768 lines
17 KiB
Python
768 lines
17 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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Multiply 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.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 .filters import special_case
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multiply_doc = """ Multiply MOs
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:param left: left MO
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:param right: right MO
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:returns: Tree or MO
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"""
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multiply = Dispatcher("multiply", doc=multiply_doc)
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def multiply_filter(left, right):
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""" Automatic multiply 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(1)
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>>> b = MOFraction(1, 2)
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>>> multiply(a, b)
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<MOFraction 1 / 2>
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>>> multiply(b, a)
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<MOFraction 1 / 2>
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>>> a = MOnumber(0)
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>>> b = MOFraction(1, 2)
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>>> multiply(a, b)
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<MOnumber 0>
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"""
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try:
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if left == 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 right == 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 left == 1:
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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 == 1:
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return left
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except TypeError:
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pass
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@multiply.register(MOnumber, MOnumber)
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@special_case(multiply_filter)
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def monumber_monumber(left, right):
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""" Simply multiply values
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>>> a = MOnumber(4)
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>>> b = MOnumber(6)
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>>> multiply(a, b)
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<MOnumber 24>
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"""
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return MO.factory(left.value * right.value)
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@multiply.register(MOnumber, MOFraction)
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@special_case(multiply_filter)
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def monumber_mofraction(left, right):
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""" Return division Tree with on the numertor MOnumber times numerator of MOFraction
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>>> a = MOnumber(4)
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>>> b = MOFraction(6, 5)
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>>> print(multiply(a, b))
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/
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> *
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| > 4
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| > 6
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> 5
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>>> b = MOFraction(6, 5, True)
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>>> print(multiply(a, b))
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/
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> *
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| > 4
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| > -
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| | > None
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| | > 6
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> 5
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"""
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num = Tree("*", left, right.numerator)
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return Tree("/", num, right._denominator)
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@multiply.register(MOFraction, MOnumber)
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@special_case(multiply_filter)
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def mofraction_monumber(left, right):
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""" Return division Tree with on the numertor MOnumber times numerator of MOFraction
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>>> a = MOFraction(6, 5)
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>>> b = MOnumber(4)
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>>> print(multiply(a, b))
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/
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> *
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| > 6
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| > 4
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> 5
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"""
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num = Tree("*", left.numerator, right)
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return Tree("/", num, left._denominator)
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@multiply.register(MOFraction, MOFraction)
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@special_case(multiply_filter)
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def mofraction_mofraction(left, right):
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""" Multiply two mofractions (numertors together and denominators together)
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>>> a = MOFraction(1, 5)
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>>> b = MOFraction(4, 5)
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>>> print(multiply(a, b))
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/
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> *
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| > 1
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| > 4
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> *
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| > 5
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| > 5
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"""
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num = Tree("*", left.numerator, right.numerator)
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denom = Tree("*", left.denominator, right.denominator)
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return Tree("/", num, denom)
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@multiply.register((MOnumber, MOFraction), MOMonomial)
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@special_case(multiply_filter)
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def moscalar_monomonial(left, right):
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""" Multiply a scalar with a monomial
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>>> a = MOnumber(4)
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>>> x = MOstrPower('x', 4)
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>>> b = MOMonomial(5, x)
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>>> print(multiply(a, b))
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*
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> *
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| > 4
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| > 5
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> ^
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| > x
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| > 4
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"""
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coefficient = Tree('*', left, right.coefficient)
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return Tree('*', coefficient, right.strpower)
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@multiply.register(MOMonomial, (MOnumber, MOFraction))
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@special_case(multiply_filter)
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def monomonial_moscalar(left, right):
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""" Multiply a momonial with a scalar
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>>> x = MOstrPower('x', 4)
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>>> a = MOMonomial(5, x)
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>>> b = MOnumber(4)
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>>> print(multiply(a, b))
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*
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> *
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| > 4
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| > 5
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> ^
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| > x
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| > 4
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"""
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coefficient = Tree('*', right, left.coefficient)
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return Tree('*', coefficient, left.strpower)
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@multiply.register(MOstr, MOstrPower)
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@special_case(multiply_filter)
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def mostr_mostrpower(left, right):
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""" Multiply a MOstr and a MOstrPower
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>>> a = MOstr('x')
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>>> b = MOstrPower('x', 4)
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>>> multiply(a, b)
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<MOstrPower x^5>
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>>> a = MOstr('x')
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>>> b = MOstrPower('y', 4)
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>>> multiply(a, b)
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Traceback (most recent call last):
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...
