I am using LaTeX to show the solution to some equations which requires a lot of tedious and repetitive changing of terms. There are plenty of online solvers that can actually solve the equations themselves. However, are there any tools (packages or otherwise) that take TeX equations as input, parse and solve them, and then output the step-by-step solution as TeX?
For example, if I give it the following input:
\[ \frac{x^2}{2} = 1 \]
I would like it to return
\[ x^2 = 2 \]
\[ x = \sqrt{2} \]
The solution exists :-) but for me it is necessary one year :-)...before to understand and to build a code. You can try to use the calculator and calculus packages (see pag. 24).
I have only copy and past the code of the page 26 as example. For my humble opinion it is not very easy.
\documentclass[a4paper,12pt]{article}
\usepackage{mathtools,amssymb}
\usepackage{calculator,calculus}
\begin{document}
% exp(-t)
\SCALEVARIABLEfunction
{-1}{\EXPfunction}
{\NEGEXPfunction}
% exp(-t)cos(t)
\PRODUCTfunction
{\NEGEXPfunction}
{\COSfunction}
{\NEGEXPCOSfunction}
% 3t^2-2exp(-t)cos(t)
\LINEARCOMBINATIONfunction
{3}{\SQUAREfunction}
{-2}{\NEGEXPCOSfunction}
{\myfunction}
\myfunction{5}{\sol}{\Dsol}
If
[
f(t)=3t^2-2\mathrm{e}^{-t}\cos t
]
then
[
\begin{gathered}
f(5)=\sol\
f'(5)=\Dsol
\end{gathered}
]
\end{document}
If you use Mathematica 12, exist a package called latexalpha2 that execute the Wolfram Language (Mathematica) source codes in a LaTeX document. For example to pag. 4 there is a step to solve an equation of second degree.
A solution with Mathematica (not PSTricks) only for either fun or comparison purposes.
nEqns = 250;
coeffs = {};
While[Length[coeffs] < nEqns,
candidate = {#1 #3, #2 #3 + #1 #4, #2 #4} & @@
RandomInteger[{-10, 10}, 4];
acceptable = (Not[MemberQ[coeffs, #]] && First[#] != 0 &&
GCD @@ # == 1) &@candidate;
If[acceptable, AppendTo[coeffs, candidate]];]
({x^2, x, 1}.# == 0) & /@ coeffs // TableForm // TeXForm
All equations below can be factorized.
\begin{array}{c}
-72 x^2+35 x+50=0 \\
21 x^2+50 x+25=0 \\
-x^2-19 x-90=0 \\
70 x^2-33 x-4=0 \\
14 x^2-19 x-3=0 \\
60 x^2+32 x-7=0 \\
-63 x^2-47 x+6=0 \\
80 x^2+122 x+45=0 \\
2 x^2+x-36=0 \\
-4 x^2+49 x-90=0 \\
21 x^2-52 x+7=0 \\
35 x^2-18 x-81=0 \\
-7 x^2+65 x-72=0 \\
-21 x^2-79 x-30=0 \\
42 x^2+13 x+1=0 \\
36 x^2-77 x+40=0 \\
10 x^2-79 x+63=0 \\
5 x^2+31 x+6=0 \\
-35 x^2+31 x-6=0 \\
-10 x^2-31 x+63=0 \\
27 x^2+102 x+40=0 \\
6 x^2+23 x-35=0 \\
-12 x^2+8 x-1=0 \\
x^2+8 x+16=0 \\
