310 lines
9.7 KiB
Python
310 lines
9.7 KiB
Python
#!/usr/bin/env python
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# encoding: utf-8
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from .explicable import Explicable
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from .expression import Expression
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from .step import Step
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from .decorators import no_repetition
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from .polynom import Polynom
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from .fraction import Fraction
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from .random_expression import RdExpression
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__all__ = ['Equation']
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class Equation(object):
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"""A calculus expression. Today it can andle only expression with numbers later it will be able to manipulate unknown"""
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@classmethod
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def random(self, form="", conditions=[], val_min=2, val_max=30):
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"""Create a random expression from form and with conditions
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:param form: the form of the expression (/!\ variables need to be in brackets {})
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:param conditions: condition on variables (/!\ variables need to be in brackets {})
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:param val_min: min value for generate variables
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:param val_max: max value for generate variables
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>>> Equation.random("{a}x + {b} = 0") # doctest:+ELLIPSIS
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< Equation [..., 0]>
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>>> Equation.random("{a}x + {b} = _", conditions = ["{a}==2"]) # doctest:+ELLIPSIS
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< Equation [2 x ...]>
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"""
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random_generator = RdExpression(form, conditions)
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return Equation(random_generator(val_min, val_max))
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def __init__(self, exp_str = "", left_poly = Expression([0]), right_poly = Expression([0])):
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"""Create the equation
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:param exp_str: the equality string which represent the equation
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:param left_poly: the left polynom of the equation
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:param right_poly: the right polynom of the equation
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>>> e = Equation("2x+3 = 4x+5")
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>>> e
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< Equation [2 x + 3, 4 x + 5]>
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>>> Pl = Polynom([1, 2])
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>>> Pr = Polynom([3, 4])
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>>> e = Equation(left_poly = Pl)
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>>> e
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< Equation [2 x + 1, 0]>
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>>> e = Equation(right_poly = Pr)
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>>> e
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< Equation [0, 4 x + 3]>
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>>> e = Equation(left_poly = Pl, right_poly = Pr)
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>>> e
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< Equation [2 x + 1, 4 x + 3]>
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"""
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if exp_str:
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l_part, r_part = exp_str.split("=")
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self.l_exp = Expression(l_part)
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self.r_exp = Expression(r_part)
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else:
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self.l_exp = left_poly
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self.r_exp = right_poly
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self.smpl_each_part()
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def smpl_each_part(self):
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""" Simplify left and right part, transform them into polynom and stock them in smpl_*_exp
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"""
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self.smpl_l_exp = self.l_exp.simplify()
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self.smpl_l_exp.steal_history(self.l_exp)
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self.smpl_r_exp = self.r_exp.simplify()
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self.smpl_r_exp.steal_history(self.r_exp)
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try:
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self.smpl_r_exp = self.smpl_l_exp.conv2poly(self.smpl_r_exp)
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except AttributeError:
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pass
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try:
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self.smpl_l_exp = self.smpl_r_exp.conv2poly(self.smpl_l_exp)
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except AttributeError:
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raise EquationError("None of left and right parts are polynoms. \
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Can't use it to make an equation.")
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# TODO: On pourrait rajouter des tests sur les inconnues |mar. mars 22 10:17:12 EAT 2016
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def __str__(self):
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return str(self.l_exp) + " = " + str(self.r_exp)
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def __repr__(self):
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return "< {cls} [{l}, {r}]>".format(
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cls = str(self.__class__).split('.')[-1][:-2],
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l = self.l_exp,
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r = self.r_exp,
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)
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#@no_repetition(lambda x, y: (x[0] == y[0]) & (x[1] == y[1]))
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@no_repetition()
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def solve(self):
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r"""Solve the equation but yielding each steps
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>>> e = Equation("x + 123 = 0")
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>>> for i in e.solve():
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... print(" = ".join([str(j) for j in i]))
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x + 123 = 0
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x + 123 - 123 = 0 - 123
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x + 123 - 123 = 0 - 123
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x + 123 - 123 = -123
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x = -123
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>>> e = Equation("2x = x + 2")
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>>> for i in e.solve():
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... print(" = ".join([str(j) for j in i]))
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2 x = x + 2
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2 x - x = x + 2 - x
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2 x - x = x + 2 - x
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( 2 - 1 ) x = x - x + 2
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x = ( 1 - 1 ) x + 2
