math> || <code>diff(u, y) = - diff(v, x)</code> || <code>D[u, y] == - D[v, x]</code> || Successful || Successful || - || Successful [Tested: 300]
|-
| [https://dlmf.nist.gov/1.9.E26 1.9.E26] || [[Item:Q301|<math>\pderiv[2]{u}{x}+\pderiv[2]{u}{y} = \pderiv[2]{v}{x}+\pderiv[2]{v}{y}</math>]]<br><code>\pderiv[2]{u}{x}+\pderiv[2]{u}{y} = \pderiv[2]{v}{x}+\pderiv[2]{v}{y}</code> || <math></math> || <code>diff(u, [x$(2)])+ diff(u, [y$(2)]) = diff(v, [x$(2)])+ diff(v, [y$(2)])</code> || <code>D[u, {x, 2}]+ D[u, {y, 2}] == D[v, {x, 2}]+ D[v, {y, 2}]</code> || Successful || Successful || - || Successful [Tested: 300]
|-
| [https://dlmf.nist.gov/1.9.E26 1.9.E26] || [[Item:Q301|<math>\pderiv[2]{v}{x}+\pderiv[2]{v}{y} = 0</math>]]<br><code>\pderiv[2]{v}{x}+\pderiv[2]{v}{y} = 0</code> || <math></math> || <code>diff(v, [x$(2)])+ diff(v, [y$(2)]) = 0</code> || <code>D[v, {x, 2}]+ D[v, {y, 2}] == 0</code> || Successful || Successful || - || Successful [Tested: 180]
|-
| [https://dlmf.nist.gov/1.9.E27 1.9.E27] || [[Item:Q302|<math>\pderiv[2]{u}{r}+\frac{1}{r}\pderiv{u}{r}+\frac{1}{r^{2}}\pderiv[2]{u}{\theta} = 0</math>]]<br><code>\pderiv[2]{u}{r}+\frac{1}{r}\pderiv{u}{r}+\frac{1}{r^{2}}\pderiv[2]{u}{\theta} = 0</code> || <math></math> || <code>diff(u, [r$(2)])+(1)/(r)*diff(u, r)+(1)/((r)^(2))*diff(u, [theta$(2)]) = 0</code> || <code>D[u, {r, 2}]+Divide[1,r]*D[u, r]+Divide[1,(r)^(2)]*D[u, {\[Theta], 2}] == 0</code> || Successful || Successful || - || Successful [Tested: 300]
|-
| [https://dlmf.nist.gov/1.9.E33 1.9.E33] || [[Item:Q308|<math>u(z) = \frac{1}{2\pi}\int^{2\pi}_{0}u(z+re^{i\phi})\diff{\phi}</math>]]<br><code>u(z) = \frac{1}{2\pi}\int^{2\pi}_{0}u(z+re^{i\phi})\diff{\phi}</code> || <math></math> || <code>u(z) = (1)/(2*Pi)*int(u(z + r*exp(I*phi)), phi = 0..2*Pi)</code> || <code>u[z] == Divide[1,2*Pi]*Integrate[u[z + r*Exp[I*\[Phi]]], {\[Phi], 0, 2*Pi}, GenerateConditions->None]</code> || Successful || Successful || - || Successful [Tested: 300]
|-
| [https://dlmf.nist.gov/1.9.E34 1.9.E34] || [[Item:Q309|<math>u(re^{i\theta}) = \frac{1}{2\pi}\int^{2\pi}_{0}\frac{(R^{2}-r^{2})h(Re^{i\phi})\diff{\phi}}{R^{2}-2Rr\cos@{\phi-\theta}+r^{2}}</math>]]<br><code>u(re^{i\theta}) = \frac{1}{2\pi}\int^{2\pi}_{0}\frac{(R^{2}-r^{2})h(Re^{i\phi})\diff{\phi}}{R^{2}-2Rr\cos@{\phi-\theta}+r^{2}}</code> || <math></math> || <code>u(r*exp(I*theta)) = (1)/(2*Pi)*int((((R)^(2)- (r)^(2))*h(R*exp(I*phi)))/((R)^(2)- 2*R*r*cos(phi - theta)+ (r)^(2)), phi = 0..2*Pi)</code> || <code>u[r*Exp[I*\[Theta]]] == Divide[1,2*Pi]*Integrate[Divide[((R)^(2)- (r)^(2))*h[R*Exp[I*\[Phi]]],(R)^(2)- 2*R*r*Cos[\[Phi]- \[Theta]]+ (r)^(2)], {\[Phi], 0, 2*Pi}, GenerateConditions->None]</code> || Aborted || Failure || Skipped - Because timed out || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><code>{Complex[-0.1639294614698989, -0.894905511379796] <- {Rule[h, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[r, -1.5], Rule[R, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[u, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[θ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br><code>Complex[-0.6307543640677387, -0.014887794479775784] <- {Rule[h, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[r, -1.5], Rule[R, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[u, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[θ, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</code><br></div></div>
|-
| [https://dlmf.nist.gov/1.9.E36 1.9.E36] || [[Item:Q311|<math>\infty+ z = z+\infty</math>]]<br><code>\infty+ z = z+\infty</code> || <math></math> || <code>infinity + z = z + infinity</code> || <code>Infinity + z == z + Infinity</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
|-
| [https://dlmf.nist.gov/1.9.E37 1.9.E37] || [[Item:Q312|<math>\infty\cdot z = z\cdot\infty</math>]]<br><code>\infty\cdot z = z\cdot\infty</code> || <math></math> || <code>infinity * z = z * infinity</code> || <code>Infinity * z == z * Infinity</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
|-
| [https://dlmf.nist.gov/1.9.E38 1.9.E38] || [[Item:Q313|<math>z/\infty = 0</math>]]<br><code>z/\infty = 0</code> || <math></math> || <code>z/infinity = 0</code> || <code>z/Infinity == 0</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
|-
| [https://dlmf.nist.gov/1.9.E39 1.9.E39] || [[Item:Q314|<math>z/0 = \infty</math>]]<br><code>z/0 = \infty</code> || <math>z \neq 0</math> || <code>z/0 = infinity</code> || <code>z/0 == Infinity</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
|-
| [https://dlmf.nist.gov/1.9.E44 1.9.E44] || [[Item:Q320|<math>z = \frac{dw-b}{-cw+a}</math>]]<br><code>z = \frac{dw-b}{-cw+a}</code> || <math></math> || <code>z = (d*w - b)/(- c*w + a)</code> || <code>z == Divide[d*w - b,- c*w + a]</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
|-
| [https://dlmf.nist.gov/1.9.E48 1.9.E48] || [[Item:Q324|<math>a_{n} = \frac{f^{(n)}(z_{0})}{n!}</math>]]<br><code>a_{n} = \frac{f^{(n)}(z_{0})}{n!}</code> || <math></math> || <code>a[n] = ((f(z[0]))^(n))/(factorial(n))</code> || <code>Subscript[a, n] == Divide[(f[Subscript[z, 0]])^(n),(n)!]</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
|-
| [https://dlmf.nist.gov/1.9.E50 1.9.E50] || [[Item:Q326|<math>\sum^{\infty}_{n=0}(a_{n}+ b_{n})z^{n} = \sum^{\infty}_{n=0}a_{n}z^{n}+\sum^{\infty}_{n=0}b_{n}z^{n}</math>]]<br><code>\sum^{\infty}_{n=0}(a_{n}+ b_{n})z^{n} = \sum^{\infty}_{n=0}a_{n}z^{n}+\sum^{\infty}_{n=0}b_{n}z^{n}</code> || <math></math> || <code>sum((a[n]+ b[n])*(z)^(n), n = 0..infinity) = sum(a[n]*(z)^(n), n = 0..infinity)+ sum(b[n]*(z)^(n), n = 0..infinity)</code> || <code>Sum[(Subscript[a, n]+ Subscript[b, n])*(z)^(n), {n, 0, Infinity}, GenerateConditions->None] == Sum[Subscript[a, n]*(z)^(n), {n, 0, Infinity}, GenerateConditions->None]+ Sum[Subscript[b, n]*(z)^(n), {n, 0, Infinity}, GenerateConditions->None]</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
|-
| [https://dlmf.nist.gov/1.9.E51 1.9.E51] || [[Item:Q327|<math>\left(\sum^{\infty}_{n=0}a_{n}z^{n}\right)\left(\sum^{\infty}_{n=0}b_{n}z^{n}\right) = \sum^{\infty}_{n=0}c_{n}z^{n}</math>]]<br><code>\left(\sum^{\infty}_{n=0}a_{n}z^{n}\right)\left(\sum^{\infty}_{n=0}b_{n}z^{n}\right) = \sum^{\infty}_{n=0}c_{n}z^{n}</code> || <math></math> || <code>(sum(a[n]*(z)^(n), n = 0..infinity))*(sum(b[n]*(z)^(n), n = 0..infinity)) = sum(c[n]*(z)^(n), n = 0..infinity)</code> || <code>(Sum[Subscript[a, n]*(z)^(n), {n, 0, Infinity}, GenerateConditions->None])*(Sum[Subscript[b, n]*(z)^(n), {n, 0, Infinity}, GenerateConditions->None]) == Sum[Subscript[c, n]*(z)^(n), {n, 0, Infinity}, GenerateConditions->None]</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
|-
| [https://dlmf.nist.gov/1.9.E52 1.9.E52] || [[Item:Q328|<math>c_{n} = \sum^{n}_{k=0}a_{k}b_{n-k}</math>]]<br><code>c_{n} = \sum^{n}_{k=0}a_{k}b_{n-k}</code> || <math></math> || <code>c[n] = sum(a[k]*b[n - k], k = 0..n)</code> || <code>Subscript[c, n] == Sum[Subscript[a, k]*Subscript[b, n - k], {k, 0, n}, GenerateConditions->None]</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
|-
| [https://dlmf.nist.gov/1.9#Ex13 1.9#Ex13] || [[Item:Q331|<math>b_{0} = 1/a_{0}</math>]]<br><code>b_{0} = 1/a_{0}</code> || <math></math> || <code>b[0] = 1/a[0]</code> || <code>Subscript[b, 0] == 1/Subscript[a, 0]</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
|-
| [https://dlmf.nist.gov/1.9#Ex14 1.9#Ex14] || [[Item:Q332|<math>b_{1} = -a_{1}/a_{0}^{2}</math>]]<br><code>b_{1} = -a_{1}/a_{0}^{2}</code> || <math></math> || <code>b[1] = - a[1]/(a[0])^(2)</code> || <code>Subscript[b, 1] == - Subscript[a, 1]/(Subscript[a, 0])^(2)</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
|-
| [https://dlmf.nist.gov/1.9#Ex15 1.9#Ex15] || [[Item:Q333|<math>b_{2} = (a_{1}^{2}-a_{0}a_{2})/a_{0}^{3}</math>]]<br><code>b_{2} = (a_{1}^{2}-a_{0}a_{2})/a_{0}^{3}</code> || <math></math> || <code>b[2] = ((a[1])^(2)- a[0]*a[2])/(a[0])^(3)</code> || <code>Subscript[b, 2] == ((Subscript[a, 1])^(2)- Subscript[a, 0]*Subscript[a, 2])/(Subscript[a, 0])^(3)</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
|-
| [https://dlmf.nist.gov/1.9#Ex16 1.9#Ex16] || [[Item:Q336|<math>q_{1} = a_{1}</math>]]<br><code>q_{1} = a_{1}</code> || <math></math> || <code>q[1] = a[1]</code> || <code>Subscript[q, 1] == Subscript[a, 1]</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
|-
| [https://dlmf.nist.gov/1.9#Ex17 1.9#Ex17] || [[Item:Q337|<math>q_{2} = (2a_{2}-a_{1}^{2})/2</math>]]<br><code>q_{2} = (2a_{2}-a_{1}^{2})/2</code> || <math></math> || <code>q[2] = (2*a[2]- (a[1])^(2))/2</code> || <code>Subscript[q, 2] == (2*Subscript[a, 2]- (Subscript[a, 1])^(2))/2</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
|-
| [https://dlmf.nist.gov/1.9#Ex18 1.9#Ex18] || [[Item:Q338|<math>q_{3} = (3a_{3}-3a_{1}a_{2}+a_{1}^{3})/3</math>]]<br><code>q_{3} = (3a_{3}-3a_{1}a_{2}+a_{1}^{3})/3</code> || <math></math> || <code>q[3] = (3*a[3]- 3*a[1]*a[2]+ (a[1])^(3))/3</code> || <code>Subscript[q, 3] == (3*Subscript[a, 3]- 3*Subscript[a, 1]*Subscript[a, 2]+ (Subscript[a, 1])^(3))/3</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
