603 lines
21 KiB
Python
603 lines
21 KiB
Python
#!/usr/bin/env python
|
|
# encoding: utf-8
|
|
|
|
from .explicable import Explicable
|
|
from .expression import Expression
|
|
from .operator import op
|
|
from .generic import spe_zip, expand_list, isNumber, transpose_fill, flatten_list, isPolynom, isNumerand, postfix_op
|
|
from .render import txt, tex
|
|
from functools import wraps
|
|
|
|
|
|
def power_cache(fun):
|
|
"""Decorator which cache calculated powers of polynoms """
|
|
cache = {}
|
|
|
|
@wraps(fun)
|
|
def cached_fun(self, power):
|
|
#print("cache -> ", cache)
|
|
if (tuple(self._coef), power) in cache.keys():
|
|
return cache[(tuple(self._coef), power)]
|
|
else:
|
|
poly_powered = fun(self, power)
|
|
cache[(tuple(self._coef), power)] = poly_powered
|
|
return poly_powered
|
|
return cached_fun
|
|
|
|
|
|
class AbstractPolynom(Explicable):
|
|
|
|
"""The mathematic definition of a polynom. It will be the parent class of Polynom (classical polynoms) and later of SquareRoot polynoms"""
|
|
|
|
def __init__(self, coefs=[1], letter="x", name="P"):
|
|
"""Initiate the polynom
|
|
|
|
:param coef: coefficients of the polynom (ascending degree sorted)
|
|
3 possibles type of coefficent:
|
|
- a : simple "number". [1,2] designate 1 + 2x
|
|
- [a,b,c]: list of coeficient for same degree. [1,[2,3],4] designate 1 + 2x + 3x + 4x^2
|
|
- a: a Expression. [1, Expression("2+3"), 4] designate 1 + (2+3)x + 4x^2
|
|
:param letter: the string describing the unknown
|
|
:param name: Name of the polynom
|
|
|
|
>>> P = AbstractPolynom([1, 2, 3])
|
|
>>> P.mainOp
|
|
+
|
|
>>> P.name
|
|
'P'
|
|
>>> P._letter
|
|
'x'
|
|
>>> AbstractPolynom([1]).mainOp
|
|
*
|
|
>>> AbstractPolynom([0, 0, 3]).mainOp
|
|
*
|
|
>>> AbstractPolynom([1, 2, 3])._letter
|
|
'x'
|
|
>>> AbstractPolynom([1, 2, 3], "y")._letter
|
|
'y'
|
|
>>> AbstractPolynom([1, 2, 3], name = "Q").name
|
|
'Q'
|
|
"""
|
|
super(AbstractPolynom, self).__init__()
|
|
|
|
try:
|
|
# Remove 0 at the end of the coefs
|
|
while coefs[-1] == 0:
|
|
coefs = coefs[:-1]
|
|
except IndexError:
|
|
pass
|
|
|
|
if coefs == []:
|
|
coefs = [0]
|
|
|
|
self.feed_coef(coefs)
|
|
self._letter = letter
|
|
self.name = name
|
|
|
|
if self.is_monom():
|
|
self.mainOp = op.mul
|
|
else:
|
|
self.mainOp = op.add
|
|
|
|
self._isPolynom = 1
|
|
|
|
def feed_coef(self, l_coef):
|
|
"""Feed coef of the polynom. Manage differently whether it's a number or an expression
|
|
|
|
:l_coef: list of coef
|
|
"""
|
|
self._coef = []
|
|
for coef in l_coef:
|
|
if isinstance(coef, list) and len(coef) == 1:
|
|
self._coef.append(coef[0])
|
|
else:
|
|
self._coef.append(coef)
|
|
|
|
@property
|
|
def degree(self):
|
|
"""Getting the degree fo the polynom
|
|
|
|
:returns: the degree of the polynom
|
|
|
|
>>> AbstractPolynom([1, 2, 3]).degree
|
|
2
|
|
>>> AbstractPolynom([1]).degree
|
|
0
|
|
"""
|
|
return len(self._coef) - 1
|
|
|
|
def is_monom(self):
|
|
"""is the polynom a monom (only one coefficent)
|
|
|
|
:returns: 1 if yes 0 otherwise
|
