1.2: Difference between revisions
Jump to navigation
Jump to search
Admin moved page Main Page to Verifying DLMF with Maple and Mathematica |
Admin moved page Main Page to Verifying DLMF with Maple and Mathematica |
||
(One intermediate revision by the same user not shown) | |||
Line 1: | Line 1: | ||
{{DISPLAYTITLE:Algebraic and Analytic Methods - 1.2 Elementary Algebra}} | |||
<div style="width: 100%; height: 75vh; overflow: auto;"> | <div style="width: 100%; height: 75vh; overflow: auto;"> | ||
{| class="wikitable sortable" style="margin: 0;" | {| class="wikitable sortable" style="margin: 0;" | ||
Line 12: | Line 14: | ||
! scope="col" style="position: sticky; top: 0;" | Numeric<br>Mathematica | ! scope="col" style="position: sticky; top: 0;" | Numeric<br>Mathematica | ||
|- | |- | ||
| [https://dlmf.nist.gov/1.2.E1 1.2.E1] | | | [https://dlmf.nist.gov/1.2.E1 1.2.E1] || <math qid="Q30">\binom{n}{k} = \frac{n!}{(n-k)!k!}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\binom{n}{k} = \frac{n!}{(n-k)!k!}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>binomial(n,k) = (factorial(n))/(factorial(n - k)*factorial(k))</syntaxhighlight> || <syntaxhighlight lang=mathematica>Binomial[n,k] == Divide[(n)!,(n - k)!*(k)!]</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 9] | ||
|- | |- | ||
| [https://dlmf.nist.gov/1.2.E1 1.2.E1] | | | [https://dlmf.nist.gov/1.2.E1 1.2.E1] || <math qid="Q30">\frac{n!}{(n-k)!k!} = \binom{n}{n-k}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\frac{n!}{(n-k)!k!} = \binom{n}{n-k}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>(factorial(n))/(factorial(n - k)*factorial(k)) = binomial(n,n - k)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Divide[(n)!,(n - k)!*(k)!] == Binomial[n,n - k]</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 9] | ||
|- | |- | ||
| [https://dlmf.nist.gov/1.2.E6 1.2.E6] | | | [https://dlmf.nist.gov/1.2.E6 1.2.E6] || <math qid="Q35">\frac{(-1)^{k}\Pochhammersym{-z}{k}}{k!} = (-1)^{k}\binom{k-z-1}{k}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\frac{(-1)^{k}\Pochhammersym{-z}{k}}{k!} = (-1)^{k}\binom{k-z-1}{k}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>((- 1)^(k)* pochhammer(- z, k))/(factorial(k)) = (- 1)^(k)*binomial(k - z - 1,k)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Divide[(- 1)^(k)* Pochhammer[- z, k],(k)!] == (- 1)^(k)*Binomial[k - z - 1,k]</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 21] | ||
|- | |- | ||
| [https://dlmf.nist.gov/1.2.E7 1.2.E7] | | | [https://dlmf.nist.gov/1.2.E7 1.2.E7] || <math qid="Q36">\binom{z+1}{k} = \binom{z}{k}+\binom{z}{k-1}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\binom{z+1}{k} = \binom{z}{k}+\binom{z}{k-1}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>binomial(z + 1,k) = binomial(z,k)+binomial(z,k - 1)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Binomial[z + 1,k] == Binomial[z,k]+Binomial[z,k - 1]</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 21] | ||
|- | |- | ||
| [https://dlmf.nist.gov/1.2.E8 1.2.E8] | | | [https://dlmf.nist.gov/1.2.E8 1.2.E8] || <math qid="Q37">\sum^{m}_{k=0}\binom{z+k}{k} = \binom{z+m+1}{m}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\sum^{m}_{k=0}\binom{z+k}{k} = \binom{z+m+1}{m}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>sum(binomial(z + k,k), k = 0..m) = binomial(z + m + 1,m)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Sum[Binomial[z + k,k], {k, 0, m}, GenerateConditions->None] == Binomial[z + m + 1,m]</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 21] | ||