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NotImplementedError: Can't multiply MOstr and MOstrPower if they don'thave same variable (got x and y)
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"""
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if left.variable != right.variable:
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raise NotImplementedError("Can't multiply MOstr and MOstrPower if they don't"
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f"have same variable (got {left.variable} and {right.variable})")
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return MOstrPower(left.variable, right.power.value+1)
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@multiply.register(MOstrPower, MOstr)
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@special_case(multiply_filter)
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def mostr_mostrpower(left, right):
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""" Multiply a MOstr and a MOstrPower
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>>> a = MOstrPower('x', 4)
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>>> b = MOstr('x')
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>>> multiply(a, b)
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<MOstrPower x^5>
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>>> a = MOstrPower('y', 4)
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>>> b = MOstr('x')
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>>> multiply(a, b)
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Traceback (most recent call last):
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...
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NotImplementedError: Can't multiply MOstr and MOstrPower if they don'thave same variable (got x and y)
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"""
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if left.variable != right.variable:
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raise NotImplementedError("Can't multiply MOstr and MOstrPower if they don't"
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f"have same variable (got {left.variable} and {right.variable})")
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return MOstrPower(left.variable, left.power.value+1)
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@multiply.register(MOstr, MOstr)
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@special_case(multiply_filter)
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def mostr_mostr(left, right):
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""" Multiply a MOstr and a MOstr
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:example:
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>>> a = MOstr('x')
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>>> b = MOstr('x')
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>>> multiply(a, b)
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<MOstrPower x^2>
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>>> a = MOstr('y')
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>>> b = MOstr('x')
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>>> multiply(a, b)
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Traceback (most recent call last):
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...
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NotImplementedError: Can't multiply MOstr and MOstr if they don'thave same variable (got y and x)
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"""
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if left.variable != right.variable:
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raise NotImplementedError("Can't multiply MOstr and MOstr if they don't"
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f"have same variable (got {left.variable} and {right.variable})")
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return MOstrPower(left.variable, 2)
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@multiply.register(MOstrPower, MOstrPower)
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@special_case(multiply_filter)
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def mostr_mostrpower(left, right):
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""" Multiply a MOstrPower and a MOstrPower
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>>> a = MOstrPower('x', 2)
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>>> b = MOstrPower('x', 4)
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>>> print(multiply(a, b))
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^
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> x
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> +
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| > 2
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| > 4
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>>> a = MOstrPower('x', 2)
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>>> b = MOstrPower('y', 4)
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>>> multiply(a, b)
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Traceback (most recent call last):
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...
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NotImplementedError: Can't multiply MOstrPower and MOstrPower if they don'thave same variable (got x and y)
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"""
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if left.variable != right.variable:
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raise NotImplementedError("Can't multiply MOstrPower and MOstrPower if they don't"
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f"have same variable (got {left.variable} and {right.variable})")
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power = Tree("+", left.power, right.power)
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return Tree("^", left.variable, power)
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@multiply.register(MOstrPower, MOMonomial)
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@special_case(multiply_filter)
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def mostr_momonomial(left, right):
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""" Multiply a MOstrPower and a MOMonomial
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>>> a = MOstrPower('x', 2)
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>>> b = MOMonomial(2, 'x', 4)
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>>> print(multiply(a, b))
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*
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> 2
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> ^
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| > x
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| > +
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| | > 2
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| | > 4
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>>> a = MOstrPower('x', 2)
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>>> b = MOMonomial(2, 'y', 4)
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>>> multiply(a, b)
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Traceback (most recent call last):
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...
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NotImplementedError: Can't multiply MOstrPower and Monomial if they don'thave same variable (got x and y)
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"""
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if left.variable != right.variable:
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raise NotImplementedError("Can't multiply MOstrPower and Monomial if they don't"
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f"have same variable (got {left.variable} and {right.variable})")
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power = Tree("+", left.power, right.power)
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monome = Tree("^", left.variable, power)
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return Tree("*", right.coefficient, monome)
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@multiply.register(MOMonomial, MOstrPower)
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@special_case(multiply_filter)
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def momonomial_mostr(left, right):
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""" Multiply a MOMonomial and a MOstrPower
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>>> a = MOMonomial(2, 'x', 4)
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>>> b = MOstrPower('x', 2)
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>>> print(multiply(a, b))
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*
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> 2
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> ^
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| > x
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| > +
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| | > 4
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| | > 2
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>>> a = MOMonomial(2, 'y', 4)
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>>> b = MOstrPower('x', 2)
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>>> multiply(a, b)
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Traceback (most recent call last):
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...