|-
| [https://dlmf.nist.gov/1.9#Ex19 1.9#Ex19] || [[Item:Q341|<math>p_{0} = 1</math>]]<br><code>p_{0} = 1</code> || <math></math> || <code>p[0] = 1</code> || <code>Subscript[p, 0] == 1</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
|-
| [https://dlmf.nist.gov/1.9#Ex20 1.9#Ex20] || [[Item:Q342|<math>p_{1} = \nu a_{1}</math>]]<br><code>p_{1} = \nu a_{1}</code> || <math></math> || <code>p[1] = nu*a[1]</code> || <code>Subscript[p, 1] == \[Nu]*Subscript[a, 1]</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
|-
| [https://dlmf.nist.gov/1.9#Ex21 1.9#Ex21] || [[Item:Q343|<math>p_{2} = \nu((\nu-1)a_{1}^{2}+2a_{2})/2</math>]]<br><code>p_{2} = \nu((\nu-1)a_{1}^{2}+2a_{2})/2</code> || <math></math> || <code>p[2] = nu*((nu - 1)*(a[1])^(2)+ 2*a[2])/2</code> || <code>Subscript[p, 2] == \[Nu]*((\[Nu]- 1)*(Subscript[a, 1])^(2)+ 2*Subscript[a, 2])/2</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
|-
| [https://dlmf.nist.gov/1.9.E63 1.9.E63] || [[Item:Q345|<math>f^{(m)}(z) = \sum_{n=0}^{\infty}\Pochhammersym{n+1}{m}a_{n+m}(z-z_{0})^{n}</math>]]<br><code>f^{(m)}(z) = \sum_{n=0}^{\infty}\Pochhammersym{n+1}{m}a_{n+m}(z-z_{0})^{n}</code> || <math>\abs{z-z_{0}} < R</math> || <code>(f(z))^(m) = sum(pochhammer(n + 1, m)*a[n + m]*(z - z[0])^(n), n = 0..infinity)</code> || <code>(f[z])^(m) == Sum[Pochhammer[n + 1, m]*Subscript[a, n + m]*(z - Subscript[z, 0])^(n), {n, 0, Infinity}, GenerateConditions->None]</code> || Failure || Failure || Skipped - Because timed out || Skipped - Because timed out
|-
| [https://dlmf.nist.gov/1.9.E64 1.9.E64] || [[Item:Q346|<math>|z_{m,n}-z| < \epsilon</math>]]<br><code>|z_{m,n}-z| < \epsilon</code> || <math></math> || <code>abs(z[m , n]- z) < epsilon</code> || <code>Abs[Subscript[z, m , n]- z] < \[Epsilon]</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
|-
| [https://dlmf.nist.gov/1.9.E66 1.9.E66] || [[Item:Q349|<math>z_{p,q} = \sum^{p}_{m=0}\sum^{q}_{n=0}\zeta_{m,n}</math>]]<br><code>z_{p,q} = \sum^{p}_{m=0}\sum^{q}_{n=0}\zeta_{m,n}</code> || <math></math> || <code>z[p , q] = sum(sum(zeta[m , n], n = 0..q), m = 0..p)</code> || <code>Subscript[z, p , q] == Sum[Sum[Subscript[\[Zeta], m , n], {n, 0, q}, GenerateConditions->None], {m, 0, p}, GenerateConditions->None]</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
|-
| [https://dlmf.nist.gov/1.9.E69 1.9.E69] || [[Item:Q353|<math>\int^{b}_{a}\sum^{\infty}_{n=0}|f_{n}(t)|\diff{t} < \infty</math>]]<br><code>\int^{b}_{a}\sum^{\infty}_{n=0}|f_{n}(t)|\diff{t} < \infty</code> || <math></math> || <code>int(sum(abs(f[n](t)), n = 0..infinity), t = a..b) < infinity</code> || <code>Integrate[Sum[Abs[Subscript[f, n][t]], {n, 0, Infinity}, GenerateConditions->None], {t, a, b}, GenerateConditions->None] < Infinity</code> || Missing Macro Error || Missing Macro Error || - || -
|-
| [https://dlmf.nist.gov/1.9.E70 1.9.E70] || [[Item:Q354|<math>\sum^{\infty}_{n=0}\int^{b}_{a}|f_{n}(t)|\diff{t} < \infty</math>]]<br><code>\sum^{\infty}_{n=0}\int^{b}_{a}|f_{n}(t)|\diff{t} < \infty</code> || <math></math> || <code>sum(int(abs(f[n](t)), t = a..b) , n = 0..infinity)< infinity</code> || <code>Sum[Integrate[Abs[Subscript[f, n][t]], {t, a, b}, GenerateConditions->None] , {n, 0, Infinity}, GenerateConditions->None]< Infinity</code> || Missing Macro Error || Missing Macro Error || - || -
|-
| [https://dlmf.nist.gov/1.9.E71 1.9.E71] || [[Item:Q355|<math>\int^{b}_{a}\sum^{\infty}_{n=0}f_{n}(t)\diff{t} = \sum^{\infty}_{n=0}\int^{b}_{a}f_{n}(t)\diff{t}</math>]]<br><code>\int^{b}_{a}\sum^{\infty}_{n=0}f_{n}(t)\diff{t} = \sum^{\infty}_{n=0}\int^{b}_{a}f_{n}(t)\diff{t}</code> || <math></math> || <code>int(sum(f[n](t), n = 0..infinity), t = a..b) = sum(int(f[n](t), t = a..b), n = 0..infinity)</code> || <code>Integrate[Sum[Subscript[f, n][t], {n, 0, Infinity}, GenerateConditions->None], {t, a, b}, GenerateConditions->None] == Sum[Integrate[Subscript[f, n][t], {t, a, b}, GenerateConditions->None], {n, 0, Infinity}, GenerateConditions->None]</code> || Successful || Aborted || - || Skipped - Because timed out
|-
| [https://dlmf.nist.gov/1.10.E20 1.10.E20] || [[Item:Q375|<math>|\ln@{1+a_{n}(z)}| \leq M_{n}</math>]]<br><code>|\ln@{1+a_{n}(z)}| \leq M_{n}</code> || <math>n \geq N</math> || <code>abs(ln(1 + a[n](z))) <= M[n]</code> || <code>Abs[Log[1 + Subscript[a, n][z]]] <= Subscript[M, n]</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [126 / 300]<div class="mw-collapsible-content"><code>126/300]: [[.7588760888 <= -1.5 <- {z = 1/2*3^(1/2)+1/2*I, M[n] = -1.5, a[n] = 1/2*3^(1/2)+1/2*I, n = 1}</code><br><code>.7588760888 <= -1.5 <- {z = 1/2*3^(1/2)+1/2*I, M[n] = -1.5, a[n] = 1/2*3^(1/2)+1/2*I, n = 2}</code><br><code>.7588760888 <= -1.5 <- {z = 1/2*3^(1/2)+1/2*I, M[n] = -1.5, a[n] = 1/2*3^(1/2)+1/2*I, n = 3}</code><br><code>1.465287519 <= -1.5 <- {z = 1/2*3^(1/2)+1/2*I, M[n] = -1.5, a[n] = -1/2+1/2*I*3^(1/2), n = 1}</code><br>... skip entries to safe data<br></div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [246 / 300]<div class="mw-collapsible-content"><code>{LessEqual[0.7588760887069661, Complex[0.8660254037844387, 0.49999999999999994]] <- {Rule[n, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[a, n], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[M, n], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br><code>LessEqual[0.7588760887069661, Complex[0.8660254037844387, 0.49999999999999994]] <- {Rule[n, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[a, n], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[M, n], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br></div></div>
|-
| [https://dlmf.nist.gov/1.10.E21 1.10.E21] || [[Item:Q376|<math>\sum^{\infty}_{n=1}M_{n} < \infty</math>]]<br><code>\sum^{\infty}_{n=1}M_{n} < \infty</code> || <math></math> || <code>sum(M[n](<)*infinity, n = 1..infinity)</code> || <code>Sum[Subscript[M, n][<]*Infinity, {n, 1, Infinity}, GenerateConditions->None]</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
|-
| [https://dlmf.nist.gov/1.10.E22 1.10.E22] || [[Item:Q377|<math>P(z) = \prod^{\infty}_{n=1}\left(1-\frac{z}{z_{n}}\right)e^{z/z_{n}}</math>]]<br><code>P(z) = \prod^{\infty}_{n=1}\left(1-\frac{z}{z_{n}}\right)e^{z/z_{n}}</code> || <math></math> || <code>P(z) = product((1 -(z)/(z[n]))*exp(z/z[n]), n = 1..infinity)</code> || <code>P[z] == Product[(1 -Divide[z,Subscript[z, n]])*Exp[z/Subscript[z, n]], {n, 1, Infinity}, GenerateConditions->None]</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
|-
| [https://dlmf.nist.gov/1.11.E3 1.11.E3] || [[Item:Q383|<math>b_{k} = \alpha b_{k+1}+a_{k}</math>]]<br><code>b_{k} = \alpha b_{k+1}+a_{k}</code> || <math>k = n-1</math> || <code>b[k] = alpha*b[k + 1]+ a[k]</code> || <code>Subscript[b, k] == \[Alpha]*Subscript[b, k + 1]+ Subscript[a, k]</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
|-
| [https://dlmf.nist.gov/1.11.E5 1.11.E5] || [[Item:Q385|<math>c_{k} = \alpha c_{k+1}+b_{k}</math>]]<br><code>c_{k} = \alpha c_{k+1}+b_{k}</code> || <math>k = n-1</math> || <code>c[k] = alpha*c[k + 1]+ b[k]</code> || <code>Subscript[c, k] == \[Alpha]*Subscript[c, k + 1]+ Subscript[b, k]</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
|-
| [https://dlmf.nist.gov/1.11#E10Xa 1.11#E10Xa] || [[Item:Q392|<math>\displaystyle\sum_{1\leq j<k\leq n}z_{j}z_{k} = a_{n-2}/a_{n}</math>]]<br><code>\displaystyle\sum_{1\leq j<k\leq n}z_{j}z_{k} = a_{n-2}/a_{n}</code> || <math></math> || <code>sum(sum(z[j]*z[k], k = j + 1..n), j = 1..k - 1) = a[n - 2]/a[n]</code> || <code>Sum[Sum[Subscript[z, j]*Subscript[z, k], {k, j + 1, n}, GenerateConditions->None], {j, 1, k - 1}, GenerateConditions->None] == Subscript[a, n - 2]/Subscript[a, n]</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
|-
| [https://dlmf.nist.gov/1.11#Ex4 1.11#Ex4] || [[Item:Q396|<math>D = b^{2}-4ac</math>]]<br><code>D = b^{2}-4ac</code> || <math></math> || <code>D = (b)^(2)- 4*a*c</code> || <code>D == (b)^(2)- 4*a*c</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
|-
| [https://dlmf.nist.gov/1.11#Ex10 1.11#Ex10] || [[Item:Q403|<math>\rho = -\tfrac{1}{2}+\tfrac{1}{2}\sqrt{-3}</math>]]<br><code>\rho = -\tfrac{1}{2}+\tfrac{1}{2}\sqrt{-3}</code> || <math></math> || <code>rho = -(1)/(2)+(1)/(2)*sqrt(- 3)</code> || <code>\[Rho] == -Divide[1,2]+Divide[1,2]*Sqrt[- 3]</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
|-
| [https://dlmf.nist.gov/1.11#Ex11 1.11#Ex11] || [[Item:Q404|<math>\rho^{2} = e^{-2\pi i/3}</math>]]<br><code>\rho^{2} = e^{-2\pi i/3}</code> || <math></math> || <code>(rho)^(2) = exp(- 2*Pi*I/3)</code> || <code>\[Rho]^(2) == Exp[- 2*Pi*I/3]</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
|-
| [https://dlmf.nist.gov/1.11#Ex13 1.11#Ex13] || [[Item:Q406|<math>p = (-3a^{2}+8b)/8</math>]]<br><code>p = (-3a^{2}+8b)/8</code> || <math></math> || <code>p = (- 3*(a)^(2)+ 8*b)/8</code> || <code>p == (- 3*(a)^(2)+ 8*b)/8</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