|
|
|
>>> AbstractPolynom([1, 2, 3]).is_monom()
|
|
0
|
|
>>> AbstractPolynom([1]).is_monom()
|
|
1
|
|
"""
|
|
if len([i for i in self._coef if i != 0]) == 1:
|
|
return 1
|
|
else:
|
|
return 0
|
|
|
|
def give_name(self, name):
|
|
self.name = name
|
|
|
|
def __str__(self):
|
|
return str(Expression(self.postfix_tokens))
|
|
|
|
def __repr__(self):
|
|
return "< " + str(self.__class__) + " " + str(self._coef) + ">"
|
|
|
|
def coef_postfix(self, a, i):
|
|
"""Return the postfix display of a coeficient
|
|
|
|
:param a: value for the coeficient (/!\ as a postfix list)
|
|
:param i: power
|
|
:returns: postfix tokens of coef
|
|
|
|
>>> p = AbstractPolynom()
|
|
>>> p.coef_postfix([3],2)
|
|
[3, 'x', 2, ^, *]
|
|
>>> p.coef_postfix([0],1)
|
|
[]
|
|
>>> p.coef_postfix([3],0)
|
|
[3]
|
|
>>> p.coef_postfix([3],1)
|
|
[3, 'x', *]
|
|
>>> p.coef_postfix([1],1)
|
|
['x']
|
|
>>> p.coef_postfix([1],2)
|
|
['x', 2, ^]
|
|
|
|
"""
|
|
ans = []
|
|
if a == [0]:
|
|
pass
|
|
elif i == 0:
|
|
ans = a
|
|
elif i == 1:
|
|
ans = a * (a != [1]) + [self._letter] + [op.mul] * (a != [1])
|
|
else:
|
|
ans = a * (a != [1]) + [self._letter, i,
|
|
op.pw] + [op.mul] * (a != [1])
|
|
|
|
return ans
|
|
|
|
@property
|
|
def postfix_tokens(self):
|
|
"""Return the postfix form of the polynom
|
|
|
|
:returns: the postfix list of polynom's tokens
|
|
|
|
>>> p = AbstractPolynom([1, 2])
|
|
>>> p.postfix_tokens
|
|
[2, 'x', *, 1, +]
|
|
>>> p = AbstractPolynom([1, -2])
|
|
>>> p.postfix_tokens
|
|
[2, 'x', *, -, 1, +]
|
|
>>> p = AbstractPolynom([1,2,3])
|
|
>>> p.postfix_tokens
|
|
[3, 'x', 2, ^, *, 2, 'x', *, +, 1, +]
|
|
>>> p = AbstractPolynom([1])
|
|
>>> p.postfix_tokens
|
|
[1]
|
|
>>> p = AbstractPolynom([0])
|
|
>>> p.postfix_tokens
|
|
[0]
|
|
>>> p = AbstractPolynom([1,[2,3]])
|
|
>>> p.postfix_tokens
|
|
[2, 'x', *, 3, 'x', *, +, 1, +]
|
|
>>> p = AbstractPolynom([1,[2,-3]])
|
|
>>> p.postfix_tokens
|
|
[2, 'x', *, 3, 'x', *, -, 1, +]
|
|
>>> p = AbstractPolynom([1,[-2,-3]])
|
|
>>> p.postfix_tokens
|
|
[2, 'x', *, -, 3, 'x', *, -, 1, +]
|
|
>>> from pymath.calculus.expression import Expression
|
|
>>> from pymath.calculus.operator import op
|
|
>>> e = Expression([2,3,op.add])
|
|
>>> p = AbstractPolynom([1,e])
|
|
>>> p.postfix_tokens
|
|
[2, 3, +, 'x', *, 1, +]
|
|
|
|
"""
|
|
if self == 0:
|
|
return [0]
|
|
# TODO: Faudrait factoriser un peu tout ça..! |dim. déc. 21 16:02:34
|
|
# CET 2014
|
|
postfix = []
|
|
for (i, a) in list(enumerate(self._coef))[::-1]:
|
|
operator = [op.add]
|
|
operator_sub1 = []
|
|
if isinstance(a, Expression):
|
|
# case coef is an arithmetic expression
|
|
c = self.coef_postfix(a.postfix_tokens, i)
|
|
if c != []:
|
|
postfix.append(c)
|
|
if len(postfix) > 1:
|
|
postfix += operator
|
|
|
|
elif isinstance(a, list):
|
|
# case need to repeat the x^i
|
|
for b in a:
|
|
operator = [op.add]
|
|
operator_sub1 = []
|
|
if len(postfix) == 0 and isNumber(b) and b < 0:
|
|
try:
|
|
b = [(-b)[-1]]
|
|
except TypeError:
|
|
b = [-b]
|
|
operator_sub1 = [op.sub1]