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NotImplementedError: Can't multiply MOstrPower and Monomial if they don'thave same variable (got y and x)
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"""
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if left.variable != right.variable:
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raise NotImplementedError("Can't multiply MOstrPower and Monomial if they don't"
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f"have same variable (got {left.variable} and {right.variable})")
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power = Tree("+", left.power, right.power)
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monome = Tree("^", left.variable, power)
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return Tree("*", left.coefficient, monome)
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@multiply.register(MOstr, MOMonomial)
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@special_case(multiply_filter)
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def mostr_momonomial(left, right):
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""" Multiply a MOstr and a MOMonomial
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>>> a = MOstr('x')
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>>> b = MOMonomial(2, 'x', 4)
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>>> print(multiply(a, b))
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*
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> 2
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> ^
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| > x
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| > 5
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>>> a = MOstr('x')
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>>> b = MOMonomial(2, 'y', 4)
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>>> multiply(a, b)
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Traceback (most recent call last):
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...
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NotImplementedError: Can't multiply MOstr and Monomial if they don'thave same variable (got x and y)
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"""
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if left.variable != right.variable:
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raise NotImplementedError("Can't multiply MOstr and Monomial if they don't"
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f"have same variable (got {left.variable} and {right.variable})")
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return MOMonomial(right.coefficient, right.variable, right.power.value+1)
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@multiply.register(MOMonomial, MOstr)
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@special_case(multiply_filter)
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def momonomial_mostr(left, right):
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""" Multiply a MOMonomial and a MOstr
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>>> a = MOMonomial(2, 'x', 4)
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>>> b = MOstr('x')
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>>> print(multiply(a, b))
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*
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> 2
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> ^
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| > x
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| > 5
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>>> a = MOMonomial(2, 'y', 4)
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>>> b = MOstr('x')
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>>> multiply(a, b)
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Traceback (most recent call last):
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...
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NotImplementedError: Can't multiply MOstr and Monomial if they don'thave same variable (got y and x)
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"""
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if left.variable != right.variable:
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raise NotImplementedError("Can't multiply MOstr and Monomial if they don't"
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f"have same variable (got {left.variable} and {right.variable})")
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return MOMonomial(left.coefficient, left.variable, left.power.value+1)
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@multiply.register(MOMonomial, MOMonomial)
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@special_case(multiply_filter)
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def momonomial_momonomial(left, right):
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""" Multiply a MOMonomial and a MOMonomial
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>>> a = MOMonomial(2, 'x', 4)
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>>> b = MOMonomial(3, 'x', 2)
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>>> print(multiply(a, b))
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*
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> *
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| > 2
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| > 3
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> ^
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| > x
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| > +
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| | > 4
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| | > 2
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>>> a = MOMonomial(2, 'y', 4)
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>>> b = MOMonomial(3, 'x', 2)
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>>> multiply(a, b)
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Traceback (most recent call last):
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...