|- style="background: #dfe6e9;" | |- style="background: #dfe6e9;" | ||
| [https://dlmf.nist.gov/1.2.E10 1.2.E10] | | | [https://dlmf.nist.gov/1.2.E10 1.2.E10] || <math qid="Q39">na+\tfrac{1}{2}n(n-1)d = \tfrac{1}{2}n(a+\ell)</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>na+\tfrac{1}{2}n(n-1)d = \tfrac{1}{2}n(a+\ell)</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">n*a +(1)/(2)*n*(n - 1)*d = (1)/(2)*n*(a + ell)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">n*a +Divide[1,2]*n*(n - 1)*d == Divide[1,2]*n*(a + \[ScriptL])</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || - | ||
|- style="background: #dfe6e9;" | |- style="background: #dfe6e9;" | ||
| [https://dlmf.nist.gov/1.2.E22 1.2.E22] | | | [https://dlmf.nist.gov/1.2.E22 1.2.E22] || <math qid="Q51">M(r) = 0</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>M(r) = 0</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">((p[1]*(a[1])^(r)+ p[2]*(a[2])^(r)+ .. + p[n]*(a[n])^(r))^(1/r)) = 0</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">((Subscript[p, 1]*(Subscript[a, 1])^(r)+ Subscript[p, 2]*(Subscript[a, 2])^(r)+ \[Ellipsis]+ Subscript[p, n]*(Subscript[a, n])^(r))^(1/r)) == 0</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || - | ||
|- style="background: #dfe6e9;" | |- style="background: #dfe6e9;" | ||
| [https://dlmf.nist.gov/1.2#Ex1 1.2#Ex1] | | | [https://dlmf.nist.gov/1.2#Ex1 1.2#Ex1] || <math qid="Q54">M(1) = A</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>M(1) = A</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">M(1) = ((a[1]+ a[2]+ .. + a[n])/(n))</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">M[1] == (Divide[Subscript[a, 1]+ Subscript[a, 2]+ \[Ellipsis]+ Subscript[a, n],n])</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || - | ||
|- style="background: #dfe6e9;" | |- style="background: #dfe6e9;" | ||
| [https://dlmf.nist.gov/1.2#Ex2 1.2#Ex2] | | | [https://dlmf.nist.gov/1.2#Ex2 1.2#Ex2] || <math qid="Q55">M(-1) = H</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>M(-1) = H</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">M(- 1) = H</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">M[- 1] == H</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || - | ||
|- style="background: #dfe6e9;" | |- style="background: #dfe6e9;" | ||
| [https://dlmf.nist.gov/1.2.E26 1.2.E26] | | | [https://dlmf.nist.gov/1.2.E26 1.2.E26] || <math qid="Q56">\lim_{r\to 0}M(r) = G</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\lim_{r\to 0}M(r) = G</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">limit((p[1]*(a[1])^(r)+ p[2]*(a[2])^(r)+ .. + p[n]*(a[n])^(r))^(1/r), r = 0) = ((a[1]*a[2] .. a[n])^(1/n))</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Limit[(Subscript[p, 1]*(Subscript[a, 1])^(r)+ Subscript[p, 2]*(Subscript[a, 2])^(r)+ \[Ellipsis]+ Subscript[p, n]*(Subscript[a, n])^(r))^(1/r), r -> 0, GenerateConditions->None] == ((Subscript[a, 1]*Subscript[a, 2] \[Ellipsis]Subscript[a, n])^(1/n))</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || - | ||
|} | |} | ||
</div> | </div> |
Latest revision as of 10:58, 28 June 2021
DLMF | Formula | Constraints | Maple | Mathematica | Symbolic Maple |
Symbolic Mathematica |
Numeric Maple |
Numeric Mathematica |
---|---|---|---|---|---|---|---|---|
1.2.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \binom{n}{k} = \frac{n!}{(n-k)!k!}}
\binom{n}{k} = \frac{n!}{(n-k)!k!} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | binomial(n,k) = (factorial(n))/(factorial(n - k)*factorial(k))
|
Binomial[n,k] == Divide[(n)!,(n - k)!*(k)!]