|
|
elif len(postfix) > 0 and isNumber(b) and b < 0:
|
|
try:
|
|
b = [(-b)[-1]]
|
|
except TypeError:
|
|
b = [-b]
|
|
operator = [op.sub]
|
|
else:
|
|
b = [b]
|
|
c = self.coef_postfix(b, i)
|
|
if c != []:
|
|
postfix.append(c)
|
|
if len(postfix) > 1:
|
|
postfix += operator_sub1
|
|
postfix += operator
|
|
postfix += operator_sub1
|
|
|
|
elif a != 0:
|
|
if len(postfix) == 0 and a < 0:
|
|
try:
|
|
a = [(-a)[-1]]
|
|
except TypeError:
|
|
a = [-a]
|
|
operator_sub1 = [op.sub1]
|
|
elif len(postfix) > 0 and a < 0:
|
|
try:
|
|
a = [(-a)[-1]]
|
|
except TypeError:
|
|
a = [-a]
|
|
operator = [op.sub]
|
|
else:
|
|
a = [a]
|
|
|
|
c = self.coef_postfix(a, i)
|
|
if c != []:
|
|
postfix.append(c)
|
|
if len(postfix) > 1:
|
|
postfix += operator_sub1
|
|
postfix += operator
|
|
postfix += operator_sub1
|
|
|
|
return flatten_list(postfix)
|
|
|
|
def conv2poly(self, other):
|
|
"""Convert anything number into a polynom
|
|
|
|
>>> P = AbstractPolynom([1,2,3])
|
|
>>> P.conv2poly(1)
|
|
< <class 'pymath.calculus.abstract_polynom.AbstractPolynom'> [1]>
|
|
>>> P.conv2poly(0)
|
|
< <class 'pymath.calculus.abstract_polynom.AbstractPolynom'> [0]>
|
|
|
|
"""
|
|
if isNumber(other) and not isPolynom(other):
|
|
return AbstractPolynom([other], letter=self._letter)
|
|
elif isPolynom(other):
|
|
return other
|
|
else:
|
|
raise ValueError(type(other) +
|
|
" can't be converted into a polynom")
|
|
|
|
def reduce(self):
|
|
"""Compute coefficients which have same degree
|
|
|
|
:returns: new AbstractPolynom with numbers coefficients
|
|
|
|
>>> P = AbstractPolynom([1,2,3])
|
|
>>> Q = P.reduce()
|
|
>>> Q
|
|
< <class 'pymath.calculus.abstract_polynom.AbstractPolynom'> [1, 2, 3]>
|
|
>>> Q.steps
|
|
[]
|
|
>>> P = AbstractPolynom([[1,2], [3,4,5], 6])
|
|
>>> Q = P.reduce()
|
|
>>> Q
|
|
< <class 'pymath.calculus.abstract_polynom.AbstractPolynom'> [3, 12, 6]>
|
|
>>> for i in Q.explain():
|
|
... print(i)
|
|
6 x^{ 2 } + 3 x + 4 x + 5 x + 1 + 2
|
|
6 x^{ 2 } + ( 3 + 4 + 5 ) x + 1 + 2
|
|
6 x^{ 2 } + ( 7 + 5 ) x + 3
|
|
6 x^{ 2 } + 12 x + 3
|
|
>>> Q.steps
|
|
[< <class 'pymath.calculus.abstract_polynom.AbstractPolynom'> [[1, 2], [3, 4, 5], 6]>, < <class 'pymath.calculus.abstract_polynom.AbstractPolynom'> [< <class 'pymath.calculus.expression.Expression'> [1, 2, +] >, < <class 'pymath.calculus.expression.Expression'> [3, 4, +, 5, +] >, 6]>, < <class 'pymath.calculus.abstract_polynom.AbstractPolynom'> [3, < <class 'pymath.calculus.expression.Expression'> [7, 5, +] >, 6]>]
|
|
"""
|
|
|
|
# TODO: It doesn't not compute quick enough |ven. févr. 27 18:04:01 CET
|
|
# 2015
|
|
|
|
# gather steps for every coefficients
|
|
coefs_steps = []
|
|
for coef in self._coef:
|
|
coef_steps = []
|
|
|
|
if isinstance(coef, list):
|
|
# Simplify each element before adding them
|
|
s = []
|
|
for c in coef:
|
|
try:
|
|
with Expression.tmp_render():
|
|
s.append(list(c.simplify().explain()))
|
|
except AttributeError:
|
|
s.append([c])
|
|
|
|
s = list(transpose_fill(s))
|
|
|
|
last = s[-1]
