706 lines
15 KiB
Python
706 lines
15 KiB
Python
#! /usr/bin/env python
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# -*- coding: utf-8 -*-
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# vim:fenc=utf-8
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#
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# Copyright © 2017 lafrite <lafrite@Poivre>
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#
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# Distributed under terms of the MIT license.
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"""
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Adding MO
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"""
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from multipledispatch import Dispatcher
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from ..tree import Tree
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from ..MO import MO, MOnumber, MOstr
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from ..MO.fraction import MOFraction
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from ..MO.monomial import MOstrPower, MOMonomial
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from ..MO.polynomial import MOpolynomial
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from ..arithmetic import lcm
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from .filters import special_case
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add_doc = """ Adding MOs
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:param left: left MO
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:param right: right MO
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:return: Tree or MO
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"""
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add = Dispatcher("add", doc=add_doc)
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def add_filter(left, right):
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""" Automatic add on MO
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:param left: MO
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:param right: MO
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:returns: MO if it is a special case, nothing other wise
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>>> a = MOnumber(0)
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>>> b = MOFraction(1, 2)
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>>> add(a, b)
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<MOFraction 1 / 2>
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>>> add(b, a)
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<MOFraction 1 / 2>
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"""
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try:
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if left == 0:
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return right
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except TypeError:
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pass
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try:
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if right == 0:
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return left
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except TypeError:
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pass
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try:
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if left.variable != right.variable:
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raise NotImplementedError("Can't add 2 polynomes with not same letter")
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except AttributeError:
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pass
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@add.register(MOnumber, MOnumber)
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@special_case(add_filter)
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def monumber_monumber(left, right):
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""" Simply add MO value
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>>> a = MOnumber(4)
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>>> b = MOnumber(6)
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>>> add(a, b)
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<MOnumber 10>
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>>> b = MOnumber('2.3')
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>>> add(a, b)
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<MOnumber 6.3>
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"""
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return MO.factory(left.value + right.value)
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@add.register(MOnumber, MOFraction)
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@special_case(add_filter)
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def monumber_mofraction(left, right):
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""" Return a tree with the MOnumber transformed into a MOFraction
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>>> a = MOnumber(4)
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>>> b = MOFraction(6, 5)
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>>> print(add(a, b))
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+
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> 4 / 1
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> 6 / 5
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"""
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left_fraction = MOFraction(left, MOnumber(1))
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return Tree("+", left_fraction, right)
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@add.register(MOFraction, MOnumber)
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@special_case(add_filter)
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def mofraction_monumber(left, right):
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""" Return a tree with the MOnumber transformed into a MOFraction
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>>> a = MOFraction(6, 5)
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>>> b = MOnumber(4)
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>>> print(add(a, b))
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+
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> 6 / 5
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> 4 / 1
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"""
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right_fraction = MOFraction(right, MOnumber(1))
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return Tree("+", left, right_fraction)
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@add.register(MOFraction, MOFraction)
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@special_case(add_filter)
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def mofraction_mofraction(left, right):
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""" 3 differents cases:
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Fractions have same denomintor -> add numerator Tree
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>>> a = MOFraction(1, 5)
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>>> b = MOFraction(4, 5)
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>>> print(add(a, b))
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/
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> +
