755 lines
24 KiB
Python
755 lines
24 KiB
Python
#!/usr/bin/env python
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# encoding: utf-8
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from .explicable import Explicable
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from .expression import Expression
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from .step import Step
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from .renderable import Renderable
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from .operator import op
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from .generic import spe_zip, isNumber, transpose_fill, flatten_list, isPolynom, postfix_op
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from functools import wraps
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def power_cache(fun):
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"""Decorator which cache calculated powers of polynoms """
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cache = {}
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@wraps(fun)
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def cached_fun(self, power):
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if (tuple(self._coef), power) in cache.keys():
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return cache[(tuple(self._coef), power)]
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else:
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poly_powered = fun(self, power)
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cache[(tuple(self._coef), power)] = poly_powered
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return poly_powered
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return cached_fun
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class AbstractPolynom(Explicable):
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"""The mathematic definition of a polynom. It will be the parent class of Polynom (classical polynoms) and later of SquareRoot polynoms"""
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def __init__(self, coefs=[1], letter="x", name="P"):
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"""Initiate the polynom
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:param coef: coefficients of the polynom (ascending degree sorted)
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3 possibles type of coefficent:
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- a : simple "number". [1,2] designate 1 + 2x
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- [a,b,c]: list of coeficient for same degree. [1,[2,3],4] designate 1 + 2x + 3x + 4x^2
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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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:param name: Name of the polynom
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>>> P = AbstractPolynom([1, 2, 3])
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>>> P.mainOp
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+
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>>> P.name
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'P'
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>>> P._letter
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'x'
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>>> AbstractPolynom([1]).mainOp
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*
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>>> AbstractPolynom([0, 0, 3]).mainOp
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*
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>>> AbstractPolynom([1, 2, 3])._letter
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'x'
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>>> AbstractPolynom([1, 2, 3], "y")._letter
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'y'
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>>> AbstractPolynom([1, 2, 3], name = "Q").name
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'Q'
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"""
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try:
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# Remove 0 at the end of the coefs
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while coefs[-1] == 0:
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coefs = coefs[:-1]
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except IndexError:
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pass
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if coefs == []:
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coefs = [0]
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self.feed_coef(coefs)
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self._letter = letter
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self.name = name
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if self.is_monom():
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self.mainOp = op.mul
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else:
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self.mainOp = op.add
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self._isPolynom = 1
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pstf_tokens = self.compute_postfix_tokens()
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super(AbstractPolynom, self).__init__(pstf_tokens)
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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 isinstance(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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@property
