Mapytex/pymath/expression.py

441 lines
13 KiB
Python

#!/usr/bin/env python
# encoding: utf-8
from .generic import Stack, flatten_list, expand_list
from .fraction import Fraction
from .renders import txt_render, post2in_fix, tex_render
from .polynom import Polynom
class Expression(object):
"""A calculus expression. Today it can andle only expression with numbers later it will be able to manipulate unknown"""
PRIORITY = {"^": 5, "*" : 3, "/": 4, ":": 3, "+": 2, "-":2, "(": 1}
def __init__(self, exp):
""" Initiate the expression
:param exp: the expression. It can be a string or a list of tokens. It can be infix or postfix expression
"""
if type(exp) == str:
self._exp = exp
self.tokens = self.str2tokens(exp) # les tokens seront alors stockés dans self.tokens temporairement
elif type(exp) == list:
self.tokens = exp
self._infix_tokens = None
self._postfix_tokens = None
self.feed_fix() # Determine le fix et range la liste dans self.[fix]_tokens
def __str__(self):
"""Overload str as it aim to be use in console the render is txt_render"""
return txt_render(self.postfix_tokens)
def render(self, render = lambda x:str(x)):
""" Same as __str__ but accept render as argument
:param render: function which render the list of token (postfix form) to string
"""
# TODO: I don't like the name of this method |ven. janv. 17 12:48:14 CET 2014
return render(self.postfix_tokens)
## ---------------------
## Mechanism functions
def simplify(self, render = lambda x:str(x)):
""" Generator which return steps for computing the expression
:param render: function which render the list of token (postfix form now) to string
"""
if not self.can_go_further():
yield render(self.postfix_tokens)
else:
self.compute_exp()
old_s = ''
for s in self.steps:
new_s = render(s)
# Astuce pour éviter d'avoir deux fois la même étape (par exemple pour la transfo d'une division en fraction)
if new_s != old_s:
old_s = new_s
yield new_s
for s in self.child.simplify(render = render):
if old_s != s:
yield s
def can_go_further(self):
"""Check whether it's a last step or not. If not create self.child the next expression.
:returns: 1 if it's not the last step, 0 otherwise
"""
if len(self.tokens) == 1:
return 0
else:
return 1
def compute_exp(self):
""" Create self.child with self.steps to go up to it """
self.steps = [self.postfix_tokens]
tokenList = self.postfix_tokens.copy()
tmpTokenList = []
while len(tokenList) > 2:
# on va chercher les motifs du genre A B + pour les calculer
if self.isNumber(tokenList[0]) and self.isNumber(tokenList[1]) and self.isOperator(tokenList[2]):
# S'il y a une opération à faire
op1 = tokenList[0]
op2 = tokenList[1]
token = tokenList[2]
res = self.doMath(token, op1, op2)
tmpTokenList.append(res)
# Comme on vient de faire le calcul, on peut détruire aussi les deux prochains termes
del tokenList[0:3]
else:
tmpTokenList.append(tokenList[0])
del tokenList[0]
tmpTokenList += tokenList
steps = expand_list(tmpTokenList)
if len(steps[:-1]) > 0:
self.steps += [flatten_list(s) for s in steps[:-1]]
self.child = Expression(steps[-1])
## ---------------------
## String parsing
## @classmethod ????
def str2tokens(self, exp):
""" Parse the expression, ie tranform a string into a list of tokens
/!\ float are not availiable yet!