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| > 1
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| > 4
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> 5
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>>> a = MOFraction(1, 5, True)
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>>> b = MOFraction(4, 5)
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>>> print(mofraction_mofraction(a, b))
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/
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> +
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| > -
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| | > None
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| | > 1
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| > 4
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> 5
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>>> a = MOFraction(1, 5)
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>>> b = MOFraction(4, 5, True)
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>>> print(mofraction_mofraction(a, b))
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/
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> +
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| > 1
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| > -
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| | > None
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| | > 4
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> 5
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A denominator is a multiple of the other
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>>> a = MOFraction(1, 2)
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>>> b = MOFraction(1, 4)
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>>> print(mofraction_mofraction(a, b))
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+
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> /
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| > *
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| | > 1
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| | > 2
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| > *
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| | > 2
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| | > 2
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> 1 / 4
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Denominators are coprime
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>>> a = MOFraction(1, 2)
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>>> b = MOFraction(1, 5)
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>>> print(mofraction_mofraction(a, b))
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+
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> /
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| > *
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| | > 1
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| | > 5
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| > *
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| | > 2
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| | > 5
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> /
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| > *
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| | > 1
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| | > 2
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| > *
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| | > 5
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| | > 2
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"""
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if left.denominator == right.denominator:
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num = Tree("+", left.numerator, right.numerator)
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return Tree("/", num, left.denominator)
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denom_lcm = lcm(left.denominator.value, right.denominator.value)
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if left.denominator.value == denom_lcm:
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left_frac = left
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else:
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multiply_by = MO.factory(denom_lcm // left.denominator.value)
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left_num = Tree("*", left.numerator, multiply_by)
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left_denom = Tree("*", left.denominator, multiply_by)
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left_frac = Tree("/", left_num, left_denom)
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if right.denominator.value == denom_lcm:
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right_frac = right
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else:
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multiply_by = MO.factory(denom_lcm // right.denominator.value)
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right_num = Tree("*", right.numerator, multiply_by)
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right_denom = Tree("*", right.denominator, multiply_by)
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right_frac = Tree("/", right_num, right_denom)
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return Tree("+", left_frac, right_frac)
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@add.register(MOstr, MOstr)
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@special_case(add_filter)
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def mostr_mostr(left, right):
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""" Add 2 MOstr
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:example:
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>>> a = MOstr("x")
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>>> b = MOstr("x")
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>>> add(a, b)
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<MOMonomial 2x>
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"""
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if left != right:
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raise NotImplementedError("Can't add 2 MOstr with not same letter")
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return MOMonomial(2, left)
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@add.register(MOstrPower, MOstrPower)
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@special_case(add_filter)
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def mostrpower_mostrpower(left, right):
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""" Add 2 MOstrPower
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:example:
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>>> a = MOstrPower("x", 2)
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>>> b = MOstrPower("x", 2)
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>>> add(a, b)
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<MOMonomial 2x^2>
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"""
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if left.power != right.power:
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raise NotImplementedError("Can't add 2 MOstrPower with not same power")
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return MOMonomial(2, left.variable, left.power)
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@add.register((MOnumber, MOFraction), MOpolynomial)