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def 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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>>> AbstractPolynom([1, 2, 3]).degree
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2
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>>> AbstractPolynom([1]).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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>>> AbstractPolynom([1, 2, 3]).is_monom()
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0
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>>> AbstractPolynom([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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else:
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return 0
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def give_name(self, name):
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self.name = name
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def __str__(self):
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return str(Expression(self.postfix_tokens))
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def __repr__(self):
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return "< {cls} {letter} {coefs}>".format(
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cls = str(self.__class__).split('.')[-1][:-2],
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letter = str(self._letter),
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coefs = 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 postfix list)
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:param i: power
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:returns: postfix tokens of coef
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>>> p = AbstractPolynom()
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>>> p.coef_postfix([3],2)
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[3, 'x', 2, ^, *]
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>>> p.coef_postfix([0],1)
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[]
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>>> p.coef_postfix([3],0)
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[3]
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>>> p.coef_postfix([3],1)
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[3, 'x', *]
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>>> p.coef_postfix([1],1)
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['x']
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>>> p.coef_postfix([1],2)
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['x', 2, ^]
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"""
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if a == [0]:
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ans = []
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elif i == 0:
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ans = a
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elif i == 1:
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ans = a * (a not in [[1], [-1]]) + \
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[self._letter] + \
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[op.mul] * (a not in [[1], [-1]]) + \
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[op.sub1] * (a == [-1])
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else:
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ans = a * (a not in [[1], [-1]]) + \
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[self._letter, i, op.pw] + \
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[op.mul] * (a not in [[1], [-1]]) + \
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[op.sub1] * (a == [-1])
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return ans
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def coefs_postifx(self):
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""" Return list of postfix coef with the the right power letter
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>>> p = AbstractPolynom([1, 2])
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>>> p.coefs_postifx()
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[[1], [2, 'x', *]]
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>>> p = AbstractPolynom([1, -2])
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>>> p.coefs_postifx()
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[[1], [-2, 'x', *]]
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>>> p = AbstractPolynom([1,2,3])
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>>> p.coefs_postifx()
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[[1], [2, 'x', *], [3, 'x', 2, ^, *]]
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>>> p = AbstractPolynom([1])
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>>> p.coefs_postifx()
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[[1]]
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>>> p = AbstractPolynom([0])
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>>> p.coefs_postifx()
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[[0]]
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>>> p = AbstractPolynom([0, 1, 1, 0])
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>>> p.coefs_postifx()
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[['x'], ['x', 2, ^]]
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>>> p = AbstractPolynom([1,[2,3]])
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>>> p.coefs_postifx()
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[[1], [3, 'x', *], [2, 'x', *]]
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>>> p = AbstractPolynom([1,[2,-3]])
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>>> p.coefs_postifx()