|-
| [https://dlmf.nist.gov/1.11#Ex14 1.11#Ex14] || [[Item:Q407|<math>q = (a^{3}-4ab+8c)/8</math>]]<br><code>q = (a^{3}-4ab+8c)/8</code> || <math></math> || <code>q = ((a)^(3)- 4*a*b + 8*c)/8</code> || <code>q == ((a)^(3)- 4*a*b + 8*c)/8</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
|-
| [https://dlmf.nist.gov/1.11#Ex15 1.11#Ex15] || [[Item:Q408|<math>r = (-3a^{4}+16a^{2}b-64ac+256d)/256</math>]]<br><code>r = (-3a^{4}+16a^{2}b-64ac+256d)/256</code> || <math></math> || <code>r = (- 3*(a)^(4)+ 16*(a)^(2)* b - 64*a*c + 256*d)/256</code> || <code>r == (- 3*(a)^(4)+ 16*(a)^(2)* b - 64*a*c + 256*d)/256</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
|-
| [https://dlmf.nist.gov/1.11.E18 1.11.E18] || [[Item:Q410|<math>z^{3}-2pz^{2}+(p^{2}-4r)z+q^{2} = 0</math>]]<br><code>z^{3}-2pz^{2}+(p^{2}-4r)z+q^{2} = 0</code> || <math></math> || <code>(z)^(3)- 2*p*(z)^(2)+((p)^(2)- 4*r)*z + (q)^(2) = 0</code> || <code>(z)^(3)- 2*p*(z)^(2)+((p)^(2)- 4*r)*z + (q)^(2) == 0</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
|-
| [https://dlmf.nist.gov/1.11.E20 1.11.E20] || [[Item:Q415|<math>\sqrt{-\theta_{1}}\;\sqrt{-\theta_{2}}\;\sqrt{-\theta_{3}} = -q</math>]]<br><code>\sqrt{-\theta_{1}}\;\sqrt{-\theta_{2}}\;\sqrt{-\theta_{3}} = -q</code> || <math></math> || <code>sqrt(- theta[1])*sqrt(- theta[2])*sqrt(- theta[3]) = - q</code> || <code>Sqrt[- Subscript[\[Theta], 1]]*Sqrt[- Subscript[\[Theta], 2]]*Sqrt[- Subscript[\[Theta], 3]] == - q</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
|-
| [https://dlmf.nist.gov/1.11.E22 1.11.E22] || [[Item:Q417|<math>z^{n} = a+ib</math>]]<br><code>z^{n} = a+ib</code> || <math></math> || <code>(z)^(n) = a + I*b</code> || <code>(z)^(n) == a + I*b</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
|-
| [https://dlmf.nist.gov/1.11#Ex20 1.11#Ex20] || [[Item:Q420|<math>D_{1} = a_{1}</math>]]<br><code>D_{1} = a_{1}</code> || <math></math> || <code>D[1] = a[1]</code> || <code>Subscript[D, 1] == Subscript[a, 1]</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
|-
| [https://dlmf.nist.gov/1.12#Ex1 1.12#Ex1] || [[Item:Q428|<math>A_{k} = b_{k}A_{k-1}+a_{k}A_{k-2}</math>]]<br><code>A_{k} = b_{k}A_{k-1}+a_{k}A_{k-2}</code> || <math></math> || <code>A[k] = b[k]*A[k - 1]+ a[k]*A[k - 2]</code> || <code>Subscript[A, k] == Subscript[b, k]*Subscript[A, k - 1]+ Subscript[a, k]*Subscript[A, k - 2]</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
|-
| [https://dlmf.nist.gov/1.12#Ex2 1.12#Ex2] || [[Item:Q430|<math>B_{k} = b_{k}B_{k-1}+a_{k}B_{k-2}</math>]]<br><code>B_{k} = b_{k}B_{k-1}+a_{k}B_{k-2}</code> || <math></math> || <code>B[k] = b[k]*B[k - 1]+ a[k]*B[k - 2]</code> || <code>Subscript[B, k] == Subscript[b, k]*Subscript[B, k - 1]+ Subscript[a, k]*Subscript[B, k - 2]</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
|-
| [https://dlmf.nist.gov/1.12#Ex3 1.12#Ex3] || [[Item:Q431|<math>A_{-1} = 1</math>]]<br><code>A_{-1} = 1</code> || <math></math> || <code>A[- 1] = 1</code> || <code>Subscript[A, - 1] == 1</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
|-
| [https://dlmf.nist.gov/1.12#Ex4 1.12#Ex4] || [[Item:Q432|<math>A_{0} = b_{0}</math>]]<br><code>A_{0} = b_{0}</code> || <math></math> || <code>A[0] = b[0]</code> || <code>Subscript[A, 0] == Subscript[b, 0]</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
|-
| [https://dlmf.nist.gov/1.12#Ex5 1.12#Ex5] || [[Item:Q433|<math>B_{-1} = 0</math>]]<br><code>B_{-1} = 0</code> || <math></math> || <code>B[- 1] = 0</code> || <code>Subscript[B, - 1] == 0</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
|-
| [https://dlmf.nist.gov/1.12#Ex6 1.12#Ex6] || [[Item:Q434|<math>B_{0} = 1</math>]]<br><code>B_{0} = 1</code> || <math></math> || <code>B[0] = 1</code> || <code>Subscript[B, 0] == 1</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
|-
| [https://dlmf.nist.gov/1.12.E7 1.12.E7] || [[Item:Q435|<math>A_{n}B_{n-1}-B_{n}A_{n-1} = (-1)^{n-1}\prod^{n}_{k=1}a_{k}</math>]]<br><code>A_{n}B_{n-1}-B_{n}A_{n-1} = (-1)^{n-1}\prod^{n}_{k=1}a_{k}</code> || <math></math> || <code>A[n]*B[n - 1]- B[n]*A[n - 1] = (- 1)^(n - 1)* product(a[k], k = 1..n)</code> || <code>Subscript[A, n]*Subscript[B, n - 1]- Subscript[B, n]*Subscript[A, n - 1] == (- 1)^(n - 1)* Product[Subscript[a, k], {k, 1, n}, GenerateConditions->None]</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
|-
| [https://dlmf.nist.gov/1.12.E8 1.12.E8] || [[Item:Q436|<math>C_{n}-C_{n-1} = \frac{(-1)^{n-1}\prod^{n}_{k=1}a_{k}}{B_{n-1}B_{n}}</math>]]<br><code>C_{n}-C_{n-1} = \frac{(-1)^{n-1}\prod^{n}_{k=1}a_{k}}{B_{n-1}B_{n}}</code> || <math></math> || <code>C[n]- C[n - 1] = ((- 1)^(n - 1)* product(a[k], k = 1..n))/(B[n - 1]*B[n])</code> || <code>Subscript[C, n]- Subscript[C, n - 1] == Divide[(- 1)^(n - 1)* Product[Subscript[a, k], {k, 1, n}, GenerateConditions->None],Subscript[B, n - 1]*Subscript[B, n]]</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
|-
| [https://dlmf.nist.gov/1.12.E10 1.12.E10] || [[Item:Q438|<math>a_{n} = \frac{A_{n-1}B_{n}-A_{n}B_{n-1}}{A_{n-1}B_{n-2}-A_{n-2}B_{n-1}}</math>]]<br><code>a_{n} = \frac{A_{n-1}B_{n}-A_{n}B_{n-1}}{A_{n-1}B_{n-2}-A_{n-2}B_{n-1}}</code> || <math></math> || <code>a[n] = (A[n - 1]*B[n]- A[n]*B[n - 1])/(A[n - 1]*B[n - 2]- A[n - 2]*B[n - 1])</code> || <code>Subscript[a, n] == Divide[Subscript[A, n - 1]*Subscript[B, n]- Subscript[A, n]*Subscript[B, n - 1],Subscript[A, n - 1]*Subscript[B, n - 2]- Subscript[A, n - 2]*Subscript[B, n - 1]]</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
|-
| [https://dlmf.nist.gov/1.12.E11 1.12.E11] || [[Item:Q439|<math>a_{n} = \frac{B_{n}}{B_{n-2}}\frac{C_{n-1}-C_{n}}{C_{n-1}-C_{n-2}}</math>]]<br><code>a_{n} = \frac{B_{n}}{B_{n-2}}\frac{C_{n-1}-C_{n}}{C_{n-1}-C_{n-2}}</code> || <math></math> || <code>a[n] = (B[n])/(B[n - 2])*(C[n - 1]- C[n])/(C[n - 1]- C[n - 2])</code> || <code>Subscript[a, n] == Divide[Subscript[B, n],Subscript[B, n - 2]]*Divide[Subscript[C, n - 1]- Subscript[C, n],Subscript[C, n - 1]- Subscript[C, n - 2]]</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
|-
| [https://dlmf.nist.gov/1.12.E12 1.12.E12] || [[Item:Q440|<math>b_{n} = \frac{A_{n}B_{n-2}-A_{n-2}B_{n}}{A_{n-1}B_{n-2}-A_{n-2}B_{n-1}}</math>]]<br><code>b_{n} = \frac{A_{n}B_{n-2}-A_{n-2}B_{n}}{A_{n-1}B_{n-2}-A_{n-2}B_{n-1}}</code> || <math></math> || <code>b[n] = (A[n]*B[n - 2]- A[n - 2]*B[n])/(A[n - 1]*B[n - 2]- A[n - 2]*B[n - 1])</code> || <code>Subscript[b, n] == Divide[Subscript[A, n]*Subscript[B, n - 2]- Subscript[A, n - 2]*Subscript[B, n],Subscript[A, n - 1]*Subscript[B, n - 2]- Subscript[A, n - 2]*Subscript[B, n - 1]]</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
|-
| [https://dlmf.nist.gov/1.12.E13 1.12.E13] || [[Item:Q441|<math>b_{n} = \frac{B_{n}}{B_{n-1}}\frac{C_{n}-C_{n-2}}{C_{n-1}-C_{n-2}}</math>]]<br><code>b_{n} = \frac{B_{n}}{B_{n-1}}\frac{C_{n}-C_{n-2}}{C_{n-1}-C_{n-2}}</code> || <math></math> || <code>b[n] = (B[n])/(B[n - 1])*(C[n]- C[n - 2])/(C[n - 1]- C[n - 2])</code> || <code>Subscript[b, n] == Divide[Subscript[B, n],Subscript[B, n - 1]]*Divide[Subscript[C, n]- Subscript[C, n - 2],Subscript[C, n - 1]- Subscript[C, n - 2]]</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
|-
| [https://dlmf.nist.gov/1.12#Ex7 1.12#Ex7] || [[Item:Q442|<math>b_{0} = A_{0}</math>]]<br><code>b_{0} = A_{0}</code> || <math></math> || <code>b[0] = A[0]</code> || <code>Subscript[b, 0] == Subscript[A, 0]</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
|-
| [https://dlmf.nist.gov/1.12#Ex8 1.12#Ex8] || [[Item:Q443|<math>b_{1} = B_{1}</math>]]<br><code>b_{1} = B_{1}</code> || <math></math> || <code>b[1] = B[1]</code> || <code>Subscript[b, 1] == Subscript[B, 1]</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
|-
| [https://dlmf.nist.gov/1.12#Ex9 1.12#Ex9] || [[Item:Q444|<math>a_{1} = A_{1}-A_{0}B_{1}</math>]]<br><code>a_{1} = A_{1}-A_{0}B_{1}</code> || <math></math> || <code>a[1] = A[1]- A[0]*B[1]</code> || <code>Subscript[a, 1] == Subscript[A, 1]- Subscript[A, 0]*Subscript[B, 1]</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
|-
| [https://dlmf.nist.gov/1.12#Ex10 1.12#Ex10] || [[Item:Q451|<math>C_{n}(w) = \frac{A_{n}+A_{n-1}w}{B_{n}+B_{n-1}w}</math>]]<br><code>C_{n}(w) = \frac{A_{n}+A_{n-1}w}{B_{n}+B_{n-1}w}</code> || <math></math> || <code>C[n](w) = (A[n]+ A[n - 1]*w)/(B[n]+ B[n - 1]*w)</code> || <code>Subscript[C, n][w] == Divide[Subscript[A, n]+ Subscript[A, n - 1]*w,Subscript[B, n]+ Subscript[B, n - 1]*w]</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
|-
| [https://dlmf.nist.gov/1.12#Ex13 1.12#Ex13] || [[Item:Q454|<math>C_{0}\not = \infty</math>]]<br><code>C_{0}\not = \infty</code> || <math></math> || <code>C[0] <> infinity</code> || <code>Subscript[C, 0] \[NotEqual]*Infinity</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
|-