70 x^2+43 x-5=0 \\
-50 x^2-55 x-14=0 \\
7 x^2-15 x+8=0 \\
-8 x^2+61 x-35=0 \\
-35 x^2+58 x+9=0 \\
-30 x^2-47 x+5=0 \\
-10 x^2+101 x-10=0 \\
35 x^2+82 x+48=0 \\
9 x^2-9 x-40=0 \\
-7 x^2-16 x+15=0 \\
-6 x^2-5 x+4=0 \\
-30 x^2+19 x+63=0 \\
5 x^2+8 x-21=0 \\
-10 x^2-29 x-18=0 \\
-7 x^2+26 x-15=0 \\
-x^2+x+20=0 \\
2 x^2+7 x+5=0 \\
-9 x^2-26 x-16=0 \\
x^2+14 x+45=0 \\
-2 x^2+11 x+63=0 \\
-21 x^2-40 x+100=0 \\
-8 x^2-79 x+10=0 \\
10 x^2+79 x-8=0 \\
7 x^2+52 x-32=0 \\
-72 x^2+5 x+25=0 \\
6 x^2-7 x-20=0 \\
-18 x^2+39 x-20=0 \\
-30 x^2-23 x+45=0 \\
15 x^2-44 x-20=0 \\
8 x^2+x-7=0 \\
7 x^2+x-8=0 \\
-21 x^2+67 x+10=0 \\
63 x^2+58 x-16=0 \\
-15 x^2-56 x-49=0 \\
-36 x^2-48 x-7=0 \\
x^2+9 x+18=0 \\
-49 x^2+42 x+27=0 \\
-2 x^2+15 x-27=0 \\
6 x^2-37 x+56=0 \\
6 x^2+41 x+30=0 \\
-9 x^2+73 x-70=0 \\
-10 x^2+17 x-3=0 \\
-10 x^2-29 x+72=0 \\
5 x^2-48 x+27=0 \\
25 x^2+10 x-48=0 \\
7 x^2+6 x-1=0 \\
x^2+6 x-7=0 \\
7 x^2-52 x+21=0 \\
-4 x^2+45 x-50=0 \\
16 x^2-34 x+15=0 \\
-63 x^2-23 x+56=0 \\
-3 x^2+2 x+1=0 \\
28 x^2-39 x+5=0 \\
90 x^2+31 x-4=0 \\
-5 x^2-23 x-12=0 \\
9 x^2-15 x-14=0 \\
-21 x^2-5 x+4=0 \\
100 x^2-80 x+7=0 \\
-70 x^2+11 x+3=0 \\
-35 x^2-38 x+9=0 \\
-63 x^2-46 x-8=0 \\
3 x^2-31 x+70=0 \\
20 x^2-7 x-6=0 \\
-10 x^2+31 x+63=0 \\
-16 x^2-8 x+35=0 \\
-20 x^2-27 x-9=0 \\
18 x^2+21 x-49=0 \\
-3 x^2+5 x+12=0 \\
7 x^2+8 x+1=0 \\
-20 x^2+27 x+8=0 \\
-63 x^2+76 x+20=0 \\
70 x^2+11 x-3=0 \\
-9 x^2-41 x+20=0 \\
-63 x^2-8 x+16=0 \\
-4 x^2-19 x+5=0 \\
50 x^2-45 x+9=0 \\
10 x^2+19 x+7=0 \\
-5 x^2+11 x+36=0 \\
4 x^2-17 x-15=0 \\
18 x^2+7 x-8=0 \\
70 x^2+139 x+63=0 \\
-14 x^2-43 x+90=0 \\
2 x^2+x-10=0 \\
10 x^2-7 x-6=0 \\
-36 x^2-85 x-9=0 \\
70 x^2+39 x-7=0 \\
18 x^2+39 x-7=0 \\
2 x^2-5 x+3=0 \\
-72 x^2-13 x+20=0 \\
-7 x^2-45 x-18=0 \\
-12 x^2+16 x-5=0 \\
8 x^2+13 x-6=0 \\
-7 x^2-24 x-20=0 \\
-24 x^2-58 x-35=0 \\
-2 x^2+5 x-2=0 \\
-35 x^2-17 x+36=0 \\
-24 x^2-34 x-5=0 \\
12 x^2+32 x+21=0 \\
30 x^2-13 x+1=0 \\
3 x^2+29 x-10=0 \\
-35 x^2+34 x+21=0 \\
12 x^2-55 x+50=0 \\
21 x^2+44 x+15=0 \\
30 x^2+29 x-35=0 \\
8 x^2-13 x+5=0 \\
-10 x^2-17 x+63=0 \\
35 x^2+96 x+64=0 \\
-30 x^2-89 x-24=0 \\
18 x^2+51 x+8=0 \\
-36 x^2-41 x-8=0 \\
40 x^2-26 x-3=0 \\
-8 x^2-39 x+54=0 \\
14 x^2-33 x-56=0 \\
-28 x^2+25 x+8=0 \\
-30 x^2-47 x-14=0 \\
-63 x^2-23 x-2=0 \\
32 x^2+12 x-5=0 \\
80 x^2-22 x-45=0 \\
35 x^2+74 x+35=0 \\
-3 x^2+40 x-100=0 \\
6 x^2-17 x-28=0 \\
-2 x^2-5 x+12=0 \\
-4 x^2-16 x-15=0 \\
6 x^2+x-7=0 \\
-7 x^2-37 x-36=0 \\
5 x^2+14 x+9=0 \\
-21 x^2+x+2=0 \\
