Mapytex/pymath/expression.py

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2013-08-09 09:35:14 +00:00
#!/usr/bin/env python
# encoding: utf-8
from .generic import Stack, flatten_list, expand_list
from .operator import Operator
from .fraction import Fraction
from .renders import txt, post2in_fix, tex
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__all__ = ['Expression']
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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}
STR_RENDER = tex
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def __init__(self, exp):
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""" Initiate the expression
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:param exp: the expression. It can be a string or a list of tokens. It can be infix or postfix expression
"""
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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
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self._infix_tokens = None
self._postfix_tokens = None
self.feed_fix() # Determine le fix et range la liste dans self.[fix]_tokens
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def __str__(self):
"""
Overload str
If you want to changer render set Expression.RENDER
"""
return self.STR_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)
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## ---------------------
## Mechanism functions
def simplify(self):
""" Generator which return steps for computing the expression """
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if not self.can_go_further():
yield self.STR_RENDER(self.postfix_tokens)
else:
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self.compute_exp()
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old_s = ''
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for s in self.steps:
new_s = self.STR_RENDER(s)
# Astuce pour éviter d'avoir deux fois la même étape (par exemple pour la transfo d'une division en fraction)
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if new_s != old_s:
old_s = new_s
yield new_s
for s in self.child.simplify():
if old_s != s:
yield s
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def can_go_further(self):
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"""Check whether it's a last step or not. If not create self.child the next expression.
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: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):
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""" Create self.child with self.steps to go up to it """
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self.steps = [self.postfix_tokens]
tokenList = self.postfix_tokens.copy()
tmpTokenList = []
while len(tokenList) > 2:
# on va chercher les motifs du genre A B +, quad l'operateur est d'arité 2, pour les calculer
if self.isNumber(tokenList[0]) and self.isNumber(tokenList[1]) \
and type(tokenList[2]) == Operator and tokenList[2].arity == 2 :
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# S'il y a une opération à faire
op1 = tokenList[0]
op2 = tokenList[1]
operator = tokenList[2]
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res = operator(op1, op2)
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tmpTokenList.append(res)
# Comme on vient de faire le calcul, on peut détruire aussi les deux prochains termes
del tokenList[0:3]
elif self.isNumber(tokenList[0]) \
and type(tokenList[1]) == Operator and tokenList[1].arity == 1 :
# S'il y a une opération à faire
op1 = tokenList[0]
operator = tokenList[1]
res = operator(op1)
tmpTokenList.append(res)
# Comme on vient de faire le calcul, on peut détruire aussi les deux prochains termes
del tokenList[0:2]
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else:
tmpTokenList.append(tokenList[0])
del tokenList[0]
tmpTokenList += tokenList
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steps = expand_list(tmpTokenList)
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if len(steps[:-1]) > 0:
self.steps += [flatten_list(s) for s in steps[:-1]]
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self.child = Expression(steps[-1])
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## ---------------------
## String parsing
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@classmethod
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def str2tokens(self, exp):
""" Parse the expression, ie tranform a string into a list of tokens
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/!\ float are not availiable yet!
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:param exp: The expression (a string)
:returns: list of token
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"""
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tokens = ['']
for character in exp:
if character.isdigit():
# for "big" numbers (like 2345)
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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)
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else:
tokens.append(int(character))
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elif character in "+-*/):^":
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tokens.append(character)
elif character in "(":
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# If "3(", ")("
if self.isNumber(tokens[-1]) \
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or tokens[-1] == ")" :
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tokens.append("*")
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tokens.append(character)
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elif character == ".":
raise ValueError("No float number please")
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elif character != " ":
raise ValueError("{} is an unvalid character".format(character))
return tokens[1:]
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# ---------------------
# "fix" recognition
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@classmethod
def get_fix(self, tokens):
""" Give the "fix" of an expression
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[A, +, B] -> infix, or if there is parenthesis it is infix
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[+, 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"
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elif "(" in tokens:
return "infix"
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elif not self.isOperator(tokens[0]) and not self.isOperator(tokens[1]):
return "postfix"
else:
return "infix"
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def feed_fix(self):
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""" Recognize the fix of self.tokens and stock tokens in self.[fix]_tokens """
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if len(self.tokens) > 1:
fix = self.get_fix(self.tokens)
else:
fix = "postfix" # Completement arbitraire mais on s'en fiche!