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@special_case(add_filter)
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def moscalar_mopolynomial(left, right):
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""" Add a scalar to a polynomial
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:example:
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>>> a = MOnumber(1)
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>>> b = MOpolynomial("x", [2, 3, 4])
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>>> print(add(a, b))
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+
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> 4x^2
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> +
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| > 3x
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| > +
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| | > 1
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| | > 2
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"""
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if 0 not in right.coefficients.keys():
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raise NotImplementedError("Polynomial with no constant, no calculus to do")
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right_const = right.monomials[0]
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right_top = [mo for deg, mo in right.monomials.items() if deg > 0][::-1]
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adds = right_top + [Tree("+", left, right_const)]
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return Tree.from_list("+", adds)
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@add.register(MOpolynomial, (MOnumber, MOFraction))
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@special_case(add_filter)
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def mopolynomial_moscalar(left, right):
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""" Add a scalar to a polynomial
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:example:
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>>> a = MOpolynomial("x", [2, 3, 4])
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>>> b = MOnumber(1)
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>>> print(add(a, b))
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+
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> 4x^2
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> +
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| > 3x
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| > +
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| | > 2
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| | > 1
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"""
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if 0 not in left.coefficients.keys():
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raise NotImplementedError("Polynomial with no constant, no calculus to do")
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left_const = left.monomials[0]
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left_top = [mo for deg, mo in left.monomials.items() if deg > 0][::-1]
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adds = left_top + [Tree("+", left_const, right)]
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return Tree.from_list("+", adds)
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@add.register(MOstr, MOpolynomial)
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@special_case(add_filter)
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def mostr_mopolynomial(left, right):
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""" Add a str to a polynomial
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:example:
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>>> a = MOstr("x")
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>>> b = MOpolynomial("x", [2, 3, 4])
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>>> print(add(a, b))
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+
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> 4x^2
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> +
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| > +
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| | > x
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| | > 3x
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| > 2
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"""
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if 1 not in right.coefficients.keys():
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raise NotImplementedError("Polynomial with no constant, no calculus to do")
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right_coef = right.monomials[1]
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add_coefs = Tree("+", left, right_coef)
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right_top = [mo for deg, mo in right.monomials.items() if deg > 1][::-1]
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right_bot = [mo for deg, mo in right.monomials.items() if deg < 1][::-1]
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adds = right_top + [add_coefs] + right_bot
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return Tree.from_list("+", adds)
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@add.register(MOpolynomial, MOstr)
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@special_case(add_filter)
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def mopolynomial_mostr(left, right):
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""" Add a str to a polynomial
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:example:
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>>> a = MOpolynomial("x", [2, 3, 4])
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>>> b = MOstr("x")
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>>> print(add(a, b))
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+
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> 4x^2
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> +
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| > +
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| | > 3x
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| | > x
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| > 2
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"""
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if 1 not in left.coefficients.keys():
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raise NotImplementedError("No degree in common")
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left_coef = left.monomials[1]
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add_coefs = Tree("+", left_coef, right)
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left_top = [mo for deg, mo in left.monomials.items() if deg > 1][::-1]
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left_bot = [mo for deg, mo in left.monomials.items() if deg < 1][::-1]
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adds = left_top + [add_coefs] + left_bot
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return Tree.from_list("+", adds)
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@add.register(MOstrPower, MOpolynomial)
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@special_case(add_filter)
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def mostrpower_mopolynomial(left, right):
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""" Add a strpower to a polynomial
