import old polynom and test_polynom from polynom branch
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lafrite
parent
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#!/usr/bin/env python
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# encoding: utf-8
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from pymath.fraction import Fraction
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from pymath.expression import Expression
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from pymath.generic import mix_list, sum_postfix, expand_list
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__all__ = ["Polynom"]
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class Polynom(object):
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"""Docstring for Polynom. """
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def __init__(self, coef = [1], letter = "x" ):
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"""Initiate the polynom
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:param coef: coefficients of the polynom (ascending degree sorted) - can be a list of list of coefficients.
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3 possibles type of list:
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- [a,b,..] simple list of coefficients. [1,2] designate 1 + 2x
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- [a, [c,b],...] list of coefficients with x^i repeated. [1,[2,3],4) designate 1 + 2x + 3x + 4x^2
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- [a, [b,c,"+"],...] list of coefficients with arithmetic expression (postfix form) in. [1, [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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"""
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self.feed_coef(coef)
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self._letter = letter
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if self.is_monom():
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self.mainOp = "*"
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else:
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self.mainOp = "+"
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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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:l_coef: list of coef
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"""
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self._coef = []
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for coef in l_coef:
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if type(coef) == list and len(coef)==1:
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self._coef.append(coef[0])
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else:
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self._coef.append(coef)
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def get_degree(self):
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"""Getting the degree fo the polynom
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:returns: the degree of the polynom
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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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"""
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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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else:
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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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from .renders import txt
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return txt(self.get_postfix())
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def __repr__(self):
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return "< Polynom " + str(self._coef) + ">"
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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 i: power
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:returns: postfix tokens of coef
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"""
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ans =[]
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if a == 0:
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return ans
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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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else:
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ans = a * (a!=[1]) + [self._letter, i, "^"] + ["*"] * (a!=[1])
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return ans
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def get_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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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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# 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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elif type(a) == list and str(a[-1]) not in "+-*^/":
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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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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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return self._postfix
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def convert_into_poly(self, other):
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"""Convert anything (int and fract) into a polynom """
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if type(other) in [int, Fraction]:
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return Polynom([other])
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elif type(other) == Polynom:
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return other
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else:
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raise ValueError(type(other) + " can't be converted into a polynom")
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def reduce(self):
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"""Compute coefficients which have same degree
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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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coef_steps = []
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if type(a) == list and str(a[-1]) in "+-*^":
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# case coef is an arithmetic expression
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exp = Expression(a)
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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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elif type(a) == list and str(a[-1]) not in "+-*^":
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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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else:
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steps.append(a)
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steps = expand_list(steps)
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return [Polynom(s) for s in steps]
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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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else:
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return x
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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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if type(other) in [int, Fraction, Polynom] or other.isnumeric():
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o_poly = self.convert_into_poly(other)
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return self._coef == o_poly._coef
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else:
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return 0
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def __add__(self, other):
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steps = []
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o_poly = self.convert_into_poly(other)
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n_coef = mix_list(self._coef, o_poly._coef)
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p = Polynom(n_coef)
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steps.append(p)
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steps += p.simplify()
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return steps
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def __radd__(self, other):
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return self.__add__(other)
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def __neg__(self):
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return Polynom([-i for i in self._coef], letter = self._letter)
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def __sub__(self, other):
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o_poly = self.convert_into_poly(other)
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o_poly = -o_poly
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return self.__add__(o_poly)
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def __rsub__(self, other):
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o_poly = self.convert_into_poly(other)
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return o_poly.__sub__(-self)
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def __mul__(self, other):
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steps = []
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o_poly = self.convert_into_poly(other)
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coefs = []
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for (i,a) in enumerate(self._coef):
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for (j,b) in enumerate(o_poly._coef):
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if a == 0 or b == 0:
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elem = 0
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else:
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elem = [a, b, "*"]
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try:
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if coefs[i+j]==0:
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coefs[i+j] = elem
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elif elem != 0:
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coefs[i+j] = [coefs[i+j], elem]
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except IndexError:
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coefs.append(elem)
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p = Polynom(coefs)
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steps.append(p)
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steps += p.simplify()
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return steps
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def __rmul__(self, other):
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o_poly = self.convert_into_poly(other)
