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Benjamin Bertrand
399
pymath/calculus/expression.py
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399
pymath/calculus/expression.py
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#!/usr/bin/env python
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# encoding: utf-8
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#debuging
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#from debug.tools import report
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from .generic import Stack, flatten_list, expand_list, isNumber, isOperator, isNumerand
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from .str2tokens import str2tokens
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from .operator import op
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from .explicable import Explicable
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from .random_expression import RdExpression
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__all__ = ['Expression']
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class Fake_int(int, Explicable):
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isNumber = True
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def __init__(self, val):
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super(Fake_int, self).__init__(val)
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self._val = val
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self.postfix_tokens = [self]
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self.steps = []
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def simplify(self):
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return Fake_int(self._val)
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class Expression(Explicable):
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"""A calculus expression. Today it can andle only expression with numbers later it will be able to manipulate unknown"""
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@classmethod
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def random(self, form="", conditions=[], val_min = -10, val_max=10):
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"""Create a random expression from form and with conditions
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:param form: the form of the expression (/!\ variables need to be in brackets {})
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:param conditions: condition on variables (/!\ variables need to be in brackets {})
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:param val_min: min value for generate variables
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:param val_max: max value for generate variables
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"""
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random_generator = RdExpression(form, conditions)
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return Expression(random_generator(val_min, val_max))
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@classmethod
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def tmp_render(cls, render = lambda _,x:Expression(x)):
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""" Same ad tmp_render for Renderable but default render is Expression
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>>> exp = Expression("2*3/5")
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>>> print(exp)
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2 \\times \\frac{ 3 }{ 5 }
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>>> for i in exp.simplify().explain():
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... print(i)
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2 \\times \\frac{ 3 }{ 5 }
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\\frac{ 3 }{ 5 } \\times 2
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\\frac{ 3 \\times 2 }{ 5 }
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\\frac{ 6 }{ 5 }
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>>> with Expression.tmp_render():
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... for i in exp.simplify().explain():
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... i
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< <class 'pymath.calculus.expression.Expression'> [2, 3, 5, '/', '*'] >
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< <class 'pymath.calculus.expression.Expression'> [2, < Fraction 3 / 5>, '*'] >
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< <class 'pymath.calculus.expression.Expression'> [3, 5, '/', 2, '*'] >
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< <class 'pymath.calculus.expression.Expression'> [3, 2, '*', 5, '/'] >
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< <class 'pymath.calculus.expression.Expression'> [6, 5, '/'] >
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>>> from .render import txt
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>>> with Expression.tmp_render(txt):
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... for i in exp.simplify().explain():
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... print(i)
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2 * 3 / 5
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3 / 5 * 2
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( 3 * 2 ) / 5
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6 / 5
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>>> for i in exp.simplify().explain():
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... print(i)
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2 \\times \\frac{ 3 }{ 5 }
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\\frac{ 3 }{ 5 } \\times 2
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\\frac{ 3 \\times 2 }{ 5 }
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\\frac{ 6 }{ 5 }
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"""
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return super(Expression, cls).tmp_render(render)
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def __new__(cls, exp):
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"""Create Expression objects
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:param exp: the expression. It can be a string or a list of postfix tokens.
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"""
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expression = object.__new__(cls)
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if type(exp) == str:
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expression.postfix_tokens = str2tokens(exp)
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elif type(exp) == list:
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# Ici on ne peut convertir les "+" en opérateur que s'ils sont d'arité 2.
