How can I solve equations in Python

Question

Let s say I have an equation   2x   6   12  With algebra we can see that x   3  How can I make a program in Python that can solve for x  I m new to programming  and I looked at eval   and exec   but I can t figure out how to make them do what I want  I do not want to use external libraries  e g  SAGE   I want to do this in just plain Python

User · Answer

If you only want to solve the extremely limited set of equations mx   c   y for positive integer m  c  y  then this will do   import re def solve linear equation   equ                Given an input string of the format  3x 2 6   solves for x      The format must be as shown - no whitespace  no decimal numbers      no negative numbers              match   re match r   d  x    d     d     equ      m  c  y   match groups       m  c  y   float m   float c   float y    Convert from strings to numbers     x    y-c  m     print   x    f    x    Some tests    gt  gt  gt  solve linear equation  2x 4 12   x   4 000000  gt  gt  gt  solve linear equation  123x 456 789   x   2 707317  gt  gt  gt     If you want to recognise and solve arbitrary equations  like sin x    e  i pi x    1  then you will need to implement some kind of symbolic maths engine  similar to maxima  Mathematica  MATLAB s solve   or Symbolic Toolbox  etc  As a novice  this is beyond your ken

User · Answer

There are two ways to approach this problem  numerically and symbolically   To solve it numerically  you have to first encode it as a  runnable  function - stick a value in  get a value out  For example   def my function x       return 2 x   6   It is quite possible to parse a string to automatically create such a function  say you parse 2x   6 into a list   6  2   where the list index corresponds to the power of x - so 6 x 0   2 x 1   Then   def makePoly arr       def fn x           return sum c x  p for p c in enumerate arr       return fn  my func   makePoly  6  2   my func 3       returns 12   You then need another function which repeatedly plugs an x-value into your function  looks at the difference between the result and what it wants to find  and tweaks its x-value to  hopefully  minimize the difference   def dx fn  x  delta 0 001       return  fn x delta  - fn x   delta  def solve fn  value  x 0 5  maxtries 1000  maxerr 0 00001       for tries in xrange maxtries           err   fn x  - value         if abs err   lt  maxerr              return x         slope   dx fn  x          x -  err slope     raise ValueError  no solution found     There are lots of potential problems here - finding a good starting x-value  assuming that the function actually has a solution  ie there are no real-valued answers to x 2   2   0   hitting the limits of computational accuracy  etc  But in this case  the error minimization function is suitable and we get a good result   solve my func  16       returns  x    5 000000000000496   Note that this solution is not absolutely  exactly correct  If you need it to be perfect  or if you want to try solving families of equations analytically  you have to turn to a more complicated beast  a symbolic solver   A symbolic solver  like Mathematica or Maple  is an expert system with a lot of built-in rules   knowledge   about algebra  calculus  etc  it  knows  that the derivative of sin is cos  that the derivative of kx p is kpx  p-1   and so on  When you give it an equation  it tries to find a path  a set of rule-applications  from where it is  the equation  to where you want to be  the simplest possible form of the equation  which is hopefully the solution    Your example equation is quite simple  a symbolic solution might look like     gt  LHS  6  2   RHS  16      rule  pull all coefficients into LHS LHS  RHS    lh-rh for lh rh in izip longest LHS  RHS  0     0     gt  LHS  -10 2   RHS  0      rule  solve first-degree poly if RHS   0  and len LHS   2      LHS  RHS    0 1    -LHS 0  LHS 1      gt  LHS  0 1   RHS  5     and there is your solution  x   5   I hope this gives the flavor of the idea  the details of implementation  finding a good  complete set of rules and deciding when each rule should be applied  can easily consume many man-years of effort

User · Answer

Python may be good  but it isn t God     There are a few different ways to solve equations  SymPy has already been mentioned  if you re looking for analytic solutions    If you re happy to just have a numerical solution  Numpy has a few routines that can help  If you re just interested in solutions to polynomials  numpy roots will work  Specifically for the case you mentioned    gt  gt  gt  import numpy  gt  gt  gt  numpy roots  2 -6   array  3 0     For more complicated expressions  have a look at scipy fsolve   Either way  you can t escape using a library

User · Answer

How about SymPy  Their solver looks like what you need  Have a look at their source code if you want to build the library yourself

User · Answer

Use a different tool  Something like Wolfram Alpha  Maple  R  Octave  Matlab or any other algebra software package   As a beginner you should probably not attempt to solve such a non-trivial problem

[python] How can I solve equations in Python?

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