18 x^2-29 x+10=0 \\
-90 x^2-131 x-45=0 \\
63 x^2-16 x+1=0 \\
-24 x^2-59 x-7=0 \\
45 x^2+61 x-36=0 \\
4 x^2+11 x+6=0 \\
7 x^2-19 x+10=0 \\
-2 x^2+19 x-9=0 \\
-40 x^2+51 x+7=0 \\
-72 x^2+23 x+35=0 \\
10 x^2-43 x+28=0 \\
-7 x^2+66 x-27=0 \\
-14 x^2-13 x+10=0 \\
7 x^2-50 x+48=0 \\
45 x^2+22 x-16=0 \\
7 x^2-13 x+6=0 \\
-36 x^2-59 x-24=0 \\
-5 x^2-9 x+2=0 \\
-3 x^2+29 x-18=0 \\
20 x^2+24 x-9=0 \\
-28 x^2-x+2=0 \\
36 x^2+19 x-6=0 \\
63 x^2+40 x-12=0 \\
x^2-12 x+20=0 \\
15 x^2-44 x+32=0 \\
5 x^2+46 x+48=0 \\
-4 x^2+x+18=0 \\
-10 x^2-37 x-30=0 \\
28 x^2-39 x-54=0 \\
-x^2-2 x+8=0 \\
-63 x^2+13 x+6=0 \\
-9 x^2+11 x+14=0 \\
-21 x^2-38 x-5=0 \\
50 x^2-15 x-2=0 \\
45 x^2-67 x-8=0 \\
-5 x^2+59 x-90=0 \\
32 x^2+12 x-27=0 \\
12 x^2+8 x+1=0 \\
-x^2-13 x-30=0 \\
15 x^2+38 x+24=0 \\
90 x^2+53 x-24=0 \\
-6 x^2+13 x+15=0 \\
30 x^2+103 x+10=0 \\
-56 x^2+65 x-14=0 \\
-6 x^2-35 x+49=0 \\
42 x^2-19 x-35=0 \\
-32 x^2+44 x+21=0 \\
-16 x^2+40 x-21=0 \\
6 x^2-59 x-10=0 \\
9 x^2-100 x+100=0 \\
7 x^2-30 x+8=0 \\
-56 x^2-127 x-72=0 \\
-15 x^2+67 x-72=0 \\
25 x^2-90 x+81=0 \\
x^2+11 x+30=0 \\
30 x^2-71 x+42=0 \\
-32 x^2+28 x+9=0 \\
-7 x^2-4 x=0 \\
-81 x^2-153 x-70=0 \\
28 x^2+25 x-8=0 \\
-4 x^2-29 x-30=0 \\
14 x^2+29 x-15=0 \\
54 x^2+57 x+10=0 \\
-35 x^2+33 x+54=0 \\
-24 x^2+10 x-1=0 \\
-56 x^2+3 x+9=0 \\
64 x^2-96 x+27=0 \\
-2 x^2+25 x-72=0 \\
50 x^2-65 x+6=0 \\
-9 x^2-53 x-40=0 \\
-3 x^2+14 x+80=0 \\
-4 x^2+32 x-63=0 \\
45 x^2-79 x+30=0 \\
-25 x^2+20 x+21=0 \\
-35 x^2+19 x+42=0 \\
-15 x^2-46 x-16=0 \\
-24 x^2-59 x+70=0 \\
8 x^2+49 x+6=0 \\
35 x^2+22 x-24=0 \\
27 x^2-12 x-32=0 \\
63 x^2+101 x+40=0 \\
27 x^2+15 x-8=0 \\
21 x^2+23 x-10=0 \\
-8 x^2-87 x-70=0 \\
4 x^2+31 x+21=0 \\
5 x^2+34 x-7=0 \\
-3 x^2+28 x-60=0 \\
-8 x^2-26 x-21=0 \\
21 x^2+38 x+5=0 \\
63 x^2+146 x+80=0 \\
-7 x^2+53 x+24=0 \\
-40 x^2-29 x+18=0 \\
28 x^2-15 x+2=0 \\
-56 x^2-25 x+4=0 \\
18 x^2-57 x-10=0 \\
15 x^2+4 x-35=0 \\
14 x^2+79 x+72=0 \\
3 x^2-16 x+20=0 \\
15 x^2-13 x-20=0 \\
\end{array}
The package latexalpha2, as it is, requires unix and pdflatex. It was adapted to windows and extended to lualatex. See https://tex.stackexchange.com/a/579254/161015
for a complete answer.
Note. Wolfram Engine must be installed and wolframscript must be fully working on the command prompt!
WolframScript enables Wolfram Language code to be run from any terminal, whether or not a Wolfram kernel is available on the system.
It is free from
$$ x = \pm \sqrt2 $$. Note the\pm. – wipet Jun 04 '20 at 12:25