Mapytex/pymath/calculus/equation.py

#!/usr/bin/env python
# encoding: utf-8


from .explicable import Explicable
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

        >>> Equation.random("{a}x + {b} = 0") # doctest:+ELLIPSIS
        < Equation [..., 0]>
        >>> Equation.random("{a}x + {b} = _", conditions = ["{a}==2"]) # doctest:+ELLIPSIS
        < Equation [2 x ...]>

        """
        random_generator = RdExpression(form, conditions)
        return Equation(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):
        r"""Solve the equation but yielding each steps

        >>> e = Equation("x + 123 = 0")
        >>> for i in e.solve():
        ...    print(i)
        [< Step ['x', 123, +]>, < Step [0]>]
        [< Step ['x']>, < Step [-123]>]
        >>> e = Equation("2x = x + 2")
        >>> for i in e.solve():
        ...    print(i)
        [< Step [2, 'x', *]>, < Step ['x', 2, +]>]
        [< Step ['x']>, < Step [2]>]
        >>> e = Equation("2x = 1")
        >>> for i in e.solve():
        ...    print(i)
        [< Step [2, 'x', *]>, < Step [1]>]
        [< Step ['x']>, < Step [1, 2, /]>]
        >>> e = Equation("2x + 1 = 4x + 2")
        >>> for i in e.solve():
        ...    print(i)
        [< Step [2, 'x', *, 1, +]>, < Step [4, 'x', *, 2, +]>]
        [< Step [2, 'x', *]>, < Step [4, 'x', *, 1, +]>]
        [< Step [-2, 'x', *]>, < Step [1]>]
        [< Step ['x']>, < Step [-1, 2, /]>]
        >>> e = Equation("2x + 3x + 1 = 4x + 2")
        >>> for i in e.solve():
        ...    print(i)
        [< Step [2, 'x', *, 3, 'x', *, +, 1, +]>, < Step [4, 'x', *, 2, +]>]
        [< Step [2, 3, +, 'x', *, 1, +]>, < Step [4, 'x', *, 2, +]>]
        [< Step [5, 'x', *, 1, +]>, < Step [4, 'x', *, 2, +]>]
        [< Step [5, 'x', *, 1, +, 1, -]>, < Step [4, 'x', *, 2, +, 1, -]>]
        [< Step [5, 'x', *]>, < Step [4, 'x', *, 1, +]>]
        [< Step ['x']>, < Step [1]>]
        """
        yield from self.gene_smpl_steps()

        if self.smpl_l_exp._coef[0] != 0:
            yield from Equation(
                    left_poly =  self.smpl_l_exp - self.smpl_l_exp._coef[0],
                    right_poly = self.smpl_r_exp - self.smpl_l_exp._coef[0]
                    ).solve()
            return

        try:
            poly_r_part = Polynom([0, self.smpl_r_exp._coef[1]])
        except IndexError:
            pass
        else:
            if self.smpl_r_exp._coef[1] != 0: 
                yield from Equation(
                        left_poly =  self.smpl_l_exp - poly_r_part,
                        right_poly = self.smpl_r_exp - poly_r_part
                        ).solve()
                return

        if self.smpl_l_exp._coef[1] != 1:
            yield from Equation(
                    left_poly =  self.smpl_l_exp / self.smpl_l_exp._coef[1],
                    right_poly = self.smpl_r_exp / self.smpl_l_exp._coef[1]
                    ).solve()
            return

    def gene_smpl_steps(self):
        r"""Generate simplification steps of the equation

        >>> e = Equation("2x + 3x + 1 = 4x + 2")
        >>> e.gene_smpl_steps() # doctest:+ELLIPSIS
        <generator object Equation.gene_smpl_steps at ...>
        >>> for i in e.gene_smpl_steps():
        ...    print(i)
        [< Step [2, 'x', *, 3, 'x', *, +, 1, +]>, < Step [4, 'x', *, 2, +]>]
        [< Step [2, 3, +, 'x', *, 1, +]>, < Step [4, 'x', *, 2, +]>]
        [< Step [5, 'x', *, 1, +]>, < Step [4, 'x', *, 2, +]>]
        >>> e = Equation("2x + 3x + 1 = 4x + 2")
        >>> for i in e.gene_smpl_steps():
        ...    print(" = ".join([str(j) for j in i]))
        2 x + 3 x + 1 = 4 x + 2
        ( 2 + 3 ) x + 1 = 4 x + 2
        5 x + 1 = 4 x + 2
        >>> e = Equation("3x / 3 = 5 / 3")
        >>> for i in e.gene_smpl_steps():
        ...    print(" = ".join([str(j) for j in i]))
        3 \times \frac{ x }{ 3 } = \frac{ 5 }{ 3 }
        \frac{ x }{ 3 } \times 3 = \frac{ 5 }{ 3 }
        \frac{ x \times 3 }{ 1 \times 3 } = \frac{ 5 }{ 3 }
        \frac{ x }{ 1 } = \frac{ 5 }{ 3 }
        x = \frac{ 5 }{ 3 }

        """
        for s in Explicable.merge_history(
                [self.smpl_l_exp, self.smpl_r_exp]
                ):
            yield s

    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

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