| [https://dlmf.nist.gov/1.12#Ex14 1.12#Ex14] || [[Item:Q455|<math>C_{n}\not = C_{n-1}</math>]]<br><code>C_{n}\not = C_{n-1}</code> || <math></math> || <code>C[n] <> C[n - 1]</code> || <code>Subscript[C, n] \[NotEqual]*Subscript[C, n - 1]</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
|-
| [https://dlmf.nist.gov/1.12.E25 1.12.E25] || [[Item:Q458|<math>|b_{n}| \geq |a_{n}|+1</math>]]<br><code>|b_{n}| \geq |a_{n}|+1</code> || <math></math> || <code>abs(b[n]) >= abs(a[n])+ 1</code> || <code>Abs[Subscript[b, n]] >= Abs[Subscript[a, n]]+ 1</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
|-
| [https://dlmf.nist.gov/1.12.E26 1.12.E26] || [[Item:Q459|<math>-\tfrac{1}{2}\pi+\delta < \phase@@{b_{n}}</math>]]<br><code>-\tfrac{1}{2}\pi+\delta < \phase@@{b_{n}}</code> || <math></math> || <code>-(1)/(2)*Pi + delta < argument(b[n])</code> || <code>-Divide[1,2]*Pi + \[Delta] < Arg[Subscript[b, n]]</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [27 / 300]<div class="mw-collapsible-content"><code>27/300]: [[-.70796327e-1 < -1.047197551 <- {delta = 1.5, b[n] = 1/2-1/2*I*3^(1/2), n = 1, n = 3}</code><br><code>-.70796327e-1 < -1.047197551 <- {delta = 1.5, b[n] = 1/2-1/2*I*3^(1/2), n = 2, n = 3}</code><br><code>-.70796327e-1 < -1.047197551 <- {delta = 1.5, b[n] = 1/2-1/2*I*3^(1/2), n = 3, n = 3}</code><br><code>-.70796327e-1 < -2.617993878 <- {delta = 1.5, b[n] = -1/2*3^(1/2)-1/2*I, n = 1, n = 3}</code><br>... skip entries to safe data<br></div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [49 / 100]<div class="mw-collapsible-content"><code>{Less[Complex[-0.7047709230104579, 0.49999999999999994], 0.5235987755982988] <- {Rule[n, 3], Rule[δ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[b, n], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br><code>Less[Complex[-0.7047709230104579, 0.49999999999999994], 2.0943951023931953] <- {Rule[n, 3], Rule[δ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[b, n], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</code><br></div></div>
|-
| [https://dlmf.nist.gov/1.12.E26 1.12.E26] || [[Item:Q459|<math>\phase@@{b_{n}} < \tfrac{1}{2}\pi-\delta</math>]]<br><code>\phase@@{b_{n}} < \tfrac{1}{2}\pi-\delta</code> || <math></math> || <code>argument(b[n]) < (1)/(2)*Pi - delta</code> || <code>Arg[Subscript[b, n]] < Divide[1,2]*Pi - \[Delta]</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [72 / 300]<div class="mw-collapsible-content"><code>72/300]: [[3.141592654 < 3.070796327 <- {delta = -1.5, b[n] = -1.5, n = 1, n = 3}</code><br><code>3.141592654 < 3.070796327 <- {delta = -1.5, b[n] = -1.5, n = 2, n = 3}</code><br><code>3.141592654 < 3.070796327 <- {delta = -1.5, b[n] = -1.5, n = 3, n = 3}</code><br><code>3.141592654 < 3.070796327 <- {delta = -1.5, b[n] = -.5, n = 1, n = 3}</code><br>... skip entries to safe data<br></div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [64 / 100]<div class="mw-collapsible-content"><code>{Less[0.5235987755982988, Complex[0.7047709230104579, -0.49999999999999994]] <- {Rule[n, 3], Rule[δ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[b, n], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br><code>Less[2.0943951023931953, Complex[0.7047709230104579, -0.49999999999999994]] <- {Rule[n, 3], Rule[δ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[b, n], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</code><br></div></div>
|-
| [https://dlmf.nist.gov/1.12.E27 1.12.E27] || [[Item:Q460|<math>-\tfrac{1}{2}\pi+\delta < \phase@@{C_{n}}</math>]]<br><code>-\tfrac{1}{2}\pi+\delta < \phase@@{C_{n}}</code> || <math></math> || <code>-(1)/(2)*Pi + delta < argument(C[n])</code> || <code>-Divide[1,2]*Pi + \[Delta] < Arg[Subscript[C, n]]</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [27 / 300]<div class="mw-collapsible-content"><code>27/300]: [[-.70796327e-1 < -1.047197551 <- {delta = 1.5, C[n] = 1/2-1/2*I*3^(1/2), n = 1, n = 3}</code><br><code>-.70796327e-1 < -1.047197551 <- {delta = 1.5, C[n] = 1/2-1/2*I*3^(1/2), n = 2, n = 3}</code><br><code>-.70796327e-1 < -1.047197551 <- {delta = 1.5, C[n] = 1/2-1/2*I*3^(1/2), n = 3, n = 3}</code><br><code>-.70796327e-1 < -2.617993878 <- {delta = 1.5, C[n] = -1/2*3^(1/2)-1/2*I, n = 1, n = 3}</code><br>... skip entries to safe data<br></div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [49 / 100]<div class="mw-collapsible-content"><code>{Less[Complex[-0.7047709230104579, 0.49999999999999994], 0.5235987755982988] <- {Rule[n, 3], Rule[δ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[C, n], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br><code>Less[Complex[-0.7047709230104579, 0.49999999999999994], 2.0943951023931953] <- {Rule[n, 3], Rule[δ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[C, n], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</code><br></div></div>
|-
| [https://dlmf.nist.gov/1.12.E27 1.12.E27] || [[Item:Q460|<math>\phase@@{C_{n}} < \tfrac{1}{2}\pi-\delta</math>]]<br><code>\phase@@{C_{n}} < \tfrac{1}{2}\pi-\delta</code> || <math></math> || <code>argument(C[n]) < (1)/(2)*Pi - delta</code> || <code>Arg[Subscript[C, n]] < Divide[1,2]*Pi - \[Delta]</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [72 / 300]<div class="mw-collapsible-content"><code>72/300]: [[3.141592654 < 3.070796327 <- {delta = -1.5, C[n] = -1.5, n = 1, n = 3}</code><br><code>3.141592654 < 3.070796327 <- {delta = -1.5, C[n] = -1.5, n = 2, n = 3}</code><br><code>3.141592654 < 3.070796327 <- {delta = -1.5, C[n] = -1.5, n = 3, n = 3}</code><br><code>3.141592654 < 3.070796327 <- {delta = -1.5, C[n] = -.5, n = 1, n = 3}</code><br>... skip entries to safe data<br></div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [64 / 100]<div class="mw-collapsible-content"><code>{Less[0.5235987755982988, Complex[0.7047709230104579, -0.49999999999999994]] <- {Rule[n, 3], Rule[δ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[C, n], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br><code>Less[2.0943951023931953, Complex[0.7047709230104579, -0.49999999999999994]] <- {Rule[n, 3], Rule[δ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[C, n], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</code><br></div></div>
|-
| [https://dlmf.nist.gov/1.12.E28 1.12.E28] || [[Item:Q461|<math>\sum^{\infty}_{n=1}|b_{n}| = \infty</math>]]<br><code>\sum^{\infty}_{n=1}|b_{n}| = \infty</code> || <math></math> || <code>sum(abs(b[n]), n = 1..infinity) = infinity</code> || <code>Sum[Abs[Subscript[b, n]], {n, 1, Infinity}, GenerateConditions->None] == Infinity</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
|-
| [https://dlmf.nist.gov/1.13.E2 1.13.E2] || [[Item:Q463|<math>w(z) = Aw_{1}(z)+Bw_{2}(z)</math>]]<br><code>w(z) = Aw_{1}(z)+Bw_{2}(z)</code> || <math></math> || <code>w(z) = Aw[1](z)+ Bw[2](z)</code> || <code>w[z] == Subscript[Aw, 1][z]+ Subscript[Bw, 2][z]</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
|-
| [https://dlmf.nist.gov/1.13#Ex1 1.13#Ex1] || [[Item:Q464|<math>w_{1}(z_{0}) = 1</math>]]<br><code>w_{1}(z_{0}) = 1</code> || <math></math> || <code>w[1](z[0]) = 1</code> || <code>Subscript[w, 1][Subscript[z, 0]] == 1</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
|-
| [https://dlmf.nist.gov/1.13#Ex3 1.13#Ex3] || [[Item:Q466|<math>w_{2}(z_{0}) = 0</math>]]<br><code>w_{2}(z_{0}) = 0</code> || <math></math> || <code>w[2](z[0]) = 0</code> || <code>Subscript[w, 2][Subscript[z, 0]] == 0</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
|-
| [https://dlmf.nist.gov/1.13.E6 1.13.E6] || [[Item:Q470|<math>Aw_{1}(z)+Bw_{2}(z) = 0</math>]]<br><code>Aw_{1}(z)+Bw_{2}(z) = 0</code> || <math></math> || <code>Aw[1](z)+ Bw[2](z) = 0</code> || <code>Subscript[Aw, 1][z]+ Subscript[Bw, 2][z] == 0</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
|-
| [https://dlmf.nist.gov/1.13.E9 1.13.E9] || [[Item:Q473|<math>w(z) = w_{0}(z)+Aw_{1}(z)+Bw_{2}(z)</math>]]<br><code>w(z) = w_{0}(z)+Aw_{1}(z)+Bw_{2}(z)</code> || <math></math> || <code>w(z) = w[0](z)+ Aw[1](z)+ Bw[2](z)</code> || <code>w[z] == Subscript[w, 0][z]+ Subscript[Aw, 1][z]+ Subscript[Bw, 2][z]</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
|-
| [https://dlmf.nist.gov/1.13.E10 1.13.E10] || [[Item:Q474|<math>w_{0}(z) = w_{2}(z)\int\frac{w_{1}(z)r(z)}{\Wronskian@{w_{1}(z),w_{2}(z)}}\diff{z}-w_{1}(z)\int\frac{w_{2}(z)r(z)}{\Wronskian@{w_{1}(z),w_{2}(z)}}\diff{z}</math>]]<br><code>w_{0}(z) = w_{2}(z)\int\frac{w_{1}(z)r(z)}{\Wronskian@{w_{1}(z),w_{2}(z)}}\diff{z}-w_{1}(z)\int\frac{w_{2}(z)r(z)}{\Wronskian@{w_{1}(z),w_{2}(z)}}\diff{z}</code> || <math></math> || <code>w[0](z) = w[2](z)* int((w[1](z)* r(z))/((w[1](z))*diff(w[2](z), z)-diff(w[1](z), z)*(w[2](z))), z)- w[1](z)* int((w[2](z)* r(z))/((w[1](z))*diff(w[2](z), z)-diff(w[1](z), z)*(w[2](z))), z)</code> || <code>Subscript[w, 0][z] == Subscript[w, 2][z]* Integrate[Divide[Subscript[w, 1][z]* r[z],Wronskian[{Subscript[w, 1][z], Subscript[w, 2][z]}, z]], z, GenerateConditions->None]- Subscript[w, 1][z]* Integrate[Divide[Subscript[w, 2][z]* r[z],Wronskian[{Subscript[w, 1][z], Subscript[w, 2][z]}, z]], z, GenerateConditions->None]</code> || Translation Error || Translation Error || - || -