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return o_poly.__mul__(self)
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def __div__(self, other):
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pass
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def __truediv__(self, other):
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pass
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def test(p,q):
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print("---------------------")
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print("---------------------")
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print("p : ",p)
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print("q : ",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(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(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(i)
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if __name__ == '__main__':
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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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q = Polynom([0, Fraction(1,2), 0, Fraction(-4,3)])
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#test(p,q)
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p = Polynom([1, 1, 1 ])
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print(p)
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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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#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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#print(p)
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#for i in p.simplify():
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# print(repr(i))
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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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@ -0,0 +1,162 @@
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#!/usr/bin/env python
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# encoding: utf-8
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import unittest
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from pymath.polynom import Polynom
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from pymath.fraction import Fraction
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class TestPolynom(unittest.TestCase):
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"""Testing functions from pymath.polynom"""
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def test_init(self):
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p = Polynom([1, 2, 3], "x")
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def test_init_multi(self):
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p = Polynom([1, [2, 3], 4], "x")
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def test_init_arith(self):
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p = Polynom([1, [2, 3, "+"], 4], "x")
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def test_init_arith_2(self):
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p = Polynom([1, [[2, 3, "*"],3], 4], "x")
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def test_deg(self):
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pass
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def test_eval(self):
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pass
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#def test_print(self):
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# p = Polynom([1,2,3])
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# ans = "1 + 2 x + 3 x^2"
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# self.assertEqual(ans, str(p))
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#def test_print_monom(self):
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# p = Polynom([0,2])
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# ans = "2 x"
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# self.assertEqual(ans, str(p))
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#def test_print_0_coef(self):
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# p = Polynom([0,1,3])
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# ans = "x + 3 x^2"
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# self.assertEqual(ans, str(p))
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#def test_print_multi_coef(self):
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# p = Polynom([1,[2, -2],3])
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# ans = "1 + 2 x - 2 x + 3 x^2"
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# self.assertEqual(ans, str(p))
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def test_get_postfix(self):
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p = Polynom([1,2,3])
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#ans = [1, 2, "x", "*", "+", 3, "x", 2, "^", "*", "+"]
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ans = [3, 'x', 2, '^', '*', 2, 'x', '*', '+', 1, '+']
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self.assertEqual(ans, p.get_postfix())
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def test_get_postfix_monom(self):
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p = Polynom([0,2])
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ans = [2, "x", "*"]
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self.assertEqual(ans, p.get_postfix())
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def test_get_postfix_0_coef(self):
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p = Polynom([0,2,0,4])
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#ans = [2, "x", "*", 4, "x", 3, "^", "*", "+"]
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ans = [4, 'x', 3, '^', '*', 2, 'x', '*', '+']
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self.assertEqual(ans, p.get_postfix())
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def test_get_postfix_1_coef(self):
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p = Polynom([0,1,1])
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#ans = ["x", "x", 2, "^", "+"]
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ans = ["x", 2, "^", "x", "+"]
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self.assertEqual(ans, p.get_postfix())
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def test_get_postfix_neg_coef(self):
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# TODO: Choix arbitraire (vis à vis des + et des -) il faudra faire en fonction de render |sam. juin 14 09:45:55 CEST 2014
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p = Polynom([-1,-2,-3])
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#ans = [-1, -2, "x", "*", "+", -3, "x", 2, "^", "*", "+"]
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ans = [-3, 'x', 2, '^', '*', -2, 'x', '*', '+', -1, '+']
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self.assertEqual(ans, p.get_postfix())
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def test_get_postfix_multi_coef(self):
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p = Polynom([1,[2, 3],4])
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#ans = [1, 2, "x", "*", "+", 3, "x", "*", "+", 4, "x", 2, "^", "*", "+"]
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ans = [4, 'x', 2, '^', '*', 2, 'x', '*', '+', 3, 'x', '*', '+', 1, '+']
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self.assertEqual(ans, p.get_postfix())
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def test_get_postfix_arithm_coef(self):
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p = Polynom([1,[2, 3, "+"],4])
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#ans = [1, 2, 3, "+", "x", "*", "+", 4, "x", 2, "^", "*", "+"]
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ans = [4, 'x', 2, '^', '*', 2, 3, '+', 'x', '*', '+', 1, '+']
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self.assertEqual(ans, p.get_postfix())
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def test_reduce_nilpo(self):
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p = Polynom([1, 2, 3])
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self.assertEqual(p, p.reduce()[-1])
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def test_reduce(self):
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p = Polynom([1, [2, 3], 4])
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reducted = Polynom([1, 5, 4])
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self.assertEqual(p.reduce()[-1],reducted)
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def test_add_int(self):
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p = Polynom([1, 2, 3])
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q = (p + 2)[-1]
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self.assertEqual(q, Polynom([3, 2, 3]))
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def test_add_frac(self):
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p = Polynom([1, 2, 3])
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f = Fraction(1, 2)
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q = (p + f)[-1]
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self.assertEqual(q, Polynom([Fraction(3, 2), 2, 3]))
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def test_add_poly(self):
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p = Polynom([1, 0, 3])
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q = Polynom([0, 2, 3])
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r = (p + q)[-1]
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self.assertEqual(r, Polynom([1, 2, 6]))
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def test_radd_int(self):
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pass
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def test_radd_frac(self):
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pass
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def test_radd_poly(self):
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pass
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def test_mul_int(self):
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pass
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def test_mul_frac(self):
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pass
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def test_mul_poly(self):
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pass
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def test_rmul_int(self):
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pass
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def test_rmul_frac(self):
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pass
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def test_rmul_poly(self):
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pass
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if __name__ == '__main__':
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unittest.main()
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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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