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