432 lines
14 KiB
Python
432 lines
14 KiB
Python
#!/usr/bin/env python
|
|
# encoding: utf-8
|
|
|
|
# debuging
|
|
#from debug.tools import report
|
|
|
|
from .generic import Stack, flatten_list, expand_list, isNumber, isOperator, isNumerand
|
|
from .str2tokens import str2tokens
|
|
from .operator import op
|
|
from .explicable import Explicable, Explicable_int, Explicable_float
|
|
|
|
from .random_expression import RdExpression
|
|
|
|
__all__ = ['Expression']
|
|
|
|
|
|
class Expression(Explicable):
|
|
"""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))
|
|
|
|
@classmethod
|
|
def tmp_render(cls, render=lambda _, x: Expression(x)):
|
|
""" Same ad tmp_render for Renderable but default render is Expression
|
|
|
|
>>> exp = Expression("2*3/5")
|
|
>>> print(exp)
|
|
2 \\times \\frac{ 3 }{ 5 }
|
|
>>> for i in exp.simplify().explain():
|
|
... print(i)
|
|
2 \\times \\frac{ 3 }{ 5 }
|
|
\\frac{ 3 }{ 5 } \\times 2
|
|
\\frac{ 3 \\times 2 }{ 5 }
|
|
\\frac{ 6 }{ 5 }
|
|
>>> with Expression.tmp_render():
|
|
... for i in exp.simplify().explain():
|
|
... i
|
|
< <class 'pymath.calculus.expression.Expression'> [2, 3, 5, '/', '*'] >
|
|
< <class 'pymath.calculus.expression.Expression'> [2, < Fraction 3 / 5>, '*'] >
|
|
< <class 'pymath.calculus.expression.Expression'> [3, 5, '/', 2, '*'] >
|
|
< <class 'pymath.calculus.expression.Expression'> [3, 2, '*', 5, '/'] >
|
|
< <class 'pymath.calculus.expression.Expression'> [6, 5, '/'] >
|
|
>>> from .render import txt
|
|
>>> with Expression.tmp_render(txt):
|
|
... for i in exp.simplify().explain():
|
|
... print(i)
|
|
2 * 3 / 5
|
|
3 / 5 * 2
|
|
( 3 * 2 ) / 5
|
|
6 / 5
|
|
>>> for i in exp.simplify().explain():
|
|
... print(i)
|
|
2 \\times \\frac{ 3 }{ 5 }
|
|
\\frac{ 3 }{ 5 } \\times 2
|
|
\\frac{ 3 \\times 2 }{ 5 }
|
|
\\frac{ 6 }{ 5 }
|
|
|
|
"""
|
|
return super(Expression, cls).tmp_render(render)
|
|
|
|
def __new__(cls, exp):
|
|
"""Create Expression objects
|
|
|
|
:param exp: the expression. It can be a string or a list of postfix tokens.
|
|
|
|
"""
|
|
expression = object.__new__(cls)
|
|
|
|
if isinstance(exp, str):
|
|
expression.postfix_tokens = str2tokens(exp)
|
|
|
|
elif isinstance(exp, list):
|
|
# Ici on ne peut convertir les "+-*/..." en opérateur que s'ils sont
|
|
# d'arité 2.
|
|
exp_mod_op = [
|
|
op.get_op(i) if op.can_be_operator(i) else i for i in exp
|
|
]
|
|
expression.postfix_tokens = flatten_list(
|
|
[tok.postfix_tokens if Expression.isExpression(tok) else tok for tok in exp_mod_op]
|
|
)
|
|
|
|
elif isinstance(exp, Expression):
|
|
return exp
|
|
|
|
elif isNumerand(exp):
|
|
expression.postfix_tokens = [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 isinstance(token, Explicable_int) or isinstance(token, int):
|
|
# return Explicable_int(token)
|
|
|
|
# # TODO: J'en arrive au soucis même soucis qu'avec les fractions qui une fois simplifiée devrait être des Explicable_int. Mais comment on ne redéfini pas les opérations, ce sont les opérations des int qui se font et donc on perd toute l'historique. |sam. févr. 13 18:57:45 EAT 2016
|
|
# if isinstance(token, Explicable_float) or isinstance(token, float):
|
|
# return Explicable_float(token)
|
|
|
|
# elif hasattr(token, 'simplify') and hasattr(token, 'explain'):
|
|
# ans = expression.postfix_tokens[0]
|
|
# return ans
|
|
|
|
# elif isinstance(token, str):
|
|
# from .polynom import Polynom
|
|
# return Polynom([0,1], letter = token)
|
|
|
|
# else:
|
|
# raise ValueError(
|
|
# "Unknow token type in Expression: {}".format(
|
|
# type(token)))
|
|
|
|
# else:
|
|
# expression._isExpression = 1
|
|
# return expression
|
|
expression._isExpression = 1
|
|
return expression
|
|
|
|
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):
|
|
return " ".join(["<", str(self.__class__),
|
|
str(self.postfix_tokens), ">"])
|
|
|
|
def simplify(self):
|
|
""" Compute entirely the expression and return the result with .steps attribute """
|
|
try:
|
|
self.compute_exp()
|
|
except ComputeError:
|
|
try:
|
|
self.simplified = self.postfix_tokens[0].simplify()
|
|
except AttributeError:
|
|
if isinstance(self.postfix_tokens[0],int):
|
|
self.simplified = Explicable_int(self.postfix_tokens[0])
|
|
elif isinstance(self.postfix_tokens[0],float):
|
|
self.simplified = Explicable_float(self.postfix_tokens[0])
|
|
else:
|
|
self.simplified = self
|
|
|
|
else:
|
|
self.simplified = self.child.simplify()
|
|
self.simplified.steps = self.child.steps + self.simplified.steps
|
|
return self.simplified