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exp_mod_op = [op.get_op(i) if op.can_be_operator(i) else i for i in exp]
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expression.postfix_tokens = flatten_list([tok.postfix_tokens if Expression.isExpression(tok) else tok for tok in exp_mod_op])
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elif type(exp) == Expression:
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return exp
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elif isNumerand(exp):
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expression.postfix_tokens = [exp]
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else:
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raise ValueError("Can't build Expression with {} object".format(type(exp)))
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if len(expression.postfix_tokens) == 1:
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token = expression.postfix_tokens[0]
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if type(token) == Fake_int or type(token) == int:
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return Fake_int(token)
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elif hasattr(token, 'simplify') and hasattr(token, 'explain'):
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ans = expression.postfix_tokens[0]
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return ans
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elif type(token) == str:
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# TODO: Pourquoi ne pas créer directement un polynom ici? |jeu. févr. 26 18:59:24 CET 2015
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# On crée un faux str en ajoutant la méthode simplify et simplified et la caractérisique isNumber
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simplify = lambda x:[x]
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is_polynom = True
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methods_attr = {'simplify':simplify, '_isPolynom': is_polynom, 'postfix_tokens': [token]}
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fake_token = type('fake_str', (str,Explicable, ), methods_attr)(token)
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return fake_token
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else:
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raise ValueError("Unknow token type in Expression: {}".format(type(token)))
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else:
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expression._isExpression = 1
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return expression
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def __str__(self):
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"""
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Overload str
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If you want to changer render use Expression.set_render(...) or use tmp_render context manager.
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"""
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return self.STR_RENDER(self.postfix_tokens)
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def __repr__(self):
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return " ".join(["<", str(self.__class__) , str(self.postfix_tokens), ">"])
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def simplify(self):
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""" Compute entirely the expression and return the result with .steps attribute """
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self.compute_exp()
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self.simplified = self.child.simplify()
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self.simplified.steps = self.child.steps + self.simplified.steps
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return self.simplified
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def compute_exp(self):
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""" Create self.child with and stock steps in it """
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ini_step = Expression(self.postfix_tokens)
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tokenList = self.postfix_tokens.copy()
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tmpTokenList = []
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while len(tokenList) > 2:
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# on va chercher les motifs du genre A B +, quand l'operateur est d'arité 2, pour les calculer
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if isNumerand(tokenList[0]) and isNumerand(tokenList[1]) \
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and isOperator(tokenList[2]) and tokenList[2].arity == 2 :
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# S'il y a une opération à faire
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op1 = tokenList[0]
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op2 = tokenList[1]
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operator = tokenList[2]
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res = operator(op1, op2)
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tmpTokenList.append(res)
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# Comme on vient de faire le calcul, on peut détruire aussi les deux prochains termes
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del tokenList[0:3]
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# Et les motifs du gens A -, quand l'operateur est d'arité 1
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elif isNumerand(tokenList[0]) \
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and isOperator(tokenList[1]) and tokenList[1].arity == 1:
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# S'il y a une opération à faire
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op1 = tokenList[0]
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operator = tokenList[1]
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res = operator(op1)
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tmpTokenList.append(res)
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# Comme on vient de faire le calcul, on peut détruire aussi les deux prochains termes
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del tokenList[0:2]
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else:
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tmpTokenList.append(tokenList[0])
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del tokenList[0]
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if len(tokenList) == 2 and isNumerand(tokenList[0]) \
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and isOperator(tokenList[1]) and tokenList[1].arity == 1:
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# S'il reste deux éléments dont un operation d'arité 1
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op1 = tokenList[0]
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operator = tokenList[1]
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res = operator(op1)
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tmpTokenList.append(res)
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# Comme on vient de faire le calcul, on peut détruire aussi les deux prochains termes
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del tokenList[0:2]
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tmpTokenList += tokenList
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self.child = Expression(tmpTokenList)
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steps = self.develop_steps(tmpTokenList)
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if self.child.postfix_tokens == ini_step.postfix_tokens:
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self.child.steps = steps
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else:
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self.child.steps = [ini_step] + steps
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def develop_steps(self, tokenList):
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""" From a list of tokens, it develops steps of each tokens """
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# TODO: Attention les étapes sont dans le mauvais sens |lun. avril 20 10:06:03 CEST 2015
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tmp_steps = []
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with Expression.tmp_render():
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for t in tokenList:
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if hasattr(t, "explain"):
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tmp_steps.append([i for i in t.explain()])
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else:
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tmp_steps.append([t])
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if max([len(i) for i in tmp_steps]) == 1:
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# Cas où rien n'a dû être expliqué.