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[[1], [-3, 'x', *], [2, 'x', *]]
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>>> p = AbstractPolynom([1,[-2,-3]])
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>>> p.coefs_postifx()
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[[1], [-3, 'x', *], [-2, 'x', *]]
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>>> p = AbstractPolynom([1,[-2,0]])
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>>> p.coefs_postifx()
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[[1], [-2, 'x', *]]
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>>> from mapytex.calculus.expression import Expression
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>>> from mapytex.calculus.operator import op
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>>> e = Expression([2,3,op.add])
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>>> p = AbstractPolynom([1,e])
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>>> p.coefs_postifx()
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[[1], [2, 3, +, 'x', *]]
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"""
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if not [i for i in self._coef if i!= 0]:
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return [[0]]
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raw_coefs = []
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for (pw, coef) in enumerate(self._coef):
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if isinstance(coef, list):
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for c in coef[::-1]:
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try:
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raw_coefs.append(self.coef_postfix(c.postfix_tokens, pw))
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except AttributeError:
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raw_coefs.append(self.coef_postfix([c], pw))
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elif coef != 0:
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try:
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raw_coefs.append(self.coef_postfix(coef.postfix_tokens, pw))
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except AttributeError:
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raw_coefs.append(self.coef_postfix([coef], pw))
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return [i for i in raw_coefs if i != []]
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def compute_postfix_tokens(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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>>> p = AbstractPolynom([1, 2])
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>>> p.postfix_tokens
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[2, 'x', *, 1, +]
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>>> p = AbstractPolynom([1, -2])
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>>> p.postfix_tokens
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[-2, 'x', *, 1, +]
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>>> p = AbstractPolynom([1,2,3])
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>>> p.postfix_tokens
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[3, 'x', 2, ^, *, 2, 'x', *, +, 1, +]
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>>> p = AbstractPolynom([1])
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>>> p.postfix_tokens
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[1]
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>>> p = AbstractPolynom([0])
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>>> p.postfix_tokens
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[0]
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>>> p = AbstractPolynom([1,[2,3]])
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>>> p.postfix_tokens
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[2, 'x', *, 3, 'x', *, +, 1, +]
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>>> p = AbstractPolynom([1,[2,-3]])
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>>> p.postfix_tokens
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[2, 'x', *, -3, 'x', *, +, 1, +]
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>>> p = AbstractPolynom([1,[-2,-3]])
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>>> p.postfix_tokens
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[-2, 'x', *, -3, 'x', *, +, 1, +]
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>>> from mapytex.calculus.expression import Expression
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>>> from mapytex.calculus.operator import op
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>>> e = Expression([2,3,op.add])
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>>> p = AbstractPolynom([1,e])
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>>> p.postfix_tokens
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[2, 3, +, 'x', *, 1, +]
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"""
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raw_coefs = self.coefs_postifx()
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pstfx = postfix_op(raw_coefs[::-1], op.add)
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return flatten_list(pstfx)
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def conv2poly(self, other):
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"""Convert anything number into a polynom
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>>> P = AbstractPolynom([1,2,3])
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>>> P.conv2poly(1)