|-
| [https://dlmf.nist.gov/1.13#Ex5 1.13#Ex5] || [[Item:Q476|<math>W(\xi) = w\left(\frac{1}{\xi}\right)</math>]]<br><code>W(\xi) = w\left(\frac{1}{\xi}\right)</code> || <math></math> || <code>W(xi) = w((1)/(xi))</code> || <code>W[\[Xi]] == w[Divide[1,\[Xi]]]</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
|-
| [https://dlmf.nist.gov/1.13.E14 1.13.E14] || [[Item:Q480|<math>\deriv[2]{W}{z}-H(z)W = 0</math>]]<br><code>\deriv[2]{W}{z}-H(z)W = 0</code> || <math></math> || <code>diff(W, [z$(2)])- H(z)* W = 0</code> || <code>D[W, {z, 2}]- H[z]* W == 0</code> || Translation Error || Translation Error || - || -
|-
| [https://dlmf.nist.gov/1.13#Ex8 1.13#Ex8] || [[Item:Q490|<math>\deriv[2]{U}{z}+IU = 0</math>]]<br><code>\deriv[2]{U}{z}+IU = 0</code> || <math></math> || <code>diff(U, [z$(2)])+ I*U = 0</code> || <code>D[U, {z, 2}]+ I*U == 0</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><code>300/300]: [[.5000000004+.8660254040*I <- {I = 1/2*3^(1/2)+1/2*I, U = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I}</code><br><code>.5000000004+.8660254040*I <- {I = 1/2*3^(1/2)+1/2*I, U = 1/2*3^(1/2)+1/2*I, z = -1/2+1/2*I*3^(1/2)}</code><br><code>.5000000004+.8660254040*I <- {I = 1/2*3^(1/2)+1/2*I, U = 1/2*3^(1/2)+1/2*I, z = 1/2-1/2*I*3^(1/2)}</code><br><code>.5000000004+.8660254040*I <- {I = 1/2*3^(1/2)+1/2*I, U = 1/2*3^(1/2)+1/2*I, z = -1/2*3^(1/2)-1/2*I}</code><br>... skip entries to safe data<br></div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [210 / 210]<div class="mw-collapsible-content"><code>{Complex[0.8660254037844387, 0.49999999999999994] <- {Rule[Complex[0, 1], 1], Rule[U, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br><code>Complex[1.7320508075688774, 0.9999999999999999] <- {Rule[Complex[0, 1], 2], Rule[U, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br></div></div>
|-
| [https://dlmf.nist.gov/1.13#Ex9 1.13#Ex9] || [[Item:Q491|<math>\deriv[2]{V}{z}+JV = 0</math>]]<br><code>\deriv[2]{V}{z}+JV = 0</code> || <math></math> || <code>diff(V, [z$(2)])+ J*V = 0</code> || <code>D[V, {z, 2}]+ J*V == 0</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><code>300/300]: [[.5000000004+.8660254040*I <- {J = 1/2*3^(1/2)+1/2*I, V = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I}</code><br><code>.5000000004+.8660254040*I <- {J = 1/2*3^(1/2)+1/2*I, V = 1/2*3^(1/2)+1/2*I, z = -1/2+1/2*I*3^(1/2)}</code><br><code>.5000000004+.8660254040*I <- {J = 1/2*3^(1/2)+1/2*I, V = 1/2*3^(1/2)+1/2*I, z = 1/2-1/2*I*3^(1/2)}</code><br><code>.5000000004+.8660254040*I <- {J = 1/2*3^(1/2)+1/2*I, V = 1/2*3^(1/2)+1/2*I, z = -1/2*3^(1/2)-1/2*I}</code><br>... skip entries to safe data<br></div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><code>{Complex[0.5000000000000001, 0.8660254037844386] <- {Rule[J, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[V, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br><code>Complex[0.5000000000000001, 0.8660254037844386] <- {Rule[J, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[V, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</code><br></div></div>
|-
| [https://dlmf.nist.gov/1.15.E1 1.15.E1] || [[Item:Q543|<math>s_{n} = \sum_{k=0}^{n}a_{k}</math>]]<br><code>s_{n} = \sum_{k=0}^{n}a_{k}</code> || <math></math> || <code>s[n] = sum(a[k], k = 0..n)</code> || <code>Subscript[s, n] == Sum[Subscript[a, k], {k, 0, n}, GenerateConditions->None]</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
|-
| [https://dlmf.nist.gov/1.15.E3 1.15.E3] || [[Item:Q545|<math>\lim_{x\to 1-}\sum^{\infty}_{n=0}a_{n}x^{n} = s</math>]]<br><code>\lim_{x\to 1-}\sum^{\infty}_{n=0}a_{n}x^{n} = s</code> || <math></math> || <code>limit(sum(a[n]*(x)^(n), n = 0..infinity), x = 1, left) = s</code> || <code>Limit[Sum[Subscript[a, n]*(x)^(n), {n, 0, Infinity}, GenerateConditions->None], x -> 1, Direction -> "FromBelow", GenerateConditions->None] == s</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
|-
| [https://dlmf.nist.gov/1.15.E7 1.15.E7] || [[Item:Q549|<math>\lim_{n\to\infty}\frac{n!}{(\alpha+1)_{n}}\sum^{n}_{k=0}\frac{(\alpha+1)_{k}}{k!}a_{n-k} = s</math>]]<br><code>\lim_{n\to\infty}\frac{n!}{(\alpha+1)_{n}}\sum^{n}_{k=0}\frac{(\alpha+1)_{k}}{k!}a_{n-k} = s</code> || <math></math> || <code>limit((factorial(n))/(alpha + 1[n])*sum((alpha + 1[k])/(factorial(k))*a[n - k], k = 0..n), n = infinity) = s</code> || <code>Limit[Divide[(n)!,Subscript[\[Alpha]+ 1, n]]*Sum[Divide[Subscript[\[Alpha]+ 1, k],(k)!]*Subscript[a, n - k], {k, 0, n}, GenerateConditions->None], n -> Infinity, GenerateConditions->None] == s</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
|-
| [https://dlmf.nist.gov/1.15.E9 1.15.E9] || [[Item:Q551|<math>\lim_{t\to\infty}e^{-t}\sum^{\infty}_{n=0}\frac{s_{n}}{n!}t^{n} = s</math>]]<br><code>\lim_{t\to\infty}e^{-t}\sum^{\infty}_{n=0}\frac{s_{n}}{n!}t^{n} = s</code> || <math></math> || <code>limit(exp(- t)*sum((s[n])/(factorial(n))*(t)^(n), n = 0..infinity), t = infinity) = s</code> || <code>Limit[Exp[- t]*Sum[Divide[Subscript[s, n],(n)!]*(t)^(n), {n, 0, Infinity}, GenerateConditions->None], t -> Infinity, GenerateConditions->None] == s</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
|-
| [https://dlmf.nist.gov/1.15.E10 1.15.E10] || [[Item:Q552|<math>\sum^{\infty}_{n=0}a_{n} = s</math>]]<br><code>\sum^{\infty}_{n=0}a_{n} = s</code> || <math></math> || <code>sum(a[n], n = 0..infinity) = s</code> || <code>Sum[Subscript[a, n], {n, 0, Infinity}, GenerateConditions->None] == s</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
|-
| [https://dlmf.nist.gov/1.15.E13 1.15.E13] || [[Item:Q555|<math>\frac{1}{2\pi}\int^{2\pi}_{0}P(r,\theta)\diff{\theta} = 1</math>]]<br><code>\frac{1}{2\pi}\int^{2\pi}_{0}P(r,\theta)\diff{\theta} = 1</code> || <math></math> || <code>(1)/(2*Pi)*int(P(r , theta), theta = 0..2*Pi) = 1</code> || <code>Divide[1,2*Pi]*Integrate[P[r , \[Theta]], {\[Theta], 0, 2*Pi}, GenerateConditions->None] == 1</code> || Successful || Aborted || - || Successful [Tested: 1]
|-
| [https://dlmf.nist.gov/1.15.E16 1.15.E16] || [[Item:Q558|<math>\frac{1}{2\pi}\int^{2\pi}_{0}K_{n}(\theta)\diff{\theta} = 1</math>]]<br><code>\frac{1}{2\pi}\int^{2\pi}_{0}K_{n}(\theta)\diff{\theta} = 1</code> || <math></math> || <code>(1)/(2*Pi)*int(K[n](theta), theta = 0..2*Pi) = 1</code> || <code>Divide[1,2*Pi]*Integrate[Subscript[K, n][\[Theta]], {\[Theta], 0, 2*Pi}, GenerateConditions->None] == 1</code> || Failure || Failure || Successful [Tested: 3] || Successful [Tested: 3]
|-
| [https://dlmf.nist.gov/1.15.E34 1.15.E34] || [[Item:Q576|<math>\frac{1}{2\pi}\int^{\infty}_{-\infty}P(x,y)\diff{x} = 1</math>]]<br><code>\frac{1}{2\pi}\int^{\infty}_{-\infty}P(x,y)\diff{x} = 1</code> || <math></math> || <code>(1)/(2*Pi)*int(P(x , y), x = - infinity..infinity) = 1</code> || <code>Divide[1,2*Pi]*Integrate[P[x , y], {x, - Infinity, Infinity}, GenerateConditions->None] == 1</code> || Successful || Successful || - || Successful [Tested: 3]
|-
| [https://dlmf.nist.gov/1.15.E39 1.15.E39] || [[Item:Q581|<math>\Phi(z) = \Phi(x+iy)</math>]]<br><code>\Phi(z) = \Phi(x+iy)</code> || <math></math> || <code>Phi*((x + y*I)) = Phi*(x + I*y)</code> || <code>\[CapitalPhi]*((x + y*I)) == \[CapitalPhi]*(x + I*y)</code> || Successful || Successful || - || Successful [Tested: 180]
|-
| [https://dlmf.nist.gov/1.15.E42 1.15.E42] || [[Item:Q584|<math>\int^{\infty}_{-\infty}K_{R}(s)\diff{s} = 1</math>]]<br><code>\int^{\infty}_{-\infty}K_{R}(s)\diff{s} = 1</code> || <math></math> || <code>int(K[R](s), s = - infinity..infinity) = 1</code> || <code>Integrate[Subscript[K, R][s], {s, - Infinity, Infinity}, GenerateConditions->None] == 1</code> || Failure || Aborted || <div class="toccolours mw-collapsible mw-collapsed">Failed [7 / 10]<div class="mw-collapsible-content"><code>7/10]: [[-.1339745960+.5000000000*I <- {R = 1/2*3^(1/2)+1/2*I}</code><br><code>-1.500000000+.8660254040*I <- {R = -1/2+1/2*I*3^(1/2)}</code><br><code>-.5000000000-.8660254040*I <- {R = 1/2-1/2*I*3^(1/2)}</code><br><code>-1.866025404-.5000000000*I <- {R = -1/2*3^(1/2)-1/2*I}</code><br>... skip entries to safe data<br></div></div> || Skipped - Because timed out
|-
| [https://dlmf.nist.gov/1.15.E48 1.15.E48] || [[Item:Q590|<math>I^{\alpha}I^{\beta} = I^{\alpha+\beta}</math>]]<br><code>I^{\alpha}I^{\beta} = I^{\alpha+\beta}</code> || <math>\realpart@@{\alpha} > 0, \realpart@@{\beta} > 0</math> || <code>(I)^(alpha)* (I)^(beta) = (I)^(alpha + beta)</code> || <code>(I)^\[Alpha]* (I)^\[Beta] == (I)^(\[Alpha]+ \[Beta])</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
|-
| [https://dlmf.nist.gov/1.15.E52 1.15.E52] || [[Item:Q594|<math>D^{k}I^{\alpha} = D^{n}I^{\alpha+n-k}</math>]]<br><code>D^{k}I^{\alpha} = D^{n}I^{\alpha+n-k}</code> || <math>k = 1</math> || <code>(D)^(k)* (I)^(alpha) = (D)^(n)* (I)^(alpha + n - k)</code> || <code>(D)^(k)* (I)^\[Alpha] == (D)^(n)* (I)^(\[Alpha]+ n - k)</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