|
|
coef_steps += s
|
|
|
|
# Convert last element into postfix addition.
|
|
postfix_add = postfix_op([i for i in last if i != 0], op.add)
|
|
# Convert it to an expression
|
|
coef_exp = Expression(postfix_add)
|
|
|
|
with Expression.tmp_render():
|
|
coef_steps += list(coef_exp.simplify().explain())
|
|
|
|
#print('\t 1.coef_steps -> ', coef_steps)
|
|
|
|
else:
|
|
try:
|
|
with Expression.tmp_render():
|
|
coef_steps += coef.simplify().explain()
|
|
except AttributeError:
|
|
coef_steps = [coef]
|
|
|
|
#print('\t 3.coef_steps -> ', coef_steps)
|
|
# On ajoute toutes ces étapes
|
|
coefs_steps.append(coef_steps)
|
|
|
|
#print('\t coefs_steps -> ', coefs_steps)
|
|
|
|
# On retourne la matrice
|
|
steps = []
|
|
for coefs in transpose_fill(coefs_steps):
|
|
steps.append(AbstractPolynom(coefs, self._letter))
|
|
|
|
ans, steps = steps[-1], steps[:-1]
|
|
ans.this_append_before(steps)
|
|
|
|
return ans
|
|
|
|
def simplify(self):
|
|
"""Same as reduce """
|
|
return self.reduce()
|
|
|
|
def __eq__(self, other):
|
|
try:
|
|
o_poly = self.conv2poly(other)
|
|
return self._coef == o_poly._coef
|
|
except TypeError:
|
|
return 0
|
|
|
|
def __add__(self, other):
|
|
""" Overload +
|
|
|
|
>>> P = AbstractPolynom([1,2,3])
|
|
>>> Q = AbstractPolynom([4,5])
|
|
>>> R = P+Q
|
|
>>> R
|
|
< <class 'pymath.calculus.abstract_polynom.AbstractPolynom'> [5, 7, 3]>
|
|
>>> for i in R.explain():
|
|
... print(i)
|
|
3 x^{ 2 } + 2 x + 1 + 5 x + 4
|
|
3 x^{ 2 } + 2 x + 5 x + 1 + 4
|
|
3 x^{ 2 } + ( 2 + 5 ) x + 1 + 4
|
|
3 x^{ 2 } + 7 x + 5
|
|
>>> R.steps
|
|
[< <class 'pymath.calculus.expression.Expression'> [3, 'x', 2, ^, *, 2, 'x', *, +, 1, +, 5, 'x', *, 4, +, +] >, < <class 'pymath.calculus.abstract_polynom.AbstractPolynom'> [[1, 4], [2, 5], 3]>, < <class 'pymath.calculus.abstract_polynom.AbstractPolynom'> [< <class 'pymath.calculus.expression.Expression'> [1, 4, +] >, < <class 'pymath.calculus.expression.Expression'> [2, 5, +] >, 3]>]
|
|
"""
|
|
o_poly = self.conv2poly(other)
|
|
|
|
n_coef = spe_zip(self._coef, o_poly._coef)
|
|
p = AbstractPolynom(n_coef, letter=self._letter)
|
|
|
|
ini_step = [Expression(self.postfix_tokens +
|
|
o_poly.postfix_tokens + [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
|
|
< <class 'pymath.calculus.abstract_polynom.AbstractPolynom'> [-1, -2, -3]>
|
|
>>> Q.steps
|
|
[< <class 'pymath.calculus.expression.Expression'> [3, 'x', 2, ^, *, 2, 'x', *, +, 1, +, -] >]
|
|
"""
|
|
ini_step = [Expression(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
|
|
< <class 'pymath.calculus.abstract_polynom.AbstractPolynom'> [-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
|
|
[< <class 'pymath.calculus.expression.Expression'> [3, 'x', 2, ^, *, 2, 'x', *, +, 1, +, 6, 'x', 2, ^, *, 5, 'x', *, +, 4, +, -] >, < <class 'pymath.calculus.expression.Expression'> [3, 'x', 2, ^, *, 2, 'x', *, +, 1, +, 6, 'x', 2, ^, *, -, 5, 'x', *, -, 4, -, +] >, < <class 'pymath.calculus.abstract_polynom.AbstractPolynom'> [[1, -4], [2, -5], [3, -6]]>, < <class 'pymath.calculus.abstract_polynom.AbstractPolynom'> [< <class 'pymath.calculus.expression.Expression'> [1, -4, +] >, < <class 'pymath.calculus.expression.Expression'> [2, -5, +] >, < <class 'pymath.calculus.expression.Expression'> [3, -6, +] >]>]
|
|
"""
|
|
o_poly = self.conv2poly(other)
|
|
ini_step = [Expression(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