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< AbstractPolynom x [1]>
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>>> P.conv2poly(0)
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< AbstractPolynom x [0]>
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>>> Q = AbstractPolynom([3, 2, 1], 'x')
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>>> P.conv2poly(Q)
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< AbstractPolynom x [3, 2, 1]>
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>>> Q = AbstractPolynom([3, 2, 1], 'y')
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>>> P.conv2poly(Q)
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< AbstractPolynom x [< AbstractPolynom y [3, 2, 1]>]>
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"""
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if (isNumber(other) and not isPolynom(other)) or \
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(isPolynom(other) and self._letter != other._letter):
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#ans = self.__class__([other], letter=self._letter)
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ans = AbstractPolynom([other], letter=self._letter)
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ans.steal_history(other)
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return ans
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elif isPolynom(other):
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return other
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else:
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raise ValueError(
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type(other) +
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" can't be converted into a polynom"
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)
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def reduce(self):
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"""Compute coefficients which have same degree
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:returns: new AbstractPolynom with numbers coefficients
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>>> P = AbstractPolynom([1,2,3])
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>>> Q = P.reduce()
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>>> Q
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< AbstractPolynom x [1, 2, 3]>
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>>> Q.steps
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[< Step [3, 'x', 2, ^, *, 2, 'x', *, +, 1, +]>, < Step [3, 'x', 2, ^, *, 2, 'x', *, +, 1, +]>]
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>>> P = AbstractPolynom([[1,2], [3,4,5], 6])
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>>> Q = P.reduce()
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>>> Q
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< AbstractPolynom x [3, 12, 6]>
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>>> for i in Q.explain():
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... print(i)
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6 x^{ 2 } + 3 x + 4 x + 5 x + 1 + 2
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6 x^{ 2 } + ( 3 + 4 + 5 ) x + 1 + 2
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6 x^{ 2 } + ( 7 + 5 ) x + 3
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6 x^{ 2 } + 12 x + 3
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>>> Q.steps
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[< Step [6, 'x', 2, ^, *, 3, 'x', *, +, 4, 'x', *, +, 5, 'x', *, +, 1, +, 2, +]>, < Step [6, 'x', 2, ^, *, 3, 4, +, 5, +, 'x', *, +, 1, 2, +, +]>, < Step [6, 'x', 2, ^, *, 7, 5, +, 'x', *, +, 3, +]>, < Step [6, 'x', 2, ^, *, 12, 'x', *, +, 3, +]>]
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>>> P = AbstractPolynom([[1,2], [3,4,5], 6], 'y')
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>>> Q = P.reduce()
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>>> Q
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< AbstractPolynom y [3, 12, 6]>
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>>> for i in Q.explain():
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... print(i)
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6 y^{ 2 } + 3 y + 4 y + 5 y + 1 + 2
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6 y^{ 2 } + ( 3 + 4 + 5 ) y + 1 + 2
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6 y^{ 2 } + ( 7 + 5 ) y + 3
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6 y^{ 2 } + 12 y + 3
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>>> P = AbstractPolynom([1,2])
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>>> Q = AbstractPolynom([P,3], 'y')
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>>> Q
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< AbstractPolynom y [< AbstractPolynom x [1, 2]>, 3]>
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>>> Q = Q.reduce()
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>>> for i in Q.explain():
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... print(i)
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3 y + 2 x + 1
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>>> P = AbstractPolynom([1,2])
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>>> Q = AbstractPolynom([[P,1],3], 'y')
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>>> Q
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< AbstractPolynom y [[< AbstractPolynom x [1, 2]>, 1], 3]>
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>>> Q = Q.reduce()
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>>> for i in Q.explain():
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... print(i)