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NotImplementedError: Can't multiply MOMonomial and Monomial if they don'thave same variable (got y and x)
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"""
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if left.variable != right.variable:
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raise NotImplementedError("Can't multiply MOMonomial and Monomial if they don't"
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f"have same variable (got {left.variable} and {right.variable})")
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powers = Tree("+", left.power, right.power)
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monome = Tree("^", left.variable, powers)
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coefs = Tree("*", left.coefficient, right.coefficient)
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return Tree("*", coefs, monome)
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@multiply.register((MOnumber, MOFraction, MOstr, MOstrPower, MOMonomial), \
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MOpolynomial)
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@special_case(multiply_filter)
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def lotsmo_mopolynomial(left, right):
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""" Multiply a scalar and a MOMonomial
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>>> a = MOnumber(2)
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>>> b = MOpolynomial('x', [1, 2, 3])
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>>> print(multiply(a, b))
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+
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> *
|
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| > 2
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| > *
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| | > 3
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| | > ^
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|
| | | > x
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| | | > 2
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> +
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| > *
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| | > 2
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| | > *
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| | | > 2
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| | | > x
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| > *
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| | > 2
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| | > 1
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>>> a = MOFraction(1, 5)
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>>> b = MOpolynomial('x', [1, 2, 3])
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>>> print(multiply(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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| > *
|
|
| | > 3
|
|
| | > ^
|
|
| | | > x
|
|
| | | > 2
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> +
|
|
| > *
|
|
| | > /
|
|
| | | > 1
|
|
| | | > 5
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|
| | > *
|
|
| | | > 2
|
|
| | | > x
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| > *
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|
| | > /
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|
| | | > 1
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|
| | | > 5
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| | > 1
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>>> a = MOstr("x")
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>>> b = MOpolynomial('x', [1, 2, 3])
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>>> print(multiply(a, b))
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+
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> *
|
|
| > x
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| > *
|
|
| | > 3
|
|
| | > ^
|
|
| | | > x
|
|
| | | > 2
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> +
|
|
| > *
|
|
| | > x
|
|
| | > *
|
|
| | | > 2
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|
| | | > x
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| > *
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|
| | > x
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| | > 1
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>>> a = MOstrPower("x", 2)
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>>> b = MOpolynomial('x', [1, 2, 3])
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>>> print(multiply(a, b))
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+
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> *
|
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| > ^
|
|
| | > x
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|
| | > 2
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| > *
|
|
| | > 3
|
|
| | > ^
|
|
| | | > x
|
|
| | | > 2
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> +
|
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| > *