:param exp: The expression (a string)
:returns: list of token
"""
tokens = ['']
for character in exp:
if character.isdigit():
# for "big" numbers (like 2345)
if type(tokens[-1]) == int:
if tokens[-1] > 0:
tokens[-1] = tokens[-1]*10 + int(character)
else:
tokens[-1] = tokens[-1]*10 - int(character)
# Special case for "-" at the begining of an expression or before "("
elif tokens[-1] == "-" and \
str(tokens[-2]) in " (+-*/:":
tokens[-1] = - int(character)
else:
tokens.append(int(character))
elif character.isalpha():
# If "3x", ")x" or "yx"
if self.isNumber(tokens[-1]) \
or tokens[-1] == ")" \
or type(tokens[-1]) == Polynom:
tokens.append("*")
tokens.append(Polynom(letter = character))
# Special case for "-" at the begining of an expression or before "("
elif tokens[-1] == "-" \
or str(tokens[-2]) in " (":
tokens[-1] = - Polynom(letter = character)
else:
tokens.append(Polynom(letter = character))
elif character in "+-*/):^":
tokens.append(character)
elif character in "(":
# If "3(", ")(" or "x("
if self.isNumber(tokens[-1]) \
or tokens[-1] == ")" \
or type(tokens[-1]) == Polynom:
tokens.append("*")
tokens.append(character)
elif character != " ":
raise ValueError("{} is an unvalid character".format(character))
return tokens[1:]
# ---------------------
# "fix" recognition
@classmethod
def get_fix(self, tokens):
""" Give the "fix" of an expression
[A, +, B] -> infix, or if there is parenthesis it is infix
[+, A, B] -> prefix
[A, B, +] -> postfix
/!\ does not verify if the expression is correct/computable!
:param exp: the expression (list of token)
:returns: the "fix" (infix, postfix, prefix)
"""
if self.isOperator(tokens[0]):
return "prefix"
elif "(" in tokens:
return "infix"
elif not self.isOperator(tokens[0]) and not self.isOperator(tokens[1]):
return "postfix"
else:
return "infix"
def feed_fix(self):
""" Recognize the fix of self.tokens and stock tokens in self.[fix]_tokens """
if len(self.tokens) > 1:
fix = self.get_fix(self.tokens)
else:
fix = "postfix" # Completement arbitraire mais on s'en fiche!
setattr(self, fix+"_tokens", self.tokens)
# ----------------------
# Expressions - tokens manipulation
@property
def infix_tokens(self):
""" Return infix list of tokens. Verify if it has already been computed and compute it if not
:returns: infix list of tokens
"""
if self._infix_tokens:
return self._infix_tokens
elif self._postfix_tokens:
self._infix_tokens = post2in_fix(self._postfix_tokens)
return self._infix_tokens
else:
raise ValueError("Unkown fix")
@infix_tokens.setter
def infix_tokens(self, val):
self._infix_tokens = val
@property
def postfix_tokens(self):
""" Return postfix list of tokens. Verify if it has already been computed and compute it if not
:returns: postfix list of tokens
"""
if self._postfix_tokens:
return self._postfix_tokens
elif self._infix_tokens:
self._postfix_tokens = self.in2post_fix(self._infix_tokens)
return self._postfix_tokens
else:
raise ValueError("Unkown fix")
@postfix_tokens.setter
def postfix_tokens(self, val):
self._postfix_tokens = val
# ----------------------
# "fix" tranformations
@classmethod
def in2post_fix(cls, infix_tokens):
""" From the infix_tokens list compute the corresponding postfix_tokens list
@param infix_tokens: the infix list of tokens to transform into postfix form.
@return: the corresponding postfix list of tokens.
>>> Expression.in2post_fix(['(', 2, '+', 5, '-', 1, ')', '/', '(', 3, '*', 4, ')'])
[2, 5, '+', 1, '-', 3, 4, '*', '/']
"""
opStack = Stack()
postfixList = []
for token in infix_tokens:
if token == "(":
opStack.push(token)
elif token == ")":
topToken = opStack.pop()
while topToken != "(":
postfixList.append(topToken)
topToken = opStack.pop()
elif cls.isOperator(token):
