Mapytex/pymath/expression.py

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#!/usr/bin/env python
# encoding: utf-8
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from .generic import Stack, flatten_list, expand_list, isNumber, isOperator, isNumerand
from .str2tokens import str2tokens
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from .operator import op
from .render import txt, tex
from .explicable import Explicable
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from .random_expression import RdExpression
__all__ = ['Expression', 'Renderable']
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class Renderable(object):
STR_RENDER = tex
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DEFAULT_RENDER = tex
@classmethod
def set_render(cls, render):
cls.STR_RENDER = render
@classmethod
def get_render(cls):
return cls.STR_RENDER
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@classmethod
def set_default_render(cls):
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cls.set_render(cls.DEFAULT_RENDER)
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@classmethod
def tmp_render(cls, render = lambda _,x:Expression(x)):
""" Create a container in which Expression render is temporary modify
The default temporary render is Expression in order to perform calculus inside numbers
>>> exp = Expression("2*3/5")
>>> print(exp)
\\frac{ 2 \\times 3 }{ 5 }
>>> for i in exp.simplify().explain():
... print(i)
\\frac{ 2 \\times 3 }{ 5 }
\\frac{ 6 }{ 5 }
>>> with Expression.tmp_render():
... for i in exp.simplify().explain():
... i
< Expression [2, 3, '*', 5, '/']>
< Expression [6, 5, '/']>
< Fraction 6 / 5>
>>> with Expression.tmp_render(txt):
... for i in exp.simplify().explain():
... print(i)
2 * 3 / 5
6 / 5
>>> for i in exp.simplify().explain():
... print(i)
\\frac{ 2 \\times 3 }{ 5 }
\\frac{ 6 }{ 5 }
"""
class TmpRenderEnv(object):
def __enter__(self):
self.old_render = Expression.get_render()
Expression.set_render(render)
def __exit__(self, type, value, traceback):
Expression.set_render(self.old_render)
return TmpRenderEnv()
class Expression(Explicable, Renderable):
"""A calculus expression. Today it can andle only expression with numbers later it will be able to manipulate unknown"""
@classmethod
def random(self, form="", conditions=[], val_min = -10, val_max=10):
"""Create a random expression from form and with conditions
:param form: the form of the expression (/!\ variables need to be in brackets {})
:param conditions: condition on variables (/!\ variables need to be in brackets {})
:param val_min: min value for generate variables
:param val_max: max value for generate variables
"""
random_generator = RdExpression(form, conditions)
return Expression(random_generator(val_min, val_max))
def __new__(cls, exp):
"""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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"""
expression = object.__new__(cls)
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if type(exp) == str:
expression.postfix_tokens = str2tokens(exp)
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elif type(exp) == list:
expression.postfix_tokens = flatten_list([tok.postfix_tokens if Expression.isExpression(tok) else tok for tok in exp])
else:
raise ValueError("Can't build Expression with {} object".format(type(exp)))
if len(expression.postfix_tokens) == 1:
token = expression.postfix_tokens[0]
if hasattr(token, 'simplify') and hasattr(token, 'explain'):
return expression.postfix_tokens[0]
elif type(token) == int:
# On crée un faux int en ajoutant la méthode simplify et simplified et la caractérisique isNumber
simplify = lambda x:x
is_number = True
methods_attr = {'simplify':simplify, 'isNumber': is_number, 'postfix_tokens': [token]}
fake_token = type('fake_int', (int,Explicable, Renderable), methods_attr)(token)
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return fake_token
elif type(token) == str:
# 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
simplify = lambda x:[x]
is_polynom = True
methods_attr = {'simplify':simplify, '_isPolynom': is_polynom, 'postfix_tokens': [token]}
fake_token = type('fake_str', (str,Explicable, Renderable), methods_attr)(token)
return fake_token
else:
raise ValueError("Unknow type in Expression: {}".format(type(token)))
else:
expression._isExpression = 1
return expression
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def __str__(self):
"""
Overload str
If you want to changer render use Expression.set_render(...) or use tmp_render context manager.
