Support for solving multivariate equations

[tkosan]

This is blocked on #128 (new parser) because it depends on how we parse equations.

I have been working on giving mathsteps the ability to solve multivariate equations as the first phase of giving it the ability to solve simultaneous equations. The following file shows what I have working so far:

solving_multivariate_equations_test.v.01.txt

Each of the equations in this document (which came from the list of problems Ahmed posted in
issue #96) was solved with mathsteps and with MathPiper's conventional solver. Their results were then checked to make sure they were equivalent. If these tests look okay, I will submit a pull request that contains this multivariate solving capability.

[kevinbarabash]

@tkosan cool stuff. It's interesting looking at the different forms of the solutions. I like how MathPiper puts the x term first, but mathsteps definitely provides much simpler solutions in general, e.g.

solveEquation("2*x + 2*y = 15", "y")
  MathSteps: y = 15/2 - x
  MathPiper: y == (-2*x + 15)/2
  Equivalent: True

[tkosan]

MathPiper's conventional equation solver can be configured to return results in different forms:

In> Solve(MathParse("2*x + 2*y = 15"), y, Rational:True, AllFac:False)
Result: [y == -x + 15/2]

[evykassirer]

cool! would love to see the code for this 😄 and what the steps along the way look like

side note: your equivalent function would be very helpful for #132 - would you up for adding that to mathsteps too?

[tkosan]

I will create a pull request for the multivariate support I am working on after the parser has been changed from mathjs to math-parser.

[evykassirer]

Sounds good, I'll prioritize that then. Depending on how similar the trees can be, it might take a few weeks to move everything over. I'll ping Kevin to clarify next steps