|
|
< <class 'pymath.calculus.abstract_polynom.AbstractPolynom'> [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
|
|
[< <class 'pymath.calculus.expression.Expression'> [2, 'x', *, 1, +, 3, *] >, < <class 'pymath.calculus.abstract_polynom.AbstractPolynom'> [3, < <class 'pymath.calculus.expression.Expression'> [2, 3, *] >]>]
|
|
>>> q = AbstractPolynom([0,0,4])
|
|
>>> q*3
|
|
< <class 'pymath.calculus.abstract_polynom.AbstractPolynom'> [0, 0, 12]>
|
|
>>> (q*3).steps
|
|
[< <class 'pymath.calculus.expression.Expression'> [4, 'x', 2, ^, *, 3, *] >, < <class 'pymath.calculus.abstract_polynom.AbstractPolynom'> [0, 0, < <class 'pymath.calculus.expression.Expression'> [4, 3, *] >]>]
|
|
>>> r = AbstractPolynom([0,1])
|
|
>>> r*3
|
|
< <class 'pymath.calculus.abstract_polynom.AbstractPolynom'> [0, 3]>
|
|
>>> (r*3).steps
|
|
[< <class 'pymath.calculus.expression.Expression'> ['x', 3, *] >]
|
|
>>> p*q
|
|
< <class 'pymath.calculus.abstract_polynom.AbstractPolynom'> [0, 0, 4, 8]>
|
|
>>> (p*q).steps
|
|
[< <class 'pymath.calculus.expression.Expression'> [2, 'x', *, 1, +, 4, 'x', 2, ^, *, *] >, < <class 'pymath.calculus.abstract_polynom.AbstractPolynom'> [0, 0, 4, < <class 'pymath.calculus.expression.Expression'> [2, 4, *] >]>]
|
|
>>> p*r
|
|
< <class 'pymath.calculus.abstract_polynom.AbstractPolynom'> [0, 1, 2]>
|
|
>>> P = AbstractPolynom([1,2,3])
|
|
>>> Q = AbstractPolynom([4,5,6])
|
|
>>> P*Q
|
|
< <class 'pymath.calculus.abstract_polynom.AbstractPolynom'> [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 = [Expression(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)
|
|
|
|
@power_cache
|
|
def __pow__(self, power):
|
|
""" Overload **
|
|
|
|
>>> p = AbstractPolynom([0,0,3])
|
|
>>> p**2
|
|
< <class 'pymath.calculus.abstract_polynom.AbstractPolynom'> [0, 0, 0, 0, 9]>
|
|
>>> (p**2).steps
|
|
[< <class 'pymath.calculus.expression.Expression'> [3, 'x', 2, ^, *, 2, ^] >, < <class 'pymath.calculus.abstract_polynom.AbstractPolynom'> [0, 0, 0, 0, < <class 'pymath.calculus.expression.Expression'> [3, 2, ^] >]>]
|
|
>>> p = AbstractPolynom([1,2])
|
|
>>> p**2
|
|
< <class 'pymath.calculus.abstract_polynom.AbstractPolynom'> [1, 4, 4]>
|
|
>>> (p**2).steps
|
|
[< <class 'pymath.calculus.expression.Expression'> [2, 'x', *, 1, +, 2, ^] >, < <class 'pymath.calculus.expression.Expression'> [2, 'x', *, 1, +, 2, 'x', *, 1, +, *] >, < <class 'pymath.calculus.abstract_polynom.AbstractPolynom'> [1, [2, 2], < <class 'pymath.calculus.expression.Expression'> [2, 2, *] >]>, < <class 'pymath.calculus.abstract_polynom.AbstractPolynom'> [1, < <class 'pymath.calculus.expression.Expression'> [2, 2, +] >, 4]>]
|
|
>>> p = AbstractPolynom([0,0,1])
|
|
>>> p**3
|
|
< <class 'pymath.calculus.abstract_polynom.AbstractPolynom'> [0, 0, 0, 0, 0, 0, 1]>
|
|
>>> p = AbstractPolynom([1,2,3])
|
|
>>> p**2
|
|
< <class 'pymath.calculus.abstract_polynom.AbstractPolynom'> [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 = [Expression(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)
|
|
|
|
if __name__ == '__main__':
|
|
P = AbstractPolynom([[1, 2], [3, 4, 5], 6])
|
|
Q = P.reduce()
|
|
for i in Q.explain():
|
|
print(i)
|
|
|
|
#import doctest
|
|
# doctest.testmod()
|
|
|
|
|
|
# -----------------------------
|
|
# Reglages pour 'vim'
|
|
# vim:set autoindent expandtab tabstop=4 shiftwidth=4:
|
|
# cursor: 16 del
|