|-
| [https://dlmf.nist.gov/1.15.E53 1.15.E53] || [[Item:Q595|<math>D^{\alpha}D^{\beta} = D^{\alpha+\beta}</math>]]<br><code>D^{\alpha}D^{\beta} = D^{\alpha+\beta}</code> || <math></math> || <code>(D)^(alpha)* (D)^(beta) = (D)^(alpha + beta)</code> || <code>(D)^\[Alpha]* (D)^\[Beta] == (D)^(\[Alpha]+ \[Beta])</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
|-
| [https://dlmf.nist.gov/1.15#Ex2 1.15#Ex2] || [[Item:Q597|<math>a_{n} > -\frac{K}{n}</math>]]<br><code>a_{n} > -\frac{K}{n}</code> || <math>n > 0, K > 0</math> || <code>a[n] > -(K)/(n)</code> || <code>Subscript[a, n] > -Divide[K,n]</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
|-
| [https://dlmf.nist.gov/1.15.E55 1.15.E55] || [[Item:Q598|<math>\sum^{\infty}_{n=0}a_{n} = s</math>]]<br><code>\sum^{\infty}_{n=0}a_{n} = s</code> || <math></math> || <code>sum(a[n], n = 0..infinity) = s</code> || <code>Sum[Subscript[a, n], {n, 0, Infinity}, GenerateConditions->None] == s</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
|-
| [https://dlmf.nist.gov/1.15.E56 1.15.E56] || [[Item:Q599|<math>\lim_{x\to 1-}(1-x)\sum^{\infty}_{n=0}a_{n}x^{n} = s</math>]]<br><code>\lim_{x\to 1-}(1-x)\sum^{\infty}_{n=0}a_{n}x^{n} = s</code> || <math></math> || <code>limit((1 - x)*sum(a[n]*(x)^(n), n = 0..infinity), x = 1, left) = s</code> || <code>Limit[(1 - x)*Sum[Subscript[a, n]*(x)^(n), {n, 0, Infinity}, GenerateConditions->None], x -> 1, Direction -> "FromBelow", GenerateConditions->None] == s</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
|-
| [https://dlmf.nist.gov/1.16.E1 1.16.E1] || [[Item:Q601|<math>\Lambda(\alpha_{1}\phi_{1}+\alpha_{2}\phi_{2}) = \alpha_{1}\Lambda(\phi_{1})+\alpha_{2}\Lambda(\phi_{2})</math>]]<br><code>\Lambda(\alpha_{1}\phi_{1}+\alpha_{2}\phi_{2}) = \alpha_{1}\Lambda(\phi_{1})+\alpha_{2}\Lambda(\phi_{2})</code> || <math></math> || <code>Lambda(alpha[1]*phi[1]+ alpha[2]*phi[2]) = alpha[1]*Lambda(phi[1])+ alpha[2]*Lambda(phi[2])</code> || <code>\[CapitalLambda][Subscript[\[Alpha], 1]*Subscript[\[Phi], 1]+ Subscript[\[Alpha], 2]*Subscript[\[Phi], 2]] == Subscript[\[Alpha], 1]*\[CapitalLambda][Subscript[\[Phi], 1]]+ Subscript[\[Alpha], 2]*\[CapitalLambda][Subscript[\[Phi], 2]]</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
|-
| [https://dlmf.nist.gov/1.16.E2 1.16.E2] || [[Item:Q602|<math>\lim_{n\to\infty}\Lambda(\phi_{n}) = \Lambda(\phi)</math>]]<br><code>\lim_{n\to\infty}\Lambda(\phi_{n}) = \Lambda(\phi)</code> || <math></math> || <code>limit(Lambda(phi[n]), n = infinity) = Lambda(phi)</code> || <code>Limit[\[CapitalLambda][Subscript[\[Phi], n]], n -> Infinity, GenerateConditions->None] == \[CapitalLambda][\[Phi]]</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
|-
| [https://dlmf.nist.gov/1.16.E17 1.16.E17] || [[Item:Q617|<math>\sigma_{n} = f^{(n)}(x_{0}+)-f^{(n)}(x_{0}-)</math>]]<br><code>\sigma_{n} = f^{(n)}(x_{0}+)-f^{(n)}(x_{0}-)</code> || <math></math> || <code>sigma[n] = (f)^(n)*(x[0]+)- (f)^(n)*(x[0]-)</code> || <code>Subscript[\[Sigma], n] == (f)^(n)*(Subscript[x, 0]+)- (f)^(n)*(Subscript[x, 0]-)</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
|-
| [https://dlmf.nist.gov/1.16.E19 1.16.E19] || [[Item:Q619|<math>x^{\alpha}_{+} = x^{\alpha}\HeavisideH@{x}</math>]]<br><code>x^{\alpha}_{+} = x^{\alpha}\HeavisideH@{x}</code> || <math></math> || <code>(x[+])^(alpha) = (x)^(alpha)* Heaviside(x)</code> || <code>(Subscript[x, +])^\[Alpha] == (x)^\[Alpha]* HeavisideTheta[x]</code> || Error || Failure || - || Error
|-
| [https://dlmf.nist.gov/1.16.E20 1.16.E20] || [[Item:Q620|<math>Dx^{\alpha}_{+} = \alpha x_{+}^{\alpha-1}</math>]]<br><code>Dx^{\alpha}_{+} = \alpha x_{+}^{\alpha-1}</code> || <math></math> || <code>D*(x[+])^(alpha) = alpha*(x[+])^(alpha - 1)</code> || <code>D*(Subscript[x, +])^\[Alpha] == \[Alpha]*(Subscript[x, +])^(\[Alpha]- 1)</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
|-
| [https://dlmf.nist.gov/1.16.E21 1.16.E21] || [[Item:Q621|<math>x^{\alpha}_{+} = \frac{1}{(\alpha+1)_{n}}D^{n}x_{+}^{\alpha+n}</math>]]<br><code>x^{\alpha}_{+} = \frac{1}{(\alpha+1)_{n}}D^{n}x_{+}^{\alpha+n}</code> || <math></math> || <code>(x[+])^(alpha) = (1)/(alpha + 1[n])*(D)^(n)* (x[+])^(alpha + n)</code> || <code>(Subscript[x, +])^\[Alpha] == Divide[1,Subscript[\[Alpha]+ 1, n]]*(D)^(n)* (Subscript[x, +])^(\[Alpha]+ n)</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
|-
| [https://dlmf.nist.gov/1.16.E22 1.16.E22] || [[Item:Q622|<math>\ln_{+}x = \HeavisideH@{x}\ln@@{x}</math>]]<br><code>\ln_{+}x = \HeavisideH@{x}\ln@@{x}</code> || <math></math> || <code>$0[+]ln()*x = Heaviside(x)*ln(x)</code> || <code>Subscript[$0, +]Log[]*x == HeavisideTheta[x]*Log[x]</code> || Translation Error || Translation Error || - || -
|-
| [https://dlmf.nist.gov/1.16.E23 1.16.E23] || [[Item:Q623|<math>(-1)^{n}n!x_{+}^{-1-n} = D^{(n+1)}\ln_{+}x</math>]]<br><code>(-1)^{n}n!x_{+}^{-1-n} = D^{(n+1)}\ln_{+}x</code> || <math></math> || <code>(- 1)^(n)* factorial(n)*(x[+])^(- 1 - n) = (D)^(n + 1)* [+]ln()*x</code> || <code>(- 1)^(n)* (n)!*(Subscript[x, +])^(- 1 - n) == Subscript[(D)^(n + 1)* , +]Log[]*x</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
|-
| [https://dlmf.nist.gov/1.16.E24 1.16.E24] || [[Item:Q624|<math>|x^{N}\phi_{n}^{(k)}| \leq c_{k,N}</math>]]<br><code>|x^{N}\phi_{n}^{(k)}| \leq c_{k,N}</code> || <math></math> || <code>abs((x)^(N)* (phi[n])^(k)) <= c[k , N]</code> || <code>Abs[(x)^(N)* (Subscript[\[Phi], n])^(k)] <= Subscript[c, k , N]</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
|-
| [https://dlmf.nist.gov/1.16.E28 1.16.E28] || [[Item:Q628|<math>|x^{m}\phi^{(k)}(x)| \leq c_{m,k}</math>]]<br><code>|x^{m}\phi^{(k)}(x)| \leq c_{m,k}</code> || <math></math> || <code>abs((x)^(m)* (phi(x)*)^(k)) <= c[m , k]</code> || <code>Abs[(x)^(m)* (\[Phi][x]*)^(k)] <= Subscript[c, m , k]</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
|-
| [https://dlmf.nist.gov/1.16#Ex2 1.16#Ex2] || [[Item:Q632|<math>D_{\boldsymbol{{\alpha}}} = \iunit^{-|\boldsymbol{{\alpha}}|}D^{\boldsymbol{{\alpha}}}</math>]]<br><code>D_{\boldsymbol{{\alpha}}} = \iunit^{-|\boldsymbol{{\alpha}}|}D^{\boldsymbol{{\alpha}}}</code> || <math></math> || <code>D[alpha] = (I)^(-abs(alpha))* (D)^(alpha)</code> || <code>Subscript[D, \[Alpha]] == (I)^(-Abs[\[Alpha]])* (D)^\[Alpha]</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><code>300/300]: [[.8660254041+1.500000000*I <- {D = 1/2*3^(1/2)+1/2*I, alpha = 1.5, D[alpha] = 1/2*3^(1/2)+1/2*I}</code><br><code>-.4999999999+1.866025404*I <- {D = 1/2*3^(1/2)+1/2*I, alpha = 1.5, D[alpha] = -1/2+1/2*I*3^(1/2)}</code><br><code>.5000000001+.1339745960*I <- {D = 1/2*3^(1/2)+1/2*I, alpha = 1.5, D[alpha] = 1/2-1/2*I*3^(1/2)}</code><br><code>-.8660254039+.5000000000*I <- {D = 1/2*3^(1/2)+1/2*I, alpha = 1.5, D[alpha] = -1/2*3^(1/2)-1/2*I}</code><br>... skip entries to safe data<br></div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><code>{Complex[0.8660254037844387, 1.5] <- {Rule[D, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[α, 1.5], Rule[Subscript[D, α], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br><code>Complex[-0.4999999999999998, 1.8660254037844388] <- {Rule[D, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[α, 1.5], Rule[Subscript[D, α], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</code><br></div></div>
|-
| [https://dlmf.nist.gov/1.16.E31 1.16.E31] || [[Item:Q633|<math>P(\mathbf{x}) = \sum_{\boldsymbol{{\alpha}}}c_{\boldsymbol{{\alpha}}}\mathbf{x}^{\boldsymbol{{\alpha}}}</math>]]<br><code>P(\mathbf{x}) = \sum_{\boldsymbol{{\alpha}}}c_{\boldsymbol{{\alpha}}}\mathbf{x}^{\boldsymbol{{\alpha}}}</code> || <math></math> || <code>P(x) = sum(c[alpha]*(x)^(alpha), $0[alpha]*c[alpha]*(x)^(alpha) = - infinity..infinity)</code> || <code>P[x] == Sum[Subscript[c, \[Alpha]]*(x)^\[Alpha], {Subscript[$0, \[Alpha]]*Subscript[c, \[Alpha]]*(x)^\[Alpha], - Infinity, Infinity}, GenerateConditions->None]</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
|-
| [https://dlmf.nist.gov/1.16.E32 1.16.E32] || [[Item:Q634|<math>P(\mathbf{D}) = \sum_{\boldsymbol{{\alpha}}}c_{\boldsymbol{{\alpha}}}\mathbf{D}^{\alpha}</math>]]<br><code>P(\mathbf{D}) = \sum_{\boldsymbol{{\alpha}}}c_{\boldsymbol{{\alpha}}}\mathbf{D}^{\alpha}</code> || <math></math> || <code>P(D) = sum(c[alpha]*(D)^(alpha), $0[alpha]*c[alpha]*(D)^(alpha) = - infinity..infinity)</code> || <code>P[D] == Sum[Subscript[c, \[Alpha]]*(D)^\[Alpha], {Subscript[$0, \[Alpha]]*Subscript[c, \[Alpha]]*(D)^\[Alpha], - Infinity, Infinity}, GenerateConditions->None]</code> || Translation Error || Translation Error || - || -
|-
| [https://dlmf.nist.gov/1.16#Ex3 1.16#Ex3] || [[Item:Q635|<math>P(D) = \sum_{\boldsymbol{{\alpha}}}c_{\boldsymbol{{\alpha}}}D_{\boldsymbol{{\alpha}}}</math>]]<br><code>P(D) = \sum_{\boldsymbol{{\alpha}}}c_{\boldsymbol{{\alpha}}}D_{\boldsymbol{{\alpha}}}</code> || <math></math> || <code>P(D) = sum(c[alpha]*D[alpha], $0[alpha]*c[alpha]*D[alpha] = - infinity..infinity)</code> || <code>P[D] == Sum[Subscript[c, \[Alpha]]*Subscript[D, \[Alpha]], {Subscript[$0, \[Alpha]]*Subscript[c, \[Alpha]]*Subscript[D, \[Alpha]], - Infinity, Infinity}, GenerateConditions->None]</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