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return []
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else:
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tmp_steps = expand_list(tmp_steps)[:-1]
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steps = [Expression(s) for s in tmp_steps]
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return steps
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@classmethod
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def isExpression(self, other):
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try:
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other._isExpression
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except AttributeError:
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return 0
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return 1
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# -----------
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# Expression act as container from self.postfix_tokens
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def __getitem__(self, index):
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return self.postfix_tokens[index]
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def __setitem__(self, index, value):
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self.postfix_tokens[index] = value
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# -----------
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# Some math manipulations
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def operate(self, other, operator):
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if type(other) == Expression:
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return Expression(self.postfix_tokens + other.postfix_tokens + [operator])
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elif type(other) == list:
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return Expression(self.postfix_tokens + other + [operator])
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else:
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return Expression(self.postfix_tokens + [other] + [operator])
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def roperate(self, other, operator):
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if type(other) == Expression:
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return Expression(other.postfix_tokens + self.postfix_tokens + [operator])
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elif type(other) == list:
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return Expression(other + self.postfix_tokens + [operator])
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else:
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return Expression([other] + self.postfix_tokens + [operator])
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def __add__(self, other):
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""" Overload +
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>>> a = Expression("1+2")
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>>> print(a.postfix_tokens)
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[1, 2, '+']
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>>> b = Expression("3+4")
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>>> print(b.postfix_tokens)
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[3, 4, '+']
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>>> c = a + b
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>>> print(c.postfix_tokens)
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[1, 2, '+', 3, 4, '+', '+']
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"""
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return self.operate(other, op.add)
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def __radd__(self, other):
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return self.roperate(other, op.add)
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def __sub__(self, other):
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""" Overload -
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>>> a = Expression("1+2")
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>>> print(a.postfix_tokens)
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[1, 2, '+']
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>>> b = Expression("3+4")
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>>> print(b.postfix_tokens)
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[3, 4, '+']
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>>> c = a - b
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>>> print(c.postfix_tokens)
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[1, 2, '+', 3, 4, '+', '-']
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"""
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return self.operate(other, op.sub)
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def __rsub__(self, other):
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return self.roperate(other, op.sub)
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def __mul__(self, other):
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""" Overload *
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>>> a = Expression("1+2")
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>>> print(a.postfix_tokens)
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[1, 2, '+']
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>>> b = Expression("3+4")
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>>> print(b.postfix_tokens)
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[3, 4, '+']
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>>> c = a * b
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>>> print(c.postfix_tokens)
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[1, 2, '+', 3, 4, '+', '*']
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"""
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return self.operate(other, op.mul)
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def __rmul__(self, other):
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return self.roperate(other, op.mul)
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def __truediv__(self, other):
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""" Overload /
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>>> a = Expression("1+2")
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>>> print(a.postfix_tokens)
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[1, 2, '+']
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>>> b = Expression("3+4")
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>>> print(b.postfix_tokens)
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[3, 4, '+']
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>>> c = a / b
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>>> print(c.postfix_tokens)
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[1, 2, '+', 3, 4, '+', '/']
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>>>
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"""
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return self.operate(other, op.div)
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def __rtruediv__(self, other):
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return self.roperate(other, op.div)
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def __pow__(self, other):
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return self.operate(other, op.pw)
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def __xor__(self, other):
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return self.operate(other, op.pw)
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def __neg__(self):
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return Expression(self.postfix_tokens + [op.sub1])
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def untest(exp):
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a = Expression(exp)
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b = a.simplify()
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for i in b.explain():
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#print(type(i))
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print(i)
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#print(type(a.simplified()), ":", a.simplified())
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print("\n")
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if __name__ == '__main__':
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print('\n')
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A = Expression("( -8 x + 8 ) ( -8 - ( -6 x ) )")
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Ar = A.simplify()
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for i in Ar.explain():
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print(i)
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#print("------------")
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#for i in Ar.explain():
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# print(i)
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#print(type(Ar))
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#print('\n-----------')
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#A = Expression("-6 / 3 + 10 / -5")
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#Ar = A.simplify()
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#for i in Ar.explain():
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# print(i)
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#print('\n-----------')
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#A = Expression("1/3 + 4/6")
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#Ar = A.simplify()
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#for i in Ar.explain():
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# print(i)
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#import doctest
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#doctest.testmod()
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# -----------------------------
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# Reglages pour 'vim'
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# vim:set autoindent expandtab tabstop=4 shiftwidth=4:
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# cursor: 16 del
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