Non-commutative sympify (or simplify)

Question

I would like to be able to simplify mathematical expressions from a string in Python. There are several \"commutative\" ways of doing it. Is there a non-commutative function f

Answer 1

Here is my solution. For the algorithm please see either my above comments or the comments in the code. I will appreciate if someone comes with a more elegant piece of code.

"""
Created on Sat Aug 22 22:15:16 2015

@author: GnacikM
"""

from sympy import *
import re
import string

"""
names for variables in a list
"""
alpha = list(string.ascii_lowercase)
Alpha = list(string.ascii_uppercase)

"""
Creating symbols
"""
def symbol_commutativity(my_symbol, name, status):
    my_symbol = Symbol(str(name), commutative=status)
    return my_symbol

symbols_lower = []
for item in alpha:
    symbols_lower.append(symbol_commutativity(item, item, False))

symbols_upper = []
for item in Alpha:
    symbols_upper.append(symbol_commutativity(item, item, False))

"""
Transforming an infix expression to Reverse Polish Notation
http://andreinc.net/2010/10/05/converting-infix-to-rpn-shunting-yard-algorithm/
"""
#Associativity constants for operators
LEFT_ASSOC = 0
RIGHT_ASSOC = 1

#Supported operators
OPERATORS = {
    '+' : (0, LEFT_ASSOC),
    '-' : (0, LEFT_ASSOC),
    '*' : (5, LEFT_ASSOC),
    '/' : (5, LEFT_ASSOC),
    '%' : (5, LEFT_ASSOC),
    '^' : (10, RIGHT_ASSOC)
}

#Test if a certain token is operator
def isOperator(token):
    return token in OPERATORS.keys()

#Test the associativity type of a certain token
def isAssociative(token, assoc):
    if not isOperator(token):
        raise ValueError('Invalid token: %s' % token)
    return OPERATORS[token][1] == assoc

#Compare the precedence of two tokens
def cmpPrecedence(token1, token2):
    if not isOperator(token1) or not isOperator(token2):
        raise ValueError('Invalid tokens: %s %s' % (token1, token2))
    return OPERATORS[token1][0] - OPERATORS[token2][0]   


#Transforms an infix expression to RPN
def infixToRPN(tokens):
    out = []
    stack = []
    #For all the input tokens [S1] read the next token [S2]
    for token in tokens:
        if isOperator(token):
            # If token is an operator (x) [S3]
            while len(stack) != 0 and isOperator(stack[-1]):
                # [S4]
                if (isAssociative(token, LEFT_ASSOC) and cmpPrecedence(token, stack[-1]) <= 0) or (isAssociative(token, RIGHT_ASSOC) and cmpPrecedence(token, stack[-1]) < 0):
                    # [S5] [S6]
                    out.append(stack.pop())
                    continue
                break
            # [S7]
            stack.append(token)
        elif token == '(':
            stack.append(token) # [S8]
        elif token == ')':
            # [S9]
            while len(stack) != 0 and stack[-1] != '(':
                out.append(stack.pop()) # [S10]
            stack.pop() # [S11]
        else:
            out.append(token) # [S12]
    while len(stack) != 0:
        # [S13]
        out.append(stack.pop())
    return out

"""
Evaluating an expression in Reverse Polish Notation, an input is a list
http://danishmujeeb.com/blog/2014/12/parsing-reverse-polish-notation-in-python
"""

def parse_rpn(expression):

  stack = []

  for val in expression:
      if val in ['-', '+', '*', '/', '^']:
          op1 = stack.pop()
          if len(stack)==0:
              op2 = 0
          else:
              op2 = stack.pop()

          if val=='-': 
              result = op2 - op1
          elif val=='+': 
              result = op2 + op1
          elif val=='*': 
              result = op2 * op1
          elif val=='/': 
              result = op2 / op1
          elif val=='^':
              result =  op2 ** op1
          stack.append(result)
      else:
          stack.append(val)
  return stack

"""
Definition of my non-commutative sympify
"""
def nc_sympify(string):
    expression_list = re.findall(r"(-\number|\b\w*[\.]?\w+\b|[\(\)\+\*\-\/^])", string)

    """ Modifying expression_list to fix the issue with negative numbers """
    t = len(expression_list) 
    i=0
    while i1 and expression_list[i][0]=='-' and expression_list[i-1]!='(':
            new_list1 = expression_list[:i]
            if i0 and expression_list[i].is_integer()==True and expression_list[i-1]!='/':
                expression_list[i]=int(expression_list[i])
            elif i==0 and expression_list[i].is_integer()==True:
                expression_list[i]=int(expression_list[i])

    output = infixToRPN(expression_list)

    return parse_rpn(output)[0]


print nc_sympify('3*x*y - y*x - 2*x*y')