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3 y + 2 x + 1 + 1
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3 y + 2 x + 2
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"""
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smpl_coef = []
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for coef in self._coef:
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if isinstance(coef, list):
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coef_exp = AbstractPolynom.smpl_coef_list(coef)
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else:
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try:
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coef_exp = coef.simplify()
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except AttributeError:
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coef_exp = coef
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smpl_coef.append(coef_exp)
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ans = AbstractPolynom(smpl_coef, self._letter)
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ini_step = [Step(self)]
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for s in Explicable.merge_history(smpl_coef):
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ini_step.append(Step(AbstractPolynom(s, self._letter)))
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ans.this_append_before(
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ini_step
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#AbstractPolynom(s)
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#for s in Expression.develop_steps(smpl_coef)
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)
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return ans
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def simplify(self):
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"""Same as reduce """
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if isNumber(self._letter):
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return self.replace_letter(self._letter).simplify()
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return self.reduce()
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@classmethod
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def smpl_coef_list(cls, coef_list):
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""" Simplify the coef when it is a list
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:param coef_list: the list discribing the coef
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:returns: the simplify coef
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>>> c = AbstractPolynom.smpl_coef_list([1, 2, 3])
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>>> c
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6
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>>> c.steps
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[< Step [1, 2, +, 3, +]>, < Step [1, 2, +, 3, +]>, < Step [3, 3, +]>, < Step [3, 3, +]>, < Step [6]>]
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>>> c = AbstractPolynom.smpl_coef_list([Expression('2*2'), 3])
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>>> c
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7
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>>> c.steps
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[< Step [2, 2, *, 3, +]>, < Step [4, 3, +]>, < Step [4, 3, +]>, < Step [7]>]
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>>> c = AbstractPolynom.smpl_coef_list([0, 2, 0])
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>>> c
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2
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>>> c.steps
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[< Step [2]>]
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"""
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# Simplify each element before adding them
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smpl_elem = []
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for c in coef_list:
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try:
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smpl_c = c.simplify()
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except AttributeError:
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smpl_c = c
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smpl_elem.append(smpl_c)
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pstfx_add = postfix_op(
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[i for i in smpl_elem if i != 0],
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op.add
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)
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steps = Expression.develop_steps(pstfx_add)
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ans = Expression(pstfx_add).simplify()
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ans.this_append_before(steps)
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return ans
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def replace_letter(self, letter):
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r""" Replace the letter in the expression
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:param letter: the new letter.
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:returns: The expression with the new letter.
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>>> A = AbstractPolynom([1, 2])
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>>> A
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< AbstractPolynom x [1, 2]>
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>>> B = A.replace_letter("y")