|
|
| | > ^
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|
| | | > x
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|
| | | > 2
|
|
| | > *
|
|
| | | > 2
|
|
| | | > x
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| > *
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|
| | > ^
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|
| | | > x
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|
| | | > 2
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| | > 1
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>>> a = MOMonomial(3, "x", 2)
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>>> b = MOpolynomial('x', [1, 2, 3])
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>>> print(multiply(a, b))
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+
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> *
|
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| > *
|
|
| | > 3
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|
| | > ^
|
|
| | | > x
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|
| | | > 2
|
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| > *
|
|
| | > 3
|
|
| | > ^
|
|
| | | > x
|
|
| | | > 2
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> +
|
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| > *
|
|
| | > *
|
|
| | | > 3
|
|
| | | > ^
|
|
| | | | > x
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|
| | | | > 2
|
|
| | > *
|
|
| | | > 2
|
|
| | | > x
|
|
| > *
|
|
| | > *
|
|
| | | > 3
|
|
| | | > ^
|
|
| | | | > x
|
|
| | | | > 2
|
|
| | > 1
|
|
|
|
|
|
"""
|
|
coefs = [Tree("*", left, monom) \
|
|
for monom in list(right.monomials.values())[::-1]\
|
|
]
|
|
return Tree.from_list("+", coefs)
|
|
|
|
@multiply.register(MOpolynomial, \
|
|
(MOnumber, MOFraction, MOstr, MOstrPower, MOMonomial))
|
|
@special_case(multiply_filter)
|
|
def mopolynomial_lotsmo(left, right):
|
|
""" Multiply a MOpolynomial with nearly everything
|
|
|
|
>>> a = MOpolynomial('x', [1, 2, 3])
|
|
>>> b = MOnumber(2)
|
|
>>> print(multiply(a, b))
|
|
+
|
|
> *
|
|
| > *
|
|
| | > 3
|
|
| | > ^
|
|
| | | > x
|
|
| | | > 2
|
|
| > 2
|
|
> +
|
|
| > *
|
|
| | > *
|
|
| | | > 2
|
|
| | | > x
|
|
| | > 2
|
|
| > *
|
|
| | > 1
|
|
| | > 2
|
|
|
|
>>> a = MOpolynomial('x', [1, 2, 3])
|
|
>>> b = MOFraction(1, 5)
|
|
>>> print(multiply(a, b))
|
|
+
|
|
> *
|
|
| > *
|
|
| | > 3
|
|
| | > ^
|
|
| | | > x
|
|
| | | > 2
|
|
| > /
|
|
| | > 1
|
|
| | > 5
|
|
> +
|
|
| > *
|
|
| | > *
|
|
| | | > 2
|
|
| | | > x
|
|
| | > /
|
|
| | | > 1
|
|
| | | > 5
|
|
| > *
|
|
| | > 1
|
|
| | > /
|
|
| | | > 1
|
|
| | | > 5
|
|
|
|
>>> a = MOpolynomial('x', [1, 2, 3])
|
|
>>> b = MOstr("x")
|
|
>>> print(multiply(a, b))
|
|
+
|
|
> *
|
|
| > *
|
|
| | > 3
|
|
| | > ^
|
|
| | | > x
|
|
| | | > 2
|
|
| > x
|
|
> +
|
|
| > *
|
|
| | > *
|
|
| | | > 2
|
|
| | | > x
|
|
| | > x
|
|
| > *
|
|
| | > 1
|
|
| | > x
|
|
|
|
>>> a = MOpolynomial('x', [1, 2, 3])
|
|
>>> b = MOstrPower("x", 2)
|
|
>>> print(multiply(a, b))
|
|
+
|
|
> *
|
|
| > *
|
|
| | > 3
|
|
| | > ^
|
|
| | | > x
|
|
| | | > 2
|
|
| > ^
|
|
| | > x
|
|
| | > 2
|
|
> +
|
|
| > *
|
|
| | > *
|
|
| | | > 2
|
|
| | | > x
|
|
| | > ^
|
|
| | | > x
|
|
| | | > 2
|
|
| > *
|
|
| | > 1
|
|
| | > ^
|
|
| | | > x
|
|
| | | > 2
|
|
|
|
>>> a = MOpolynomial('x', [1, 2, 3])
|
|
>>> b = MOMonomial(3, "x", 2)
|
|
>>> print(multiply(a, b))
|
|
+
|
|
> *
|
|
| > *
|
|
| | > 3
|
|
| | > ^
|
|
| | | > x
|
|
| | | > 2
|
|
| > *
|
|
| | > 3
|
|
| | > ^
|
|
| | | > x
|
|
| | | > 2
|
|
> +
|
|
| > *
|
|
| | > *
|
|
| | | > 2
|
|
| | | > x
|
|
| | > *
|
|
| | | > 3
|
|
| | | > ^
|
|
| | | | > x
|
|
| | | | > 2
|
|
| > *
|
|
| | > 1
|
|
| | > *
|
|
| | | > 3
|
|
| | | > ^
|
|
| | | | > x
|
|
| | | | > 2
|
|
|
|
"""
|
|
coefs = [Tree("*", monom, right) \
|
|
for monom in list(left.monomials.values())[::-1] \
|
|
]
|
|
return Tree.from_list("+", coefs)
|
|
|
|
@multiply.register(MOpolynomial, MOpolynomial)
|
|
@special_case(multiply_filter)
|
|
def mopolynomial_mopolynomial(left, right):
|
|
""" Multiply 2 MOpolynomial
|
|
|
|
>>> a = MOpolynomial('x', [1, 2, 3])
|
|
>>> b = MOpolynomial('x', [4, 5])
|
|
>>> print(multiply(a, b))
|
|
+
|
|
> +
|
|
| > *
|
|
| | > *
|
|
| | | > 3
|
|
| | | > ^
|
|
| | | | > x
|
|
| | | | > 2
|
|
| | > *
|
|
| | | > 5
|
|
| | | > x
|
|
| > +
|
|
| | > *
|
|
| | | > *
|
|
| | | | > 3
|
|
| | | | > ^
|
|
| | | | | > x
|
|
| | | | | > 2
|
|
| | | > 4
|
|
| | > *
|
|
| | | > *
|
|
| | | | > 2
|
|
| | | | > x
|
|
| | | > *
|
|
| | | | > 5
|
|
| | | | > x
|
|
> +
|
|
| > *
|
|
| | > *
|
|
| | | > 2
|
|
| | | > x
|
|
| | > 4
|
|
| > +
|
|
| | > *
|
|
| | | > 1
|
|
| | | > *
|
|
| | | | > 5
|
|
| | | | > x
|
|
| | > *
|
|
| | | > 1
|
|
| | | > 4
|
|
|
|
"""
|
|
coefs = [Tree("*", l_monom, r_monom) \
|
|
for l_monom in list(left.monomials.values())[::-1] \
|
|
for r_monom in list(right.monomials.values())[::-1] \
|
|
]
|
|
return Tree.from_list("+", coefs)
|
|
|
|
|
|
# -----------------------------
|
|
# Reglages pour 'vim'
|
|
# vim:set autoindent expandtab tabstop=4 shiftwidth=4:
|
|
# cursor: 16 del
|