Reduce and print poly ok!
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lafrite
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@ -41,15 +41,15 @@ class Expression(object):
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## ---------------------
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## Mechanism functions
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def simplify(self):
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def simplify(self, render=STR_RENDER):
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""" Generator which return steps for computing the expression """
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if not self.can_go_further():
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yield self.STR_RENDER(self.postfix_tokens)
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yield render(self.postfix_tokens)
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else:
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self.compute_exp()
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old_s = ''
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for s in self.steps:
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new_s = self.STR_RENDER(s)
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new_s = render(s)
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# 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:
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old_s = new_s
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@ -264,7 +264,23 @@ def spe_zip(l1,l2):
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ans.append(j)
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return ans
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def transpose_fill(list_lists):
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"""Transpose a list of list and if inside list have not the same length, fill with last token
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:list_lists: a list of list to transpose
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:returns: generator which generate lines of the transposed matrix
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>>> Polynom.transpose_fill([[1], [2, 3], [4, 5, 6]])
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[[1, 2, 4] , [1, 3, 5], [1, 3, 6]]
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"""
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for i in range(max([len(l) for l in list_lists])):
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col = []
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for l in list_lists:
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try:
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col.append(l[i])
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except IndexError:
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col.append(l[-1])
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yield col
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def isOperator(exp):
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"""Check if the expression is an opération in "+-*/:^"
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@ -3,8 +3,11 @@
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from .expression import Expression
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from .generic import spe_zip, sum_postfix, expand_list, isNumber
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from .operator import op
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from .generic import spe_zip, expand_list, isNumber, transpose_fill, flatten_list
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#from .generic import spe_zip, sum_postfix, expand_list, isNumber
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from .render import txt
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from itertools import chain
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__all__ = ["Polynom"]
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@ -23,6 +26,14 @@ class Polynom(object):
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- a: a Expression. [1, Expression("2+3"), 4] designate 1 + (2+3)x + 4x^2
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:param letter: the string describing the unknown
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>>> Polynom([1,2,3]).mainOp
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'+'
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>>> Polynom([1]).mainOp
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'*'
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>>> Polynom([1,2, 3])._letter
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'x'
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>>> Polynom([1, 2, 3], "y")._letter
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'y'
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"""
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self.feed_coef(coef)
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self._letter = letter
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@ -33,7 +44,7 @@ class Polynom(object):
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else:
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self.mainOp = "+"
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self._isPolynom
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self._isPolynom = 1
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def feed_coef(self, l_coef):
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"""Feed coef of the polynom. Manage differently whether it's a number or an expression
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@ -52,12 +63,22 @@ class Polynom(object):
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:returns: the degree of the polynom
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>>> Polynom([1, 2, 3]).get_degree()
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2
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>>> Polynom([1]).get_degree()
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0
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"""
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return len(self._coef) - 1
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def is_monom(self):
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"""is the polynom a monom (only one coefficent)
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:returns: 1 if yes 0 otherwise
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>>> Polynom([1, 2, 3]).is_monom()
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0
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>>> Polynom([1]).is_monom()
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1
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"""
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if len([i for i in self._coef if i != 0])==1:
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return 1
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@ -65,8 +86,7 @@ class Polynom(object):
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return 0
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def __str__(self):
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# TODO: Voir si on peut utiliser un render |sam. juin 14 08:56:16 CEST 2014
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return txt(self.get_postfix())
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return txt(self.postfix)
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def __repr__(self):
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return "< Polynom " + str(self._coef) + ">"
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@ -74,7 +94,7 @@ class Polynom(object):
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def coef_postfix(self, a, i):
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"""Return the postfix display of a coeficient
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:param a: value for the coeficient (/!\ as a list)
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:param a: value for the coeficient (/!\ as a postfix list)
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:param i: power
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:returns: postfix tokens of coef
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@ -86,46 +106,34 @@ class Polynom(object):
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if i == 0:
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ans = a
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elif i == 1:
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ans = a * (a!=[1]) + [self._letter] + ["*"] * (a!=[1])
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ans = a * (a!=[1]) + [self._letter] + [op.mul] * (a!=[1])
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else:
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ans = a * (a!=[1]) + [self._letter, i, "^"] + ["*"] * (a!=[1])
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ans = a * (a!=[1]) + [self._letter, i, op.pw] + [op.mul] * (a!=[1])
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return ans
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def get_postfix(self):
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@property
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def postfix(self):
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"""Return the postfix form of the polynom
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:returns: the postfix list of polynom's tokens
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"""
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self._postfix = []
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first_elem = 1
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postfix = []
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for (i,a) in list(enumerate(self._coef))[::-1]:
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if type(a) == list and str(a[-1]) in "+-*^/":
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if type(a) == Expression:
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# case coef is an arithmetic expression
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self._postfix += self.coef_postfix(a,i)
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if not first_elem:
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self._postfix.append("+")
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first_elem = 0
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postfix.append(self.coef_postfix(a.postfix_tokens,i))
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elif type(a) == list and str(a[-1]) not in "+-*^/":
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elif type(a) == list:
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# case need to repeat the x^i
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for b in a:
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if type(b) == list:
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self._postfix += self.coef_postfix(b,i)
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else:
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self._postfix += self.coef_postfix([b],i)
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if not first_elem:
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self._postfix.append("+")
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first_elem = 0
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postfix.append(self.coef_postfix([b],i))
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elif a != 0:
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self._postfix += self.coef_postfix([a],i)
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if not first_elem:
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self._postfix.append("+")
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first_elem = 0
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postfix.append(self.coef_postfix([a],i))
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return self._postfix
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return flatten_list(self.postfix_add(postfix))
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def conv2poly(self, other):
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"""Convert anything number into a polynom"""
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@ -149,53 +157,54 @@ class Polynom(object):
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:returns: new Polynom with numbers coefficients
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"""
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steps = []
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for a in self._coef:
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# gather steps for every coeficients
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coefs_steps = []
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for coef in self._coef:
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coef_steps = []
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if type(a) == Expression:
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# case coef is an arithmetic expression
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coef_steps = list(a.simplify(render = lambda x:x))
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steps.append(coef_steps)
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elif type(a) == list:
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# case need to repeat the x^i
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if [i for i in a if type(i) == list] != []:
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# first we simplify arithmetic exp
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# Et hop un coup de sorcelerie!