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>>> B
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< Expression [2, < Polynom y [0, 1]>, *, 1, +]>
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>>> C = A.replace_letter(2)
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>>> C
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< Expression [2, 2, *, 1, +]>
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>>> e = Expression('2+3').simplify()
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>>> D = A.replace_letter(e)
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>>> D
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< Expression [2, 5, *, 1, +]>
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>>> for i in D.explain():
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... print(i)
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2 ( 2 + 3 ) + 1
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2 \times 5 + 1
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"""
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exp_to_replace = Expression(letter)
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exp_to_replace.steal_history(letter)
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postfix_exp = [
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exp_to_replace if i == self._letter
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else i
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for i in self.postfix_tokens
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]
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ini_step = Expression.develop_steps(postfix_exp)
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ans = Expression(postfix_exp)
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ans.this_append_before(ini_step)
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return ans
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def __eq__(self, other):
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try:
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o_poly = self.conv2poly(other)
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return self._coef == o_poly._coef
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except TypeError:
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return 0
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def __add__(self, other):
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""" Overload +
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>>> P = AbstractPolynom([1,2,3])
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>>> Q = AbstractPolynom([4,5])
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>>> R = P+Q
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>>> R
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< AbstractPolynom x [5, 7, 3]>
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>>> for i in R.explain():
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... print(i)
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3 x^{ 2 } + 2 x + 1 + 5 x + 4
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3 x^{ 2 } + 2 x + 5 x + 1 + 4
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3 x^{ 2 } + ( 2 + 5 ) x + 1 + 4
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3 x^{ 2 } + 7 x + 5
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>>> R.steps
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[< Step [3, 'x', 2, ^, *, 2, 'x', *, +, 1, +, 5, 'x', *, 4, +, +]>, < Step [3, 'x', 2, ^, *, 2, 'x', *, +, 5, 'x', *, +, 1, +, 4, +]>, < Step [3, 'x', 2, ^, *, 2, 5, +, 'x', *, +, 1, 4, +, +]>, < Step [3, 'x', 2, ^, *, 7, 'x', *, +, 5, +]>]
|
|
>>> Q = AbstractPolynom([4,5], letter = 'y')
|
|
>>> R = P+Q
|
|
>>> R
|
|
< AbstractPolynom x [< AbstractPolynom y [5, 5]>, 2, 3]>
|
|
>>> for i in R.explain():
|
|
... print(i)
|
|
3 x^{ 2 } + 2 x + 1 + 5 y + 4
|
|
3 x^{ 2 } + 2 x + 5 y + 1 + 4
|
|
3 x^{ 2 } + 2 x + 5 y + 5
|
|
|
|
"""
|
|
o_poly = self.conv2poly(other)
|
|
|
|
n_coef = spe_zip(self._coef, o_poly._coef)
|
|
p = AbstractPolynom(n_coef, letter=self._letter)
|
|
|
|
ini_step = [Step([self, o_poly, op.add])]
|
|
|
|
ans = p.simplify()
|
|
ans.this_append_before(ini_step)
|
|
return ans
|
|
|
|
def __radd__(self, other):
|
|
o_poly = self.conv2poly(other)
|
|
return o_poly.__add__(self)
|
|
|
|
def __neg__(self):
|
|
""" overload - (as arity 1 operator)
|
|
|
|
>>> P = AbstractPolynom([1,2,3])
|
|
>>> Q = -P
|
|
>>> Q
|
|
< AbstractPolynom x [-1, -2, -3]>
|
|
>>> for i in Q.explain():
|
|
... print(i)
|
|
- ( 3 x^{ 2 } + 2 x + 1 )
|
|
-3 x^{ 2 } - 2 x - 1
|
|
>>> Q.steps
|
|
[< Step [3, 'x', 2, ^, *, 2, 'x', *, +, 1, +, -]>, < Step [-3, 'x', 2, ^, *, -2, 'x', *, +, -1, +]>, < Step [-3, 'x', 2, ^, *, -2, 'x', *, +, -1, +]>]
|
|
"""
|
|
ini_step = [Step(self.postfix_tokens + [op.sub1])]
|
|
ans = AbstractPolynom([-i for i in self._coef],
|
|
letter=self._letter).simplify()
|
|
ans.this_append_before(ini_step)
|
|
return ans
|
|
|
|
def __sub__(self, other):
|
|
""" overload -
|
|
|
|
>>> P = AbstractPolynom([1,2,3])
|
|
>>> Q = AbstractPolynom([4,5,6])
|
|
>>> R = P - Q
|
|
>>> R
|
|
< AbstractPolynom x [-3, -3, -3]>
|
|
>>> for i in R.explain():
|
|
... print(i)
|
|
3 x^{ 2 } + 2 x + 1 - ( 6 x^{ 2 } + 5 x + 4 )
|
|
3 x^{ 2 } + 2 x + 1 - 6 x^{ 2 } - 5 x - 4
|
|
3 x^{ 2 } - 6 x^{ 2 } + 2 x - 5 x + 1 - 4
|
|
( 3 - 6 ) x^{ 2 } + ( 2 - 5 ) x + 1 - 4
|
|
-3 x^{ 2 } - 3 x - 3
|
|
>>> R.steps
|
|
[< Step [3, 'x', 2, ^, *, 2, 'x', *, +, 1, +, 6, 'x', 2, ^, *, 5, 'x', *, +, 4, +, -]>, < Step [3, 'x', 2, ^, *, 2, 'x', *, +, 1, +, -6, 'x', 2, ^, *, -5, 'x', *, +, -4, +, +]>, < Step [3, 'x', 2, ^, *, -6, 'x', 2, ^, *, +, 2, 'x', *, +, -5, 'x', *, +, 1, +, -4, +]>, < Step [3, -6, +, 'x', 2, ^, *, 2, -5, +, 'x', *, +, 1, -4, +, +]>, < Step [-3, 'x', 2, ^, *, -3, 'x', *, +, -3, +]>]