|
|
|
|
def compute_exp(self):
|
|
""" Create self.child with and stock steps in it """
|
|
if len(self.postfix_tokens) == 1:
|
|
raise ComputeError("Nothing to compute in {}".format(self.postfix_tokens))
|
|
else:
|
|
ini_step = Expression(self.postfix_tokens)
|
|
|
|
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
|
|
if isNumerand(tokenList[0]) and isNumerand(tokenList[1]) \
|
|
and isOperator(tokenList[2]) and tokenList[2].arity == 2:
|
|
|
|
# S'il y a une opération à faire
|
|
op1 = tokenList[0]
|
|
op2 = tokenList[1]
|
|
operator = tokenList[2]
|
|
|
|
res = operator(op1, op2)
|
|
|
|
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
|
|
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]
|
|
|
|
else:
|
|
tmpTokenList.append(tokenList[0])
|
|
|
|
del tokenList[0]
|
|
|
|
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]
|
|
|
|
tmpTokenList += tokenList
|
|
self.child = Expression(tmpTokenList)
|
|
|
|
steps = self.develop_steps(tmpTokenList)
|
|
|
|
if self.child.postfix_tokens == ini_step.postfix_tokens:
|
|
self.child.steps = steps
|
|
else:
|
|
self.child.steps = [ini_step] + steps
|
|
|
|
def develop_steps(self, tokenList):
|
|
""" From a list of tokens, it develops steps of each tokens """
|
|
tmp_steps = []
|
|
for t in tokenList:
|
|
try:
|
|
with Expression.tmp_render():
|
|
tmp_steps.append([i for i in t.explain()])
|
|
except AttributeError:
|
|
tmp_steps.append([t])
|
|
|
|
if max([len(i) for i in tmp_steps]) == 1:
|
|
# Cas où rien n'a dû être expliqué.
|
|
return []
|
|
else:
|
|
tmp_steps = expand_list(tmp_steps)[:-1]
|
|
steps = [Expression(s) for s in tmp_steps]
|
|
return steps
|
|
|
|
@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
|
|
|
|
def operate(self, other, operator):
|
|
if isinstance(other, Expression):
|
|
return Expression(
|
|
self.postfix_tokens +
|
|
other.postfix_tokens +
|
|
[operator])
|
|
elif isinstance(other, list):
|
|
return Expression(self.postfix_tokens + other + [operator])
|
|
else:
|
|
return Expression(self.postfix_tokens + [other] + [operator])
|
|
|
|
def roperate(self, other, operator):
|
|
if isinstance(other, Expression):
|
|
return Expression(
|
|
other.postfix_tokens +
|
|
self.postfix_tokens +
|
|
[operator])
|
|
elif isinstance(other, list):
|
|
return Expression(other + self.postfix_tokens + [operator])
|
|
else:
|
|
return Expression([other] + self.postfix_tokens + [operator])
|
|
|
|
def __add__(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, '+', '+']
|
|
"""
|
|
return self.operate(other, op.add)
|
|
|
|
def __radd__(self, other):
|
|
return self.roperate(other, op.add)
|
|
|
|
def __sub__(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, '+', '-']
|
|
"""
|
|
return self.operate(other, op.sub)
|
|
|
|
def __rsub__(self, other):
|
|
return self.roperate(other, op.sub)
|
|
|
|
def __mul__(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, '+', '*']
|
|
"""
|
|
return self.operate(other, op.mul)
|
|
|
|
def __rmul__(self, other):
|
|
return self.roperate(other, op.mul)
|
|
|
|
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, '+', '/']
|
|
>>>
|
|
"""
|
|
return self.operate(other, op.div)
|
|
|
|
def __rtruediv__(self, other):
|
|
return self.roperate(other, op.div)
|
|
|
|
def __pow__(self, other):
|
|
return self.operate(other, op.pw)
|
|
|
|
def __xor__(self, other):
|
|
return self.operate(other, op.pw)
|
|
|
|
def __neg__(self):
|
|
return Expression(self.postfix_tokens + [op.sub1])
|
|
|
|
class ExpressionError(Exception):
|
|
pass
|
|
|
|
class ComputeError(Exception):
|
|
pass
|
|
|
|
def untest(exp):
|
|
a = Expression(exp)
|
|
b = a.simplify()
|
|
|
|
for i in b.explain():
|
|
# print(type(i))
|
|
print(i)
|
|
|
|
#print(type(a.simplified()), ":", a.simplified())
|
|
|
|
print("\n")
|
|
|
|
if __name__ == '__main__':
|
|
print('\n')
|
|
A = Expression("( -8 x + 8 ) ( -8 - ( -6 x ) )")
|
|
Ar = A.simplify()
|
|
for i in Ar.explain():
|
|
print(i)
|
|
# print("------------")
|
|
# for i in Ar.explain():
|
|
# print(i)
|
|
|
|
# print(type(Ar))
|
|
|
|
# print('\n-----------')
|
|
#A = Expression("-6 / 3 + 10 / -5")
|
|
#Ar = A.simplify()
|
|
# for i in Ar.explain():
|
|
# print(i)
|
|
|
|
# print('\n-----------')
|
|
#A = Expression("1/3 + 4/6")
|
|
#Ar = A.simplify()
|
|
# for i in Ar.explain():
|
|
# print(i)
|
|
|
|
#import doctest
|
|
# doctest.testmod()
|
|
|
|
# -----------------------------
|
|
# Reglages pour 'vim'
|
|
# vim:set autoindent expandtab tabstop=4 shiftwidth=4:
|
|
# cursor: 16 del
|