|-
| [https://dlmf.nist.gov/1.16#Ex7 1.16#Ex7] || [[Item:Q643|<math>\mathcal{F}(P(D)u) = P(-\mathbf{x})\mathcal{F}(u)</math>]]<br><code>\mathcal{F}(P(D)u) = P(-\mathbf{x})\mathcal{F}(u)</code> || <math></math> || <code>F(P(D)* u) = P(- x)* F(u)</code> || <code>F[P[D]* u] == P[- x]* F[u]</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
|-
| [https://dlmf.nist.gov/1.16#Ex8 1.16#Ex8] || [[Item:Q645|<math>\mathcal{F}(Pu) = P(D)\mathcal{F}(u)</math>]]<br><code>\mathcal{F}(Pu) = P(D)\mathcal{F}(u)</code> || <math></math> || <code>F(P*u) = P(D)* F(u)</code> || <code>F[P*u] == P[D]* F[u]</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
|-
| [https://dlmf.nist.gov/1.16.E40 1.16.E40] || [[Item:Q648|<math>\int^{\infty}_{-\infty}\Diracdelta@{t}\expe^{\iunit xt}\diff{t} = 1</math>]]<br><code>\int^{\infty}_{-\infty}\Diracdelta@{t}\expe^{\iunit xt}\diff{t} = 1</code> || <math></math> || <code>int(Dirac(t)*exp(I*x*t), t = - infinity..infinity) = 1</code> || <code>Integrate[DiracDelta[t]*Exp[I*x*t], {t, - Infinity, Infinity}, GenerateConditions->None] == 1</code> || Successful || Successful || - || Successful [Tested: 3]
|-
| [https://dlmf.nist.gov/1.16.E43 1.16.E43] || [[Item:Q651|<math>\frac{1}{2\cpi}\int^{\infty}_{-\infty}\expe^{\iunit xt}\diff{t} = \Diracdelta@{x}</math>]]<br><code>\frac{1}{2\cpi}\int^{\infty}_{-\infty}\expe^{\iunit xt}\diff{t} = \Diracdelta@{x}</code> || <math></math> || <code>(1)/(2*Pi)*int(exp(I*x*t), t = - infinity..infinity) = Dirac(x)</code> || <code>Divide[1,2*Pi]*Integrate[Exp[I*x*t], {t, - Infinity, Infinity}, GenerateConditions->None] == DiracDelta[x]</code> || Successful || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [3 / 3]<div class="mw-collapsible-content"><code>{Complex[-0.07099199156997928, 3.003857199159988*^-16] <- {Rule[x, 1.5]}</code><br><code>Complex[0.07742603591272186, 0.30312240144001046] <- {Rule[x, 0.5]}</code><br></div></div>
|-
| [https://dlmf.nist.gov/1.16.E44 1.16.E44] || [[Item:Q652|<math>\sign@{x} = 2\HeavisideH@{x}-1</math>]]<br><code>\sign@{x} = 2\HeavisideH@{x}-1</code> || <math>x \neq 0</math> || <code>signum(x) = 2*Heaviside(x)- 1</code> || <code>Sign[x] == 2*HeavisideTheta[x]- 1</code> || Failure || Failure || Successful [Tested: 3] || Successful [Tested: 3]
|-
| [https://dlmf.nist.gov/1.17.E1 1.17.E1] || [[Item:Q660|<math>\Diracdelta@{x} = 0</math>]]<br><code>\Diracdelta@{x} = 0</code> || <math>x \neq 0</math> || <code>Dirac(x) = 0</code> || <code>DiracDelta[x] == 0</code> || Failure || Successful || Successful [Tested: 3] || Successful [Tested: 1]
|-
| [https://dlmf.nist.gov/1.17.E2 1.17.E2] || [[Item:Q661|<math>\int_{-\infty}^{\infty}\Diracdelta@{x-a}\phi(x)\diff{x} = \phi(a)</math>]]<br><code>\int_{-\infty}^{\infty}\Diracdelta@{x-a}\phi(x)\diff{x} = \phi(a)</code> || <math></math> || <code>int(Dirac(x - a)*phi(x), x = - infinity..infinity) = phi(a)</code> || <code>Integrate[DiracDelta[x - a]*\[Phi][x], {x, - Infinity, Infinity}, GenerateConditions->None] == \[Phi][a]</code> || Successful || Successful || - || Successful [Tested: 10]
|-
| [https://dlmf.nist.gov/1.17.E6 1.17.E6] || [[Item:Q665|<math>\lim_{n\to\infty}\sqrt{\frac{n}{\pi}}\int_{-\infty}^{\infty}e^{-n(x-a)^{2}}\phi(x)\diff{x} = \phi(a)</math>]]<br><code>\lim_{n\to\infty}\sqrt{\frac{n}{\pi}}\int_{-\infty}^{\infty}e^{-n(x-a)^{2}}\phi(x)\diff{x} = \phi(a)</code> || <math></math> || <code>limit(sqrt((n)/(Pi))*int(exp(- n*(x - a)^(2))*phi(x), x = - infinity..infinity), n = infinity) = phi(a)</code> || <code>Limit[Sqrt[Divide[n,Pi]]*Integrate[Exp[- n*(x - a)^(2)]*\[Phi][x], {x, - Infinity, Infinity}, GenerateConditions->None], n -> Infinity, GenerateConditions->None] == \[Phi][a]</code> || Successful || Aborted || - || Successful [Tested: 60]
|-
| [https://dlmf.nist.gov/1.17.E7 1.17.E7] || [[Item:Q666|<math>\lim_{n\to\infty}\sqrt{\frac{n}{\pi}}\int_{-\infty}^{\infty}e^{-n(x-a)^{2}}\phi(x)\diff{x} = \tfrac{1}{2}\phi(a-)+\tfrac{1}{2}\phi(a+)</math>]]<br><code>\lim_{n\to\infty}\sqrt{\frac{n}{\pi}}\int_{-\infty}^{\infty}e^{-n(x-a)^{2}}\phi(x)\diff{x} = \tfrac{1}{2}\phi(a-)+\tfrac{1}{2}\phi(a+)</code> || <math></math> || <code>limit(sqrt((n)/(Pi))*int(exp(- n*(x - a)^(2))*phi(x), x = - infinity..infinity), n = infinity) = (1)/(2)*phi(a -)+(1)/(2)*phi(a +)</code> || <code>Limit[Sqrt[Divide[n,Pi]]*Integrate[Exp[- n*(x - a)^(2)]*\[Phi][x], {x, - Infinity, Infinity}, GenerateConditions->None], n -> Infinity, GenerateConditions->None] == Divide[1,2]*\[Phi][a -]+Divide[1,2]*\[Phi][a +]</code> || Error || Failure || - || Error
|-
| [https://dlmf.nist.gov/1.17.E8 1.17.E8] || [[Item:Q667|<math>\frac{1}{2\pi}\int_{-\infty}^{\infty}e^{-iat}\left(\int_{-\infty}^{\infty}\phi(x)e^{itx}\diff{x}\right)\diff{t} = \phi(a)</math>]]<br><code>\frac{1}{2\pi}\int_{-\infty}^{\infty}e^{-iat}\left(\int_{-\infty}^{\infty}\phi(x)e^{itx}\diff{x}\right)\diff{t} = \phi(a)</code> || <math></math> || <code>(1)/(2*Pi)*int(exp(- I*a*t)*(int(phi(x)* exp(I*t*x), x = - infinity..infinity)), t = - infinity..infinity) = phi(a)</code> || <code>Divide[1,2*Pi]*Integrate[Exp[- I*a*t]*(Integrate[\[Phi][x]* Exp[I*t*x], {x, - Infinity, Infinity}, GenerateConditions->None]), {t, - Infinity, Infinity}, GenerateConditions->None] == \[Phi][a]</code> || Failure || Aborted || <div class="toccolours mw-collapsible mw-collapsed">Failed [60 / 60]<div class="mw-collapsible-content"><code>60/60]: [[Float(undefined)+.7500000000*I <- {a = -1.5, phi = 1/2*3^(1/2)+1/2*I}</code><br><code>Float(undefined)+1.299038106*I <- {a = -1.5, phi = -1/2+1/2*I*3^(1/2)}</code><br><code>Float(undefined)-1.299038106*I <- {a = -1.5, phi = 1/2-1/2*I*3^(1/2)}</code><br><code>Float(undefined)-.7500000000*I <- {a = -1.5, phi = -1/2*3^(1/2)-1/2*I}</code><br>... skip entries to safe data<br></div></div> || Skipped - Because timed out
|-
| [https://dlmf.nist.gov/1.17.E9 1.17.E9] || [[Item:Q668|<math>\int_{-\infty}^{\infty}\left(\frac{1}{2\pi}\int_{-\infty}^{\infty}e^{i(x-a)t}\diff{t}\right)\phi(x)\diff{x} = \phi(a)</math>]]<br><code>\int_{-\infty}^{\infty}\left(\frac{1}{2\pi}\int_{-\infty}^{\infty}e^{i(x-a)t}\diff{t}\right)\phi(x)\diff{x} = \phi(a)</code> || <math></math> || <code>int(((1)/(2*Pi)*int(exp(I*(x - a)*t), t = - infinity..infinity))*phi(x), x = - infinity..infinity) = phi(a)</code> || <code>Integrate[(Divide[1,2*Pi]*Integrate[Exp[I*(x - a)*t], {t, - Infinity, Infinity}, GenerateConditions->None])*\[Phi][x], {x, - Infinity, Infinity}, GenerateConditions->None] == \[Phi][a]</code> || Successful || Aborted || - || Skipped - Because timed out
|-
| [https://dlmf.nist.gov/1.17.E10 1.17.E10] || [[Item:Q669|<math>\frac{1}{2\pi}\int_{-\infty}^{\infty}e^{-t^{2}/(4n)}e^{i(x-a)t}\diff{t} = \sqrt{\frac{n}{\pi}}e^{-n(x-a)^{2}}</math>]]<br><code>\frac{1}{2\pi}\int_{-\infty}^{\infty}e^{-t^{2}/(4n)}e^{i(x-a)t}\diff{t} = \sqrt{\frac{n}{\pi}}e^{-n(x-a)^{2}}</code> || <math></math> || <code>(1)/(2*Pi)*int(exp(- (t)^(2)/(4*n))*exp(I*(x - a)*t), t = - infinity..infinity) = sqrt((n)/(Pi))*exp(- n*(x - a)^(2))</code> || <code>Divide[1,2*Pi]*Integrate[Exp[- (t)^(2)/(4*n)]*Exp[I*(x - a)*t], {t, - Infinity, Infinity}, GenerateConditions->None] == Sqrt[Divide[n,Pi]]*Exp[- n*(x - a)^(2)]</code> || Failure || Successful || Successful [Tested: 54] || Successful [Tested: 54]
|-
| [https://dlmf.nist.gov/1.17.E12 1.17.E12] || [[Item:Q671|<math>\Diracdelta@{x-a} = \frac{1}{2\pi}\int_{-\infty}^{\infty}e^{i(x-a)t}\diff{t}</math>]]<br><code>\Diracdelta@{x-a} = \frac{1}{2\pi}\int_{-\infty}^{\infty}e^{i(x-a)t}\diff{t}</code> || <math></math> || <code>Dirac(x - a) = (1)/(2*Pi)*int(exp(I*(x - a)*t), t = - infinity..infinity)</code> || <code>DiracDelta[x - a] == Divide[1,2*Pi]*Integrate[Exp[I*(x - a)*t], {t, - Infinity, Infinity}, GenerateConditions->None]</code> || Successful || Failure || - || Skipped - Because timed out
|-
| [https://dlmf.nist.gov/1.17.E13 1.17.E13] || [[Item:Q672|<math>\Diracdelta@{x-a} = x\int_{0}^{\infty}t\BesselJ{\nu}@{xt}\BesselJ{\nu}@{at}\diff{t}</math>]]<br><code>\Diracdelta@{x-a} = x\int_{0}^{\infty}t\BesselJ{\nu}@{xt}\BesselJ{\nu}@{at}\diff{t}</code> || <math>\realpart@@{\nu} > -1, x > 0, a > 0</math> || <code>Dirac(x - a) = x*int(t*BesselJ(nu, x*t)*BesselJ(nu, a*t), t = 0..infinity)</code> || <code>DiracDelta[x - a] == x*Integrate[t*BesselJ[\[Nu], x*t]*BesselJ[\[Nu], a*t], {t, 0, Infinity}, GenerateConditions->None]</code> || Failure || Aborted || Error || Skipped - Because timed out
|-