|
|
"""
|
|
o_poly = self.conv2poly(other)
|
|
ini_step = [Step(self.postfix_tokens +
|
|
o_poly.postfix_tokens + [op.sub])]
|
|
o_poly = -o_poly
|
|
|
|
ans = self + o_poly
|
|
ans.this_append_before(ini_step)
|
|
|
|
return ans
|
|
|
|
def __rsub__(self, other):
|
|
o_poly = self.conv2poly(other)
|
|
|
|
return o_poly.__sub__(self)
|
|
|
|
def __mul__(self, other):
|
|
r""" Overload *
|
|
|
|
>>> p = AbstractPolynom([1,2])
|
|
>>> p*3
|
|
< AbstractPolynom x [3, 6]>
|
|
>>> for i in (p*3).explain():
|
|
... print(i)
|
|
( 2 x + 1 ) \times 3
|
|
2 \times 3 x + 3
|
|
6 x + 3
|
|
>>> (p*3).steps
|
|
[< Step [2, 'x', *, 1, +, 3, *]>, < Step [2, 3, *, 'x', *, 3, +]>, < Step [2, 3, *, 'x', *, 3, +]>, < Step [6, 'x', *, 3, +]>]
|
|
>>> q = AbstractPolynom([0,0,4])
|
|
>>> q*3
|
|
< AbstractPolynom x [0, 0, 12]>
|
|
>>> for i in (q*3).explain():
|
|
... print(i)
|
|
4 x^{ 2 } \times 3
|
|
4 \times 3 x^{ 2 }
|
|
12 x^{ 2 }
|
|
>>> (q*3).steps
|
|
[< Step [4, 'x', 2, ^, *, 3, *]>, < Step [4, 3, *, 'x', 2, ^, *]>, < Step [4, 3, *, 'x', 2, ^, *]>, < Step [12, 'x', 2, ^, *]>]
|
|
>>> r = AbstractPolynom([0,1])
|
|
>>> r*3
|
|
< AbstractPolynom x [0, 3]>
|
|
>>> (r*3).steps
|
|
[< Step ['x', 3, *]>, < Step [3, 'x', *]>, < Step [3, 'x', *]>]
|
|
>>> p*q
|
|
< AbstractPolynom x [0, 0, 4, 8]>
|
|
>>> (p*q).steps
|
|
[< Step [2, 'x', *, 1, +, 4, 'x', 2, ^, *, *]>, < Step [2, 4, *, 'x', 3, ^, *, 4, 'x', 2, ^, *, +]>, < Step [2, 4, *, 'x', 3, ^, *, 4, 'x', 2, ^, *, +]>, < Step [8, 'x', 3, ^, *, 4, 'x', 2, ^, *, +]>]
|
|
>>> for i in (p*q).explain():
|
|
... print(i)
|
|
( 2 x + 1 ) \times 4 x^{ 2 }
|
|
2 \times 4 x^{ 3 } + 4 x^{ 2 }
|
|
8 x^{ 3 } + 4 x^{ 2 }
|
|
>>> p*r
|
|
< AbstractPolynom x [0, 1, 2]>
|
|
>>> P = AbstractPolynom([1,2,3])
|
|
>>> Q = AbstractPolynom([4,5,6])
|
|
>>> P*Q
|
|
< AbstractPolynom x [4, 13, 28, 27, 18]>
|
|
"""
|
|
o_poly = self.conv2poly(other)
|
|
|
|
coefs = [0] * (self.degree + o_poly.degree + 1)
|
|
for (i, a) in enumerate(self._coef):
|
|
for (j, b) in enumerate(o_poly._coef):
|
|
if a == 0 or b == 0:
|
|
elem = 0
|
|
elif a == 1:
|
|
elem = b
|
|
elif b == 1:
|
|
elem = a
|
|
else:
|
|
elem = Expression([a, b, op.mul])
|
|
|
|
if coefs[i + j] == 0:
|
|
coefs[i + j] = elem
|
|
elif elem != 0:
|
|
if isinstance(coefs[i + j], list):
|
|
coefs[i + j] += [elem]
|
|
else:
|
|
coefs[i + j] = [coefs[i + j], elem]
|
|
|
|
p = AbstractPolynom(coefs, letter=self._letter)
|
|
ini_step = [Step(self.postfix_tokens +
|
|
o_poly.postfix_tokens + [op.mul])]
|
|
ans = p.simplify()
|
|
|
|
ans.this_append_before(ini_step)
|
|
return ans
|
|
|
|
def __rmul__(self, other):
|
|
o_poly = self.conv2poly(other)
|
|
|
|
return o_poly.__mul__(self)
|
|
|
|
def __truediv__(self, other):
|
|
r""" Overload /
|
|
|
|
>>> P = AbstractPolynom([1, 2, 4])
|
|
>>> P / 2
|
|
< AbstractPolynom x [< Fraction 1 / 2>, 1, 2]>
|
|
>>> for i in (P/2).explain():
|
|
... print(i)
|
|
\frac{ 4 x^{ 2 } + 2 x + 1 }{ 2 }
|
|
\frac{ 4 }{ 2 } x^{ 2 } + \frac{ 2 }{ 2 } x + \frac{ 1 }{ 2 }
|
|
2 x^{ 2 } + x + \frac{ 1 }{ 2 }
|
|
|
|
|
|
"""
|
|
ans_coefs = [Expression([c, other, op.div]) if c != 0
|
|
else 0
|
|
for c in self._coef
|
|
]
|
|
|
|
ans = AbstractPolynom(ans_coefs, letter=self._letter)
|
|
ini_step = [Step(
|
|
self.postfix_tokens +
|
|
[other, op.div]
|
|
)]
|
|
|
|
ans = ans.simplify()
|
|
ans.this_append_before(ini_step)
|
|
return ans
|
|
|
|
@power_cache
|
|
def __pow__(self, power):
|
|
r""" Overload **
|
|
|
|
>>> p = AbstractPolynom([0,0,3])
|
|
>>> p**2
|
|
< AbstractPolynom x [0, 0, 0, 0, 9]>
|
|
>>> (p**2).steps
|
|
[< Step [3, 'x', 2, ^, *, 2, ^]>, < Step [3, 2, ^, 'x', 4, ^, *]>, < Step [3, 2, ^, 'x', 4, ^, *]>, < Step [9, 'x', 4, ^, *]>]
|
|
>>> for i in (p**2).explain():
|
|
... print(i)
|
|
( 3 x^{ 2 } )^{ 2 }
|
|
3^{ 2 } x^{ 4 }
|
|
9 x^{ 4 }
|
|
>>> p = AbstractPolynom([1,2])
|
|
>>> p**2
|
|
< AbstractPolynom x [1, 4, 4]>
|
|
>>> (p**2).steps
|
|
[< Step [2, 'x', *, 1, +, 2, ^]>, < Step [2, 'x', *, 1, +, 2, 'x', *, 1, +, *]>, < Step [2, 2, *, 'x', 2, ^, *, 2, 'x', *, +, 2, 'x', *, +, 1, +]>, < Step [2, 2, *, 'x', 2, ^, *, 2, 2, +, 'x', *, +, 1, +]>, < Step [4, 'x', 2, ^, *, 4, 'x', *, +, 1, +]>]
|
|
>>> for i in (p**2).explain():
|
|
... print(i)
|
|
( 2 x + 1 )^{ 2 }
|
|
( 2 x + 1 ) ( 2 x + 1 )
|
|
2 \times 2 x^{ 2 } + 2 x + 2 x + 1
|
|
2 \times 2 x^{ 2 } + ( 2 + 2 ) x + 1
|
|
4 x^{ 2 } + 4 x + 1
|
|
>>> p = AbstractPolynom([0,0,1])
|
|
>>> p**3
|
|
< AbstractPolynom x [0, 0, 0, 0, 0, 0, 1]>
|
|
>>> p = AbstractPolynom([1,2,3])
|
|
>>> p**2
|
|
< AbstractPolynom x [1, 4, 10, 12, 9]>
|
|
|
|
"""
|
|
if not type(power):
|
|
raise ValueError(
|
|
"Can't raise {obj} to {pw} power".format(
|
|
obj=self.__class__, pw=str(power)))
|
|
|
|
ini_step = [Step(self.postfix_tokens + [power, op.pw])]
|
|
|
|
if self.is_monom():
|
|
if self._coef[self.degree] == 1:
|
|
coefs = [0] * self.degree * power + [1]
|
|
p = AbstractPolynom(coefs, letter=self._letter)
|
|
ans = p
|
|
else:
|
|
coefs = [0] * self.degree * power + \
|
|
[Expression([self._coef[self.degree], power, op.pw])]
|
|
p = AbstractPolynom(coefs, letter=self._letter)
|
|
ans = p.simplify()
|
|
else:
|
|
if power == 2:
|
|
ans = self * self
|
|
else:
|
|
# TODO: faudrait changer ça c'est pas très sérieux |ven. févr.
|
|
# 27 22:08:00 CET 2015
|
|
raise AttributeError(
|
|
"__pw__ not implemented yet when power is greatter than 2")
|
|
|
|
ans.this_append_before(ini_step)
|
|
return ans
|
|
|
|
def __xor__(self, power):
|
|
return self.__pow__(power)
|
|
|
|
# -----------------------------
|
|
# Reglages pour 'vim'
|
|
# vim:set autoindent expandtab tabstop=4 shiftwidth=4:
|
|
# cursor: 16 del
|