# On doit ajouter la condition == str sinon python ne veut pas tester l'appartenance à la chaine de caractère.
while (not opStack.isEmpty()) and (cls.PRIORITY[opStack.peek()] >= cls.PRIORITY[token]):
postfixList.append(opStack.pop())
opStack.push(token)
else:
postfixList.append(token)
while not opStack.isEmpty():
postfixList.append(opStack.pop())
return postfixList
## ---------------------
## Computing the expression
@staticmethod
def doMath(op, op1, op2):
"""Compute "op1 op op2" or create a fraction
:param op: operator
:param op1: first operande
:param op2: second operande
:returns: string representing the result
"""
if op == "/":
ans = [Fraction(op1, op2)]
ans += ans[0].simplify()
return ans
else:
if type(op2) != int:
operations = {"+": "__radd__", "-": "__rsub__", "*": "__rmul__"}
return getattr(op2,operations[op])(op1)
else:
operations = {"+": "__add__", "-": "__sub__", "*": "__mul__", "^": "__pow__"}
return getattr(op1,operations[op])(op2)
## ---------------------
## Recognize numbers and operators
@staticmethod
def isNumber(exp):
"""Check if the expression can be a number
:param exp: an expression
:returns: True if the expression can be a number and false otherwise
"""
return type(exp) == int or \
type(exp) == Fraction or \
type(exp) == Polynom
@staticmethod
def isOperator(exp):
"""Check if the expression is an opération in "+-*/:^"
:param exp: an expression
:returns: boolean
"""
return (type(exp) == str and exp in "+-*/:^")
def test(exp):
a = Expression(exp)
#for i in a.simplify():
#for i in a.simplify(render = txt_render):
for i in a.simplify(render = tex_render):
print(i)
print("\n")
if __name__ == '__main__':
#exp = "2 ^ 3 * 5"
#test(exp)
#exp = "1 + 3 * 5"
#test(exp)
#exp = "2 * 3 * 3 * 5"
#test(exp)
#exp = "2 * 3 + 3 * 5"
#test(exp)
#exp = "2 * ( 3 + 4 ) + 3 * 5"
#test(exp)
#exp = "2 * ( 3 + 4 ) + ( 3 - 4 ) * 5"
#test(exp)
#
#exp = "2 * ( 2 - ( 3 + 4 ) ) + ( 3 - 4 ) * 5"
#test(exp)
#
#exp = "2 * ( 2 - ( 3 + 4 ) ) + 5 * ( 3 - 4 )"
#test(exp)
#
#exp = "2 + 5 * ( 3 - 4 )"
#test(exp)
#exp = "( 2 + 5 ) * ( 3 - 4 )^4"
#test(exp)
#exp = "( 2 + 5 ) * ( 3 * 4 )"
#test(exp)
#exp = "( 2 + 5 - 1 ) / ( 3 * 4 )"
#test(exp)
#exp = "( 2 + 5 ) / ( 3 * 4 ) + 1 / 12"
#test(exp)
#exp = "( 2+ 5 )/( 3 * 4 ) + 1 / 2"
#test(exp)
#exp="(-2+5)/(3*4)+1/12+5*5"
#test(exp)
#exp="-2*4(12 + 1)(3-12)"
#test(exp)
exp="-2+a+(12 + 1)(3-12) / 34a"
#test(exp)
e = Expression(exp)
print(e.render(render = tex_render))
#exp="-2*b+a(12 + 1)(3-12)"
#test(exp)
#exp="(-2+5)/(3*4)+1/12+5*5"
#test(exp)
# TODO: The next one doesn't work |ven. janv. 17 14:56:58 CET 2014
#exp="-2*(-a)(12 + 1)(3-12)"
#e = Expression(exp)
#print(e)
exp="-2+a+(12 + 1)(3-12) : 34a"
#test(exp)
#exp="-2+a+(12 + 1)(3-12) : 34a"
##test(exp)
#e = Expression(exp)
#print(e.render(render = tex_render))
#exp="-2*b+a(12 + 1)(3-12)"
#test(exp)
# TODO: The next one doesn't work |ven. janv. 17 14:56:58 CET 2014
#exp="-2*(-a)(12 + 1)(3-12)"
#e = Expression(exp)
#print(e)
## Can't handle it yet!!
#exp="-(-2)"
#test(exp)
import doctest
doctest.testmod()
# -----------------------------
# Reglages pour 'vim'
# vim:set autoindent expandtab tabstop=4 shiftwidth=4:
# cursor: 16 del