| [https://dlmf.nist.gov/1.17.E14 1.17.E14] || [[Item:Q673|<math>\Diracdelta@{x-a} = \frac{2xa}{\pi}\int_{0}^{\infty}t^{2}\sphBesselJ{\ell}@{xt}\sphBesselJ{\ell}@{at}\diff{t}</math>]]<br><code>\Diracdelta@{x-a} = \frac{2xa}{\pi}\int_{0}^{\infty}t^{2}\sphBesselJ{\ell}@{xt}\sphBesselJ{\ell}@{at}\diff{t}</code> || <math>x > 0, a > 0</math> || <code>Error</code> || <code>DiracDelta[x - a] == Divide[2*x*a,Pi]*Integrate[(t)^(2)* SphericalBesselJ[\[ScriptL], x*t]*SphericalBesselJ[\[ScriptL], a*t], {t, 0, Infinity}, GenerateConditions->None]</code> || Missing Macro Error || Aborted || - || Skipped - Because timed out
|-
| [https://dlmf.nist.gov/1.17.E16 1.17.E16] || [[Item:Q675|<math>\Diracdelta@{x-a} = \int_{-\infty}^{\infty}\AiryAi@{t-x}\AiryAi@{t-a}\diff{t}</math>]]<br><code>\Diracdelta@{x-a} = \int_{-\infty}^{\infty}\AiryAi@{t-x}\AiryAi@{t-a}\diff{t}</code> || <math></math> || <code>Dirac(x - a) = int(AiryAi(t - x)*AiryAi(t - a), t = - infinity..infinity)</code> || <code>DiracDelta[x - a] == Integrate[AiryAi[t - x]*AiryAi[t - a], {t, - Infinity, Infinity}, GenerateConditions->None]</code> || Failure || Aborted || Skipped - Because timed out || Skipped - Because timed out
|-
| [https://dlmf.nist.gov/1.17.E17 1.17.E17] || [[Item:Q676|<math>\frac{1}{2\pi}\sum_{k=-\infty}^{\infty}e^{-ika}\left(\int_{-\pi}^{\pi}\phi(x)e^{ikx}\diff{x}\right) = \phi(a)</math>]]<br><code>\frac{1}{2\pi}\sum_{k=-\infty}^{\infty}e^{-ika}\left(\int_{-\pi}^{\pi}\phi(x)e^{ikx}\diff{x}\right) = \phi(a)</code> || <math></math> || <code>(1)/(2*Pi)*sum(exp(- I*k*a)*(int(phi(x)* exp(I*k*x), x = - Pi..Pi)), k = - infinity..infinity) = phi(a)</code> || <code>Divide[1,2*Pi]*Sum[Exp[- I*k*a]*(Integrate[\[Phi][x]* Exp[I*k*x], {x, - Pi, Pi}, GenerateConditions->None]), {k, - Infinity, Infinity}, GenerateConditions->None] == \[Phi][a]</code> || Error || Failure || - || Successful [Tested: 60]
|-
| [https://dlmf.nist.gov/1.17.E18 1.17.E18] || [[Item:Q677|<math>\int_{-\pi}^{\pi}\phi(x)\left(\frac{1}{2\pi}\sum_{k=-\infty}^{\infty}e^{ik(x-a)}\right)\diff{x} = \phi(a)</math>]]<br><code>\int_{-\pi}^{\pi}\phi(x)\left(\frac{1}{2\pi}\sum_{k=-\infty}^{\infty}e^{ik(x-a)}\right)\diff{x} = \phi(a)</code> || <math></math> || <code>int(phi(x)*((1)/(2*Pi)*sum(exp(I*k*(x - a)), k = - infinity..infinity)), x = - Pi..Pi) = phi(a)</code> || <code>Integrate[\[Phi][x]*(Divide[1,2*Pi]*Sum[Exp[I*k*(x - a)], {k, - Infinity, Infinity}, GenerateConditions->None]), {x, - Pi, Pi}, GenerateConditions->None] == \[Phi][a]</code> || Aborted || Aborted || Skipped - Because timed out || Skipped - Because timed out
|-
| [https://dlmf.nist.gov/1.17.E21 1.17.E21] || [[Item:Q680|<math>\Diracdelta@{x-a} = \frac{1}{2\pi}\sum_{k=-\infty}^{\infty}e^{ik(x-a)}</math>]]<br><code>\Diracdelta@{x-a} = \frac{1}{2\pi}\sum_{k=-\infty}^{\infty}e^{ik(x-a)}</code> || <math></math> || <code>Dirac(x - a) = (1)/(2*Pi)*sum(exp(I*k*(x - a)), k = - infinity..infinity)</code> || <code>DiracDelta[x - a] == Divide[1,2*Pi]*Sum[Exp[I*k*(x - a)], {k, - Infinity, Infinity}, GenerateConditions->None]</code> || Failure || Failure || Skipped - Because timed out || <div class="toccolours mw-collapsible mw-collapsed">Failed [18 / 18]<div class="mw-collapsible-content"><code>{Times[-0.15915494309189535, NSum[Power[E, Times[Complex[0.0, 3.0], k]] <- {k, DirectedInfinity[-1], DirectedInfinity[1]}, Rule[GenerateConditions, None]]], {Rule[a, -1.5], Rule[x, 1.5]}</code><br><code>Times[-0.15915494309189535, NSum[Power[E, Times[Complex[0.0, 2.0], k]] <- {k, DirectedInfinity[-1], DirectedInfinity[1]}, Rule[GenerateConditions, None]]], {Rule[a, -1.5], Rule[x, 0.5]}</code><br></div></div>
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| [https://dlmf.nist.gov/1.17.E22 1.17.E22] || [[Item:Q681|<math>\Diracdelta@{x-a} = \sum_{k=0}^{\infty}(k+\tfrac{1}{2})\LegendrepolyP{k}@{x}\LegendrepolyP{k}@{a}</math>]]<br><code>\Diracdelta@{x-a} = \sum_{k=0}^{\infty}(k+\tfrac{1}{2})\LegendrepolyP{k}@{x}\LegendrepolyP{k}@{a}</code> || <math></math> || <code>Dirac(x - a) = sum((k +(1)/(2))*LegendreP(k, x)*LegendreP(k, a), k = 0..infinity)</code> || <code>DiracDelta[x - a] == Sum[(k +Divide[1,2])*LegendreP[k, x]*LegendreP[k, a], {k, 0, Infinity}, GenerateConditions->None]</code> || Failure || Failure || Error || <div class="toccolours mw-collapsible mw-collapsed">Failed [18 / 18]<div class="mw-collapsible-content"><code>{Times[-1.0, NSum[Times[Plus[Rational[1, 2], k], LegendreP[k, -1.5], LegendreP[k, 1.5]] <- {k, 0, DirectedInfinity[1]}, Rule[GenerateConditions, None]]], {Rule[a, -1.5], Rule[x, 1.5]}</code><br><code>Times[-1.0, NSum[Times[Plus[Rational[1, 2], k], LegendreP[k, -1.5], LegendreP[k, 0.5]] <- {k, 0, DirectedInfinity[1]}, Rule[GenerateConditions, None]]], {Rule[a, -1.5], Rule[x, 0.5]}</code><br></div></div>
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| [https://dlmf.nist.gov/1.17.E23 1.17.E23] || [[Item:Q682|<math>\Diracdelta@{x-a} = e^{-(x+a)/2}\sum_{k=0}^{\infty}\LaguerrepolyL[]{k}@{x}\LaguerrepolyL[]{k}@{a}</math>]]<br><code>\Diracdelta@{x-a} = e^{-(x+a)/2}\sum_{k=0}^{\infty}\LaguerrepolyL[]{k}@{x}\LaguerrepolyL[]{k}@{a}</code> || <math></math> || <code>Dirac(x - a) = exp(-(x + a)/2)*sum(LaguerreL(k, x)*LaguerreL(k, a), k = 0..infinity)</code> || <code>DiracDelta[x - a] == Exp[-(x + a)/2]*Sum[LaguerreL[k, x]*LaguerreL[k, a], {k, 0, Infinity}, GenerateConditions->None]</code> || Failure || Failure || Error || <div class="toccolours mw-collapsible mw-collapsed">Failed [18 / 18]<div class="mw-collapsible-content"><code>{Times[-1.0, NSum[Times[LaguerreL[k, -1.5], LaguerreL[k, 1.5]] <- {k, 0, DirectedInfinity[1]}, Rule[GenerateConditions, None]]], {Rule[a, -1.5], Rule[x, 1.5]}</code><br><code>Times[-1.6487212707001282, NSum[Times[LaguerreL[k, -1.5], LaguerreL[k, 0.5]] <- {k, 0, DirectedInfinity[1]}, Rule[GenerateConditions, None]]], {Rule[a, -1.5], Rule[x, 0.5]}</code><br></div></div>
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| [https://dlmf.nist.gov/1.17.E24 1.17.E24] || [[Item:Q683|<math>\Diracdelta@{x-a} = \frac{e^{-(x^{2}+a^{2})/2}}{\sqrt{\pi}}\sum_{k=0}^{\infty}\frac{\HermitepolyH{k}@{x}\HermitepolyH{k}@{a}}{2^{k}k!}</math>]]<br><code>\Diracdelta@{x-a} = \frac{e^{-(x^{2}+a^{2})/2}}{\sqrt{\pi}}\sum_{k=0}^{\infty}\frac{\HermitepolyH{k}@{x}\HermitepolyH{k}@{a}}{2^{k}k!}</code> || <math></math> || <code>Dirac(x - a) = (exp(-((x)^(2)+ (a)^(2))/2))/(sqrt(Pi))*sum((HermiteH(k, x)*HermiteH(k, a))/((2)^(k)* factorial(k)), k = 0..infinity)</code> || <code>DiracDelta[x - a] == Divide[Exp[-((x)^(2)+ (a)^(2))/2],Sqrt[Pi]]*Sum[Divide[HermiteH[k, x]*HermiteH[k, a],(2)^(k)* (k)!], {k, 0, Infinity}, GenerateConditions->None]</code> || Failure || Failure || Skipped - Because timed out || <div class="toccolours mw-collapsible mw-collapsed">Failed [18 / 18]<div class="mw-collapsible-content"><code>{Times[-0.05946514461181468, NSum[Times[Power[2, Times[-1, k]], Power[Factorial[k], -1], HermiteH[k, -1.5], HermiteH[k, 1.5]] <- {k, 0, DirectedInfinity[1]}, Rule[GenerateConditions, None]]], {Rule[a, -1.5], Rule[x, 1.5]}</code><br><code>Times[-0.16164302202498515, NSum[Times[Power[2, Times[-1, k]], Power[Factorial[k], -1], HermiteH[k, -1.5], HermiteH[k, 0.5]] <- {k, 0, DirectedInfinity[1]}, Rule[GenerateConditions, None]]], {Rule[a, -1.5], Rule[x, 0.5]}</code><br></div></div>
|-
| [https://dlmf.nist.gov/1.17.E25 1.17.E25] || [[Item:Q684|<math>\Diracdelta@{\cos@@{\theta_{1}}-\cos@@{\theta_{2}}}\Diracdelta@{\phi_{1}-\phi_{2}} = \sum_{\ell=0}^{\infty}\sum_{m=-\ell}^{\ell}\sphharmonicY{\ell}{m}@{\theta_{1}}{\phi_{1}}\conj{\sphharmonicY{\ell}{m}@{\theta_{2}}{\phi_{2}}}</math>]]<br><code>\Diracdelta@{\cos@@{\theta_{1}}-\cos@@{\theta_{2}}}\Diracdelta@{\phi_{1}-\phi_{2}} = \sum_{\ell=0}^{\infty}\sum_{m=-\ell}^{\ell}\sphharmonicY{\ell}{m}@{\theta_{1}}{\phi_{1}}\conj{\sphharmonicY{\ell}{m}@{\theta_{2}}{\phi_{2}}}</code> || <math></math> || <code>Dirac(cos(theta[1])- cos(theta[2]))*Dirac(phi[1]- phi[2]) = sum(sum(SphericalY(ell, m, theta[1], phi[1])*conjugate(SphericalY(ell, m, theta[2], phi[2])), m = - ell..ell), ell = 0..infinity)</code> || <code>DiracDelta[Cos[Subscript[\[Theta], 1]]- Cos[Subscript[\[Theta], 2]]]*DiracDelta[Subscript[\[Phi], 1]- Subscript[\[Phi], 2]] == Sum[Sum[SphericalHarmonicY[\[ScriptL], m, Subscript[\[Theta], 1], Subscript[\[Phi], 1]]*Conjugate[SphericalHarmonicY[\[ScriptL], m, Subscript[\[Theta], 2], Subscript[\[Phi], 2]]], {m, - \[ScriptL], \[ScriptL]}, GenerateConditions->None], {\[ScriptL], 0, Infinity}, GenerateConditions->None]</code> || Aborted || Failure || Skipped - Because timed out || Skipped - Because timed out
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|}

Latest revision as of 15:05, 25 May 2021

Notation
1.1 Special Notation
Areas
1.2 Elementary Algebra
1.3 Determinants
1.4 Calculus of One Variable
1.5 Calculus of Two or More Variables
1.6 Vectors and Vector-Valued Functions
1.7 Inequalities
1.8 Fourier Series
1.9 Calculus of a Complex Variable
1.10 Functions of a Complex Variable
1.11 Zeros of Polynomials
1.12 Continued Fractions
1.13 Differential Equations
1.14 Integral Transforms
1.15 Summability Methods
1.16 Distributions
1.17 Integral and Series Representations of the Dirac Delta
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