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:example:
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>>> a = MOstrPower("x", 2)
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>>> b = MOpolynomial("x", [2, 3, 4])
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>>> print(add(a, b))
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+
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> +
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| > x^2
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| > 4x^2
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> +
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| > 3x
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| > 2
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>>> b = MOpolynomial("x", [2, 3, 4, 5])
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>>> print(add(a, b))
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+
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> +
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| > 5x^3
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| > +
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| | > x^2
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| | > 4x^2
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> +
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| > 3x
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| > 2
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"""
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if left.power not in right.coefficients.keys():
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raise NotImplementedError("No degree in common")
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right_mono = right.monomials[left.power]
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add_coefs = Tree("+", left, right_mono)
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right_top = [mo for deg, mo in right.monomials.items() if deg > left.power][::-1]
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right_bot = [mo for deg, mo in right.monomials.items() if deg < left.power][::-1]
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adds = right_top + [add_coefs] + right_bot
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return Tree.from_list("+", adds)
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@add.register(MOpolynomial, MOstrPower)
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@special_case(add_filter)
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def mopolynomial_mostrpower(left, right):
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""" Add a strpower to a polynomial
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:example:
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>>> a = MOpolynomial("x", [2, 3, 4])
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>>> b = MOstrPower("x", 2)
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>>> print(add(a, b))
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+
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> +
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| > 4x^2
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| > x^2
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> +
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| > 3x
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| > 2
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>>> a = MOpolynomial("x", [2, 3, 4, 5])
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>>> print(add(a, b))
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+
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> +
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| > 5x^3
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| > +
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| | > 4x^2
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| | > x^2
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> +
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| > 3x
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| > 2
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"""
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if right.power not in left.coefficients.keys():
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raise NotImplementedError("No degree in common")
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left_mono = left.monomials[right.power]
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add_coefs = Tree("+", left_mono, right)
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left_top = [mo for deg, mo in left.monomials.items() if deg > right.power][::-1]
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left_bot = [mo for deg, mo in left.monomials.items() if deg < right.power][::-1]
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adds = left_top + [add_coefs] + left_bot
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return Tree.from_list("+", adds)
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@add.register(MOMonomial, MOpolynomial)
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@special_case(add_filter)
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def momonomial_mopolynomial(left, right):
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""" Add a monomial to a polynomial
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:example:
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>>> a = MOMonomial(10, "x", 2)
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>>> b = MOpolynomial("x", [2, 3, 4])
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>>> print(add(a, b))
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+
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> +
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| > 10x^2
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| > 4x^2
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> +
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| > 3x
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| > 2
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>>> b = MOpolynomial("x", [2, 3, 4, 5])
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>>> print(add(a, b))
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+
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> +
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| > 5x^3
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| > +
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| | > 10x^2
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| | > 4x^2
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> +
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| > 3x
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| > 2
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"""
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if left.power not in right.coefficients.keys():
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raise NotImplementedError("No degree in common")
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right_mono = right.monomials[left.power]
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add_coefs = Tree("+", left, right_mono)
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right_top = [mo for deg, mo in right.monomials.items() if deg > left.power][::-1]
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right_bot = [mo for deg, mo in right.monomials.items() if deg < left.power][::-1]
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adds = right_top + [add_coefs] + right_bot
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return Tree.from_list("+", adds)
