diff --git a/pymath/calculus/equation.py b/pymath/calculus/equation.py new file mode 100644 index 0000000..b03d95e --- /dev/null +++ b/pymath/calculus/equation.py @@ -0,0 +1,180 @@ +#!/usr/bin/env python +# encoding: utf-8 + + +from .expression import Expression +from .polynom import Polynom +from .fraction import Fraction + +from .random_expression import RdExpression + +__all__ = ['Equation'] + + +class Equation(object): + """A calculus expression. Today it can andle only expression with numbers later it will be able to manipulate unknown""" + +# @classmethod +# def random(self, form="", conditions=[], val_min=-10, val_max=10): +# """Create a random expression from form and with conditions +# +# :param form: the form of the expression (/!\ variables need to be in brackets {}) +# :param conditions: condition on variables (/!\ variables need to be in brackets {}) +# :param val_min: min value for generate variables +# :param val_max: max value for generate variables +# +# """ +# random_generator = RdExpression(form, conditions) +# return Expression(random_generator(val_min, val_max)) +# + + def __init__(self, exp_str = "", left_poly = Expression([0]), right_poly = Expression([0])): + """Create the equation + + :param exp_str: the equality string which represent the equation + :param left_poly: the left polynom of the equation + :param right_poly: the right polynom of the equation + + >>> e = Equation("2x+3 = 4x+5") + >>> e + < Equation [2 x + 3, 4 x + 5]> + >>> Pl = Polynom([1, 2]) + >>> Pr = Polynom([3, 4]) + >>> e = Equation(left_poly = Pl) + >>> e + < Equation [2 x + 1, 0]> + >>> e = Equation(right_poly = Pr) + >>> e + < Equation [0, 4 x + 3]> + >>> e = Equation(left_poly = Pl, right_poly = Pr) + >>> e + < Equation [2 x + 1, 4 x + 3]> + + """ + if exp_str: + l_part, r_part = exp_str.split("=") + self.l_exp = Expression(l_part) + self.r_exp = Expression(r_part) + else: + self.l_exp = left_poly + self.r_exp = right_poly + + self.smpl_each_part() + + def smpl_each_part(self): + """ Simplify left and right part, transform them into polynom and stock them in smpl_*_exp + """ + self.smpl_l_exp = self.l_exp.simplify() + self.smpl_r_exp = self.r_exp.simplify() + + try: + self.smpl_r_exp = self.smpl_l_exp.conv2poly(self.smpl_r_exp) + except AttributeError: + pass + + try: + self.smpl_l_exp = self.smpl_r_exp.conv2poly(self.smpl_l_exp) + except AttributeError: + raise EquationError("None of left and right parts are polynoms. \ + Can't use it to make an equation.") + + # TODO: On pourrait rajouter des tests sur les inconnues |mar. mars 22 10:17:12 EAT 2016 + + def __str__(self): + return str(self.l_exp) + " = " + str(self.r_exp) + + def __repr__(self): + return "< {cls} [{l}, {r}]>".format( + cls = str(self.__class__).split('.')[-1][:-2], + l = self.l_exp, + r = self.r_exp, + ) + + def solve(self): + """Solve the equation but yielding each steps + + """ + pass + + def solution(self): + """Return the solution of the equation + + :returns: the solution + + >>> e = Equation("2x + 1 = x + 2") + >>> e.solution() + 1 + >>> e = Equation("2x + 1 = 1") + >>> e.solution() + 0 + >>> e = Equation("1 = 2x + 1") + >>> e.solution() + 0 + >>> e = Equation("3x = 2x") + >>> e.solution() + 0 + >>> e = Equation("3x + 1 = 0") + >>> e.solution() + < Fraction -1 / 3> + >>> e = Equation("6x + 2 = 0") + >>> e.solution() + < Fraction -1 / 3> + + """ + num = self.smpl_r_exp._coef[0] - self.smpl_l_exp._coef[0] + + try: + denom = self.smpl_l_exp._coef[1] + except IndexError: + denom = 0 + try: + denom -= self.smpl_r_exp._coef[1] + except IndexError: + pass + + if denom == 0 and num == 0: + raise EquationError("All number are solution") + elif denom == 0: + raise NoSolutionError("This equation has no solution") + + return Fraction(num, denom).simplify() + + def is_solution(self, num): + """ Tell if a number is a solution. + + :param num: the number to test + + >>> e = Equation("2x + 1 = x + 2") + >>> e.is_solution(2) + False + >>> e.is_solution(1) + True + >>> e = Equation("3x = 2x") + >>> e.is_solution(1) + False + >>> e.is_solution(0) + True + >>> e = Equation("3x + 1 = 0") + >>> e.is_solution(0) + False + >>> e.is_solution(Fraction(-1, 3)) + True + >>> e.is_solution(Fraction(-2, 6)) + True + + """ + l_part = self.smpl_l_exp.replace_letter(num).simplify() + r_part = self.smpl_r_exp.replace_letter(num).simplify() + return l_part == r_part + +class EquationError(Exception): + pass + + +class NoSolutionError(EquationError): + pass + +# ----------------------------- +# Reglages pour 'vim' +# vim:set autoindent expandtab tabstop=4 shiftwidth=4: +# cursor: 16 del