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setattr(self, fix+"_tokens", self.tokens)
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# ----------------------
# 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
"""
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if self._infix_tokens:
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return self._infix_tokens
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elif self._postfix_tokens:
self._infix_tokens = post2in_fix(self._postfix_tokens)
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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
"""
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if self._postfix_tokens:
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return self._postfix_tokens
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elif self._infix_tokens:
self._postfix_tokens = self.in2post_fix(self._infix_tokens)
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return self._postfix_tokens
else:
raise ValueError("Unkown fix")
@postfix_tokens.setter
def postfix_tokens(self, val):
self._postfix_tokens = val
# ----------------------
# "fix" tranformations
@classmethod
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def in2post_fix(cls, infix_tokens):
""" From the infix_tokens list compute the corresponding postfix_tokens list
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@param infix_tokens: the infix list of tokens to transform into postfix form.
@return: the corresponding postfix list of tokens.
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>>> Expression.in2post_fix(['(', 2, '+', 5, '-', 1, ')', '/', '(', 3, '*', 4, ')'])
[2, 5, '+', 1, '-', 3, 4, '*', '/']
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>>> Expression.in2post_fix(['-', '(', '-', 2, ')'])
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[2, '-', '-']
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>>> Expression.in2post_fix(['-', '(', '-', 2, '+', 3, "*", 4, ')'])
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[2, '-', 3, 4, '*', '+', '-']
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"""
# Stack where operator will be stocked
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opStack = Stack()
# final postfix list of tokens
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postfix_tokens = []
# stack with the nbr of tokens still to compute in postfix_tokens
arity_Stack = Stack()
arity_Stack.push(0)
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for (pos_token,token) in enumerate(infix_tokens):
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# # Pour voir ce qu'il se passe dans cette procédure
# print(str(postfix_tokens), " | ", str(opStack), " | ", str(infix_tokens[(pos_token+1):]), " | ", str(arity_Stack))
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if token == "(":
opStack.push(token)
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# Set next arity counter
arity_Stack.push(0)
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elif token == ")":
op = opStack.pop()
while op != "(":
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postfix_tokens.append(op)
op = opStack.pop()
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# Go back to old arity
arity_Stack.pop()
# Raise the arity
arity = arity_Stack.pop()
arity_Stack.push(arity + 1)
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elif cls.isOperator(token):
while (not opStack.isEmpty()) and (cls.PRIORITY[opStack.peek()] >= cls.PRIORITY[token]):
op = opStack.pop()
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postfix_tokens.append(op)
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arity = arity_Stack.pop()
opStack.push(Operator(token, arity + 1))
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# print("--", token, " -> ", str(arity + 1))
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# Reset arity to 0 in case there is other operators (the real operation would be "-op.arity + 1")
arity_Stack.push(0)
else:
postfix_tokens.append(token)
arity = arity_Stack.pop()
arity_Stack.push(arity + 1)
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while not opStack.isEmpty():
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op = opStack.pop()
postfix_tokens.append(op)
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# # Pour voir ce qu'il se passe dans cette procédure
# print(str(postfix_tokens), " | ", str(opStack), " | ", str(infix_tokens[(pos_token+1):]), " | ", str(arity_Stack))
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if arity_Stack.peek() != 1:
raise ValueError("Unvalid expression. The arity Stack is ", str(arity_Stack))
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return postfix_tokens
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## ---------------------
## Recognize numbers and operators
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@staticmethod
def isNumber(exp):
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"""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 \
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type(exp) == Fraction
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@staticmethod
def isOperator(exp):
"""Check if the expression is an opération in "+-*/:^"
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:param exp: an expression
:returns: boolean
"""
return (type(exp) == str and exp in "+-*/:^")
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def test(exp):
a = Expression(exp)
for i in a.simplify():
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print(i)
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print("\n")
if __name__ == '__main__':
Expression.STR_RENDER = txt
exp = "2 ^ 3 * 5"
test(exp)
exp = "1 + 3 * 5"
test(exp)
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#exp = "2 * 3 * 3 * 5"
#test(exp)
#exp = "2 * 3 + 3 * 5"
#test(exp)
#exp = "2 * ( 3 + 4 ) + 3 * 5"
#test(exp)
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#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)
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#exp = "( 2 + 5 ) * ( 3 - 4 )^4"
#test(exp)
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#exp = "( 2 + 5 ) * ( 3 * 4 )"
#test(exp)
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#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+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)
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## Can't handle it yet!!
#exp="-(-2)"
#test(exp)
import doctest
doctest.testmod()
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# -----------------------------
# Reglages pour 'vim'
# vim:set autoindent expandtab tabstop=4 shiftwidth=4:
# cursor: 16 del