|
Successful | Successful | - | Successful [Tested: 9] |
1.2.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{n!}{(n-k)!k!} = \binom{n}{n-k}}
\frac{n!}{(n-k)!k!} = \binom{n}{n-k} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | (factorial(n))/(factorial(n - k)*factorial(k)) = binomial(n,n - k)
|
Divide[(n)!,(n - k)!*(k)!] == Binomial[n,n - k]
|
Successful | Successful | - | Successful [Tested: 9] |
1.2.E6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{(-1)^{k}\Pochhammersym{-z}{k}}{k!} = (-1)^{k}\binom{k-z-1}{k}}
\frac{(-1)^{k}\Pochhammersym{-z}{k}}{k!} = (-1)^{k}\binom{k-z-1}{k} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | ((- 1)^(k)* pochhammer(- z, k))/(factorial(k)) = (- 1)^(k)*binomial(k - z - 1,k)
|
Divide[(- 1)^(k)* Pochhammer[- z, k],(k)!] == (- 1)^(k)*Binomial[k - z - 1,k]
|
Successful | Successful | - | Successful [Tested: 21] |
1.2.E7 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \binom{z+1}{k} = \binom{z}{k}+\binom{z}{k-1}}
\binom{z+1}{k} = \binom{z}{k}+\binom{z}{k-1} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | binomial(z + 1,k) = binomial(z,k)+binomial(z,k - 1)
|
Binomial[z + 1,k] == Binomial[z,k]+Binomial[z,k - 1]
|
Successful | Successful | - | Successful [Tested: 21] |
1.2.E8 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sum^{m}_{k=0}\binom{z+k}{k} = \binom{z+m+1}{m}}
\sum^{m}_{k=0}\binom{z+k}{k} = \binom{z+m+1}{m} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | sum(binomial(z + k,k), k = 0..m) = binomial(z + m + 1,m)
|
Sum[Binomial[z + k,k], {k, 0, m}, GenerateConditions->None] == Binomial[z + m + 1,m]
|
Successful | Successful | - | Successful [Tested: 21] |
1.2.E10 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle na+\tfrac{1}{2}n(n-1)d = \tfrac{1}{2}n(a+\ell)}
na+\tfrac{1}{2}n(n-1)d = \tfrac{1}{2}n(a+\ell) |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | n*a +(1)/(2)*n*(n - 1)*d = (1)/(2)*n*(a + ell) |
n*a +Divide[1,2]*n*(n - 1)*d == Divide[1,2]*n*(a + \[ScriptL]) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
1.2.E22 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle M(r) = 0}
M(r) = 0 |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | ((p[1]*(a[1])^(r)+ p[2]*(a[2])^(r)+ .. + p[n]*(a[n])^(r))^(1/r)) = 0 |
((Subscript[p, 1]*(Subscript[a, 1])^(r)+ Subscript[p, 2]*(Subscript[a, 2])^(r)+ \[Ellipsis]+ Subscript[p, n]*(Subscript[a, n])^(r))^(1/r)) == 0 |
Skipped - no semantic math | Skipped - no semantic math | - | - |
1.2#Ex1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle M(1) = A}
M(1) = A |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | M(1) = ((a[1]+ a[2]+ .. + a[n])/(n)) |
M[1] == (Divide[Subscript[a, 1]+ Subscript[a, 2]+ \[Ellipsis]+ Subscript[a, n],n]) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
1.2#Ex2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle M(-1) = H}
M(-1) = H |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | M(- 1) = H |
M[- 1] == H |
Skipped - no semantic math | Skipped - no semantic math | - | - |
1.2.E26 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \lim_{r\to 0}M(r) = G}
\lim_{r\to 0}M(r) = G |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | limit((p[1]*(a[1])^(r)+ p[2]*(a[2])^(r)+ .. + p[n]*(a[n])^(r))^(1/r), r = 0) = ((a[1]*a[2] .. a[n])^(1/n)) |
Limit[(Subscript[p, 1]*(Subscript[a, 1])^(r)+ Subscript[p, 2]*(Subscript[a, 2])^(r)+ \[Ellipsis]+ Subscript[p, n]*(Subscript[a, n])^(r))^(1/r), r -> 0, GenerateConditions->None] == ((Subscript[a, 1]*Subscript[a, 2] \[Ellipsis]Subscript[a, n])^(1/n)) |
Skipped - no semantic math | Skipped - no semantic math | - | - |