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elem = [list(Expression(i).simplify(render = lambda x:self.list_or_num(x))) if type(i) == list else i for i in a ]
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elem = expand_list(elem)
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coef_steps += elem
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exp = elem[-1]
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else:
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exp = a
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exp = sum_postfix(exp)
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exp = Expression(exp)
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coef_steps += list(exp.simplify(render = lambda x:x))
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steps.append(coef_steps)
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if type(coef) != Expression:
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# On converti en postfix avec une addition
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postfix_add = self.postfix_add(coef)
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# On converti en Expression
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coef_exp = Expression(postfix_add)
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else:
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steps.append(a)
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coef_exp = coef
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steps = expand_list(steps)
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return [Polynom(s) for s in steps]
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# On fait réduire l'expression puis on ajoute dans steps
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coef_steps = list(coef_exp.simplify(render = lambda x:Expression(x)))
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# On ajoute toutes ces étapes
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coefs_steps.append(coef_steps)
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# On retourne la matrice
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for coefs in transpose_fill(coefs_steps):
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yield Polynom(coefs, self._letter)
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@staticmethod
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def list_or_num(x):
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if len(x) == 1:
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return x[0]
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def postfix_add(numbers):
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"""Convert a list of numbers into a postfix addition
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:numbers: list of numbers
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:returns: Postfix list of succecive attition of number
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>>> Polynom.postfix_add([1])
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[1]
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>>> Polynom.postfix_add([1, 2])
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[1, 2, '+']
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>>> Polynom.postfix_add([1, 2, 3])
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[1, 2, '+', 3, '+']
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>>> Polynom.postfix_add(1)
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[1]
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"""
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if not type(numbers) == list:
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return [numbers]
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else:
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return x
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ans = [[a, op.add] if i!=0 else [a] for (i,a) in enumerate(numbers)]
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return list(chain.from_iterable(ans))
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def simplify(self):
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"""Same as reduce """
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return self.reduce()
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def __eq__(self, other):
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o_poly = self.conv2poly(other)
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return self._coef == o_poly._coef
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@ -275,23 +284,24 @@ def test(p,q):
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print("\n Plus ------")
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for i in (p + q):
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#print(repr(i))
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#print("\t", str(i.get_postfix()))
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#print("\t", str(i.postfix))
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print(i)
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print("\n Moins ------")
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for i in (p - q):
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#print(repr(i))
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#print("\t", str(i.get_postfix()))
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#print("\t", str(i.postfix))
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print(i)
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print("\n Multiplier ------")
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for i in (p * q):
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#print(repr(i))
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#print("\t", str(i.get_postfix()))
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#print("\t", str(i.postfix))
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print(i)
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if __name__ == '__main__':
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from .fraction import Fraction
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p = Polynom([1, -2 ])
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q = Polynom([4, 7])
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#test(p,q)
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@ -304,10 +314,10 @@ if __name__ == '__main__':
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#print("-- Poly étrange --")
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#p = Polynom([1, [[2, 3, "*"],3], 4], "x")
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#print(repr(p))
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#for i in p.simplify():
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# print(repr(i))
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p = Polynom([1, [2, 3], 4], "x")
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print(repr(p))
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for i in p.simplify():
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print(i)
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#print("-- Poly étrange --")
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#p = Polynom([1, [[2, 3, "*"], [4,5,"*"]], 4], "x")
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#print(repr(p))
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@ -315,6 +325,9 @@ if __name__ == '__main__':
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#for i in p.simplify():
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# print(repr(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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