"""
return self.STR_RENDER(self.postfix_tokens)
def __repr__(self):
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return " ".join(["<", str(self.__class__) , str(self.postfix_tokens), ">"])
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def simplify(self):
""" Compute entirely the expression and return the result with .steps attribute """
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self.compute_exp()
self.simplified = self.child.simplify()
try:
self.simplified.steps = self.child.steps + self.simplified.steps
except AttributeError:
pass
return self.simplified
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def compute_exp(self):
""" Create self.child with and stock steps in it """
child_steps = [self.postfix_tokens]
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tokenList = self.postfix_tokens.copy()
tmpTokenList = []
while len(tokenList) > 2:
# 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]) \
and isOperator(tokenList[2]) 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]
# Et les motifs du gens A -, quand l'operateur est d'arité 1
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elif isNumerand(tokenList[0]) \
and isOperator(tokenList[1]) 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]
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if len(tokenList) == 2 and isNumerand(tokenList[0]) \
and isOperator(tokenList[1]) and tokenList[1].arity == 1:
# S'il reste deux éléments dont un operation d'arité 1
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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tmpTokenList += tokenList
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steps = expand_list(tmpTokenList)
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if len(steps[:-1]) > 0:
child_steps += [flatten_list(s) for s in steps[:-1]]
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self.child = Expression(steps[-1])
self.child.steps = child_steps
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@classmethod
def isExpression(self, other):
try:
other._isExpression
except AttributeError:
return 0
return 1
# -----------
# Expression act as container from self.postfix_tokens
def __getitem__(self, index):
return self.postfix_tokens[index]
def __setitem__(self, index, value):
self.postfix_tokens[index] = value
# -----------
# Some math manipulations
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def operate(self, other, operator):
if type(other) == Expression:
return Expression(self.postfix_tokens + other.postfix_tokens + [operator])
elif type(other) == list:
return Expression(self.postfix_tokens + other + [operator])
else:
return Expression(self.postfix_tokens + [other] + [operator])
def roperate(self, other, operator):
if type(other) == Expression:
return Expression(other.postfix_tokens + self.postfix_tokens + [operator])
elif type(other) == list:
return Expression(other + self.postfix_tokens + [operator])
else:
return Expression([other] + self.postfix_tokens + [operator])
def __add__(self, other):
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""" Overload +
>>> a = Expression("1+2")
>>> print(a.postfix_tokens)
[1, 2, '+']
>>> b = Expression("3+4")
>>> print(b.postfix_tokens)
[3, 4, '+']
>>> c = a + b
>>> print(c.postfix_tokens)
[1, 2, '+', 3, 4, '+', '+']
"""
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return self.operate(other, op.add)
def __radd__(self, other):
return self.roperate(other, op.add)
def __sub__(self, other):
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""" Overload -
>>> a = Expression("1+2")
>>> print(a.postfix_tokens)
[1, 2, '+']
>>> b = Expression("3+4")
>>> print(b.postfix_tokens)
[3, 4, '+']
>>> c = a - b
>>> print(c.postfix_tokens)
[1, 2, '+', 3, 4, '+', '-']
"""
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return self.operate(other, op.sub)
def __rsub__(self, other):
return self.roperate(other, op.sub)
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def __mul__(self, other):
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""" Overload *
>>> a = Expression("1+2")
>>> print(a.postfix_tokens)
[1, 2, '+']
>>> b = Expression("3+4")
>>> print(b.postfix_tokens)
[3, 4, '+']
>>> c = a * b
>>> print(c.postfix_tokens)
[1, 2, '+', 3, 4, '+', '*']
"""
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return self.operate(other, op.mul)
def __rmul__(self, other):
return self.roperate(other, op.mul)
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def __truediv__(self, other):
""" Overload /
>>> a = Expression("1+2")
>>> print(a.postfix_tokens)
[1, 2, '+']
>>> b = Expression("3+4")
>>> print(b.postfix_tokens)
[3, 4, '+']
>>> c = a / b
>>> print(c.postfix_tokens)
[1, 2, '+', 3, 4, '+', '/']
"""
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return self.operate(other, op.div)
def __rdiv__(self, other):
return self.roperate(other, op.div)
def __pow__(self, other):
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return self.operate(other, op.pw)
def __xor__(self, other):
return self.operate(other, op.pw)
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def __neg__(self):
return Expression(self.postfix_tokens + [op.sub1])
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def test(exp):
a = Expression(exp)
b = a.simplify()
for i in b.explain():
#print(type(i))
print(i)
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#print(type(a.simplified()), ":", a.simplified())
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print("\n")
if __name__ == '__main__':
#render = lambda _,x : str(x)
#Expression.set_render(render)
#exp = Expression("1/2 - 4")
#print(list(exp.simplify()))
#Expression.set_render(txt)
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#exp = "2 ^ 3 * 5"
#test(exp)
#exp = "2x + 5"
#test(exp)
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#Expression.set_render(tex)
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#test(exp1)
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#from pymath.operator import op
#exp = [2, 3, op.pw, 5, op.mul]
#test(exp)
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#test([Expression(exp1), Expression(exp), op.add])
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#exp = "1 + 3 * 5"
#e = Expression(exp)
#f = -e
#print(f)
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#exp = "2 * 3 * 3 * 5"
#test(exp)
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#exp = "2 * 3 + 3 * 5"
#test(exp)
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#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)
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#exp = "( 2 + 5 ) / ( 3 * 4 ) + 1 / 12"
#test(exp)
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#exp = "( 2+ 5 )/( 3 * 4 ) + 1 / 2"
#test(exp)
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#exp="(-2+5)/(3*4)+1/12+5*5"
#test(exp)
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#exp="-2*4(12 + 1)(3-12)"
#test(exp)
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#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)
#print("\n")
#exp = Expression.random("({a} + 3)({b} - 1)", ["{a} > 4"])
#for i in exp.simplify():
# print(i)
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import doctest
doctest.testmod()
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# -----------------------------
# Reglages pour 'vim'
# vim:set autoindent expandtab tabstop=4 shiftwidth=4:
# cursor: 16 del