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@add.register(MOpolynomial, MOMonomial)
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@special_case(add_filter)
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def mopolynomial_momonomial(left, right):
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""" Add a monomial to a polynomial
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:example:
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>>> a = MOpolynomial("x", [2, 3, 4])
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>>> b = MOMonomial(10, "x", 2)
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>>> print(add(a, b))
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+
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> +
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| > 4x^2
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| > 10x^2
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> +
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| > 3x
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| > 2
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>>> a = MOpolynomial("x", [2, 3, 4, 5])
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>>> print(add(a, b))
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+
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> +
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| > 5x^3
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| > +
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| | > 4x^2
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| | > 10x^2
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> +
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| > 3x
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| > 2
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"""
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if right.power not in left.coefficients.keys():
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raise NotImplementedError("No degree in common")
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left_mono = left.monomials[right.power]
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add_coefs = Tree("+", left_mono, right)
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left_top = [mo for deg, mo in left.monomials.items() if deg > right.power][::-1]
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left_bot = [mo for deg, mo in left.monomials.items() if deg < right.power][::-1]
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adds = left_top + [add_coefs] + left_bot
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return Tree.from_list("+", adds)
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@add.register(MOpolynomial, MOpolynomial)
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@special_case(add_filter)
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def mopolynomial_mopolynomial(left, right):
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""" Add a polynomial to a polynomial
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:example:
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>>> a = MOpolynomial("x", [2, 3, 4])
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>>> b = MOpolynomial("x", [5, 6, 7])
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>>> print(add(a, b))
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+
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> +
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| > 4x^2
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| > 7x^2
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> +
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| > +
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| | > 3x
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| | > 6x
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| > +
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| | > 2
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| | > 5
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>>> b = MOpolynomial("x", [0, 3, 4])
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>>> print(add(a, b))
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+
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> +
|
|
| > 4x^2
|
|
| > 4x^2
|
|
> +
|
|
| > +
|
|
| | > 3x
|
|
| | > 3x
|
|
| > 2
|
|
|
|
>>> b = MOpolynomial("x", [0, 3, 0, 5])
|
|
>>> print(add(a, b))
|
|
+
|
|
> +
|
|
| > 5x^3
|
|
| > 4x^2
|
|
> +
|
|
| > +
|
|
| | > 3x
|
|
| | > 3x
|
|
| > 2
|
|
|
|
"""
|
|
common_degree = set(left.monomials.keys()).intersection(right.monomials.keys())
|
|
if not common_degree:
|
|
raise NotImplementedError("No degree in common, no calculus to do")
|
|
|
|
merge_monomials = {**left.monomials, **right.monomials}
|
|
for deg in common_degree:
|
|
merge_monomials[deg] = Tree("+", left.monomials[deg], right.monomials[deg])
|
|
|
|
return Tree.from_list("+", list(merge_monomials.values())[::-1])
|
|
|
|
|
|
@add.register(MOstr, MOMonomial)
|
|
@special_case(add_filter)
|
|
def mostr_momonomial(left, right):
|
|
""" Add a str to a Monomial
|
|
|
|
:example:
|
|
>>> a = MOstr("x")
|
|
>>> b = MOMonomial(2, "x")
|
|
>>> print(add(a, b))
|
|
*
|
|
> +
|
|
| > 1
|
|
| > 2
|
|
> x
|
|
"""
|
|
if right.power != 1:
|
|
raise NotImplementedError("Monomial is more than deg 1")
|
|
add_scal = Tree("+", 1, right.coefficient)
|
|
return Tree("*", add_scal, left)
|
|
|
|
|
|
@add.register(MOMonomial, MOstr)
|
|
@special_case(add_filter)
|
|
def momonomial_mostr(left, right):
|
|
""" Add a str to a Monomial
|
|
|
|
:example:
|
|
>>> a = MOMonomial(2, "x")
|
|
>>> b = MOstr("x")
|
|
>>> print(add(a, b))
|
|
*
|
|
> +
|
|
| > 2
|
|
| > 1
|
|
> x
|
|
"""
|
|
if left.power != 1:
|
|
raise NotImplementedError("Monomial is more than deg 1")
|
|
add_scal = Tree("+", left.coefficient, 1)
|
|
return Tree("*", add_scal, right)
|
|
|
|
|
|
@add.register(MOstrPower, MOMonomial)
|
|
@special_case(add_filter)
|
|
def mostrpower_momonomial(left, right):
|
|
""" Add a strpower to a Monomial
|
|
|
|
:example:
|
|
>>> a = MOstrPower("x", 2)
|
|
>>> b = MOMonomial(3, "x", 2)
|
|
>>> print(add(a, b))
|
|
*
|
|
> +
|
|
| > 1
|
|
| > 3
|
|
> x^2
|
|
"""
|
|
if right.power != left.power:
|
|
raise NotImplementedError("MOs does not have same degree")
|
|
add_scal = Tree("+", 1, right.coefficient)
|
|
return Tree("*", add_scal, left)
|
|
|
|
|
|
@add.register(MOMonomial, MOstrPower)
|
|
@special_case(add_filter)
|
|
def momonomial_mostrpower(left, right):
|
|
""" Add a strpower to a Monomial
|
|
|
|
:example:
|
|
>>> a = MOMonomial(3, "x", 2)
|
|
>>> b = MOstrPower("x", 2)
|
|
>>> print(add(a, b))
|
|
*
|
|
> +
|
|
| > 3
|
|
| > 1
|
|
> x^2
|
|
"""
|
|
if left.power != right.power:
|
|
raise NotImplementedError("MOs does not have same degree")
|
|
add_scal = Tree("+", left.coefficient, 1)
|
|
return Tree("*", add_scal, right)
|
|
|
|
|
|
@add.register(MOMonomial, MOMonomial)
|
|
@special_case(add_filter)
|
|
def momonomial_momonomial(left, right):
|
|
""" Add a Monomial to a Monomial
|
|
|
|
:example:
|
|
>>> a = MOMonomial(3, "x", 2)
|
|
>>> b = MOMonomial(4, "x", 2)
|
|
>>> print(add(a, b))
|
|
*
|
|
> +
|
|
| > 3
|
|
| > 4
|
|
> x^2
|
|
|
|
"""
|
|
if left.power != right.power:
|
|
raise NotImplementedError("MOs does not have same degree")
|
|
add_scal = Tree("+", left.coefficient, right.coefficient)
|
|
return Tree("*", add_scal, right.strpower)
|
|
|
|
|
|
# -----------------------------
|
|
# Reglages pour 'vim'
|
|
# vim:set autoindent expandtab tabstop=4 shiftwidth=4:
|
|
# cursor: 16 del
|