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x = 2
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>>> e = Equation("2x = 1")
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>>> for i in e.solve():
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... print(" = ".join([str(j) for j in i]))
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2 x = 1
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2 x \times 2 = 1 \times 2
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\frac{ 2 }{ 2 } x = \frac{ 1 }{ 2 }
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x = \frac{ 1 }{ 2 }
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>>> e = Equation("2x + 1 = 4x + 2")
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>>> for i in e.solve():
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... print(" = ".join([str(j) for j in i]))
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2 x + 1 = 4 x + 2
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2 x + 1 - 1 = 4 x + 2 - 1
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2 x + 1 - 1 = 4 x + 2 - 1
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2 x + 1 - 1 = 4 x + 2 - 1
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2 x = 4 x + 1
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2 x - 4 x = 4 x + 1 - 4 x
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2 x - 4 x = 4 x + 1 - 4 x
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( 2 - 4 ) x = 4 x - 4 x + 1
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-2 x = ( 4 - 4 ) x + 1
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-2 x = 1
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-2 x \times ( -2 ) = 1 \times ( -2 )
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\frac{ -2 }{ -2 } x = \frac{ 1 }{ -2 }
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x = \frac{ -1 }{ 2 }
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>>> e = Equation("2x + 3x + 1 = 4x + 2")
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>>> for i in e.solve():
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... print(" = ".join([str(j) for j in i]))
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2 x + 3 x + 1 = 4 x + 2
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( 2 + 3 ) x + 1 = 4 x + 2
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5 x + 1 = 4 x + 2
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5 x + 1 - 1 = 4 x + 2 - 1
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5 x + 1 - 1 = 4 x + 2 - 1
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5 x + 1 - 1 = 4 x + 2 - 1
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5 x = 4 x + 1
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5 x - 4 x = 4 x + 1 - 4 x
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5 x - 4 x = 4 x + 1 - 4 x
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( 5 - 4 ) x = 4 x - 4 x + 1
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x = ( 4 - 4 ) x + 1
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x = 1
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"""
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yield from self.gene_smpl_steps()
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if self.smpl_l_exp._coef[0] != 0:
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eq = Equation(
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left_poly = self.smpl_l_exp - self.smpl_l_exp._coef[0],
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right_poly = self.smpl_r_exp - self.smpl_l_exp._coef[0]
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)
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yield from eq.solve()
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return
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try:
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poly_r_part = Polynom([0, self.smpl_r_exp._coef[1]])
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except IndexError:
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pass
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else:
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if self.smpl_r_exp._coef[1] != 0:
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yield from Equation(
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left_poly = self.smpl_l_exp - poly_r_part,
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right_poly = self.smpl_r_exp - poly_r_part
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).solve()
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return
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if self.smpl_l_exp._coef[1] != 1:
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yield from Equation(
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left_poly = self.smpl_l_exp / self.smpl_l_exp._coef[1],
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right_poly = self.smpl_r_exp / self.smpl_l_exp._coef[1]
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).solve()
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return
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@no_repetition()
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def gene_smpl_steps(self):
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r"""Generate simplification steps of the equation
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>>> e = Equation("2x + 3x + 1 = 4x + 2")
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>>> e.gene_smpl_steps() # doctest:+ELLIPSIS
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<generator object Equation.gene_smpl_steps at ...>
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>>> for i in e.gene_smpl_steps():
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... print(i)
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[< Step [2, 'x', *, 3, 'x', *, +, 1, +]>, < Step [4, 'x', *, 2, +]>]
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[< Step [2, 3, +, 'x', *, 1, +]>, < Step [4, 'x', *, 2, +]>]
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[< Step [5, 'x', *, 1, +]>, < Step [4, 'x', *, 2, +]>]
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>>> e = Equation("2x + 3x + 1 = 4x + 2")
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>>> for i in e.gene_smpl_steps():
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... print(" = ".join([str(j) for j in i]))
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2 x + 3 x + 1 = 4 x + 2
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( 2 + 3 ) x + 1 = 4 x + 2
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5 x + 1 = 4 x + 2
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>>> e = Equation("3x / 3 = 5 / 3")
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>>> for i in e.gene_smpl_steps():
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... print(" = ".join([str(j) for j in i]))
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3 \times \frac{ x }{ 3 } = \frac{ 5 }{ 3 }
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\frac{ x }{ 3 } \times 3 = \frac{ 5 }{ 3 }
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\frac{ x \times 3 }{ 1 \times 3 } = \frac{ 5 }{ 3 }
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\frac{ x }{ 1 } = \frac{ 5 }{ 3 }
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x = \frac{ 5 }{ 3 }
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"""
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#yield [Step(self.l_exp), Step(self.r_exp)]
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for s in Explicable.merge_history(
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[self.smpl_l_exp, self.smpl_r_exp]
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):
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yield s
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def solution(self):
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"""Return the solution of the equation
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:returns: the solution
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>>> e = Equation("2x + 1 = x + 2")
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>>> e.solution()
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1
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>>> e = Equation("2x + 1 = 1")
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>>> e.solution()
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0
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>>> e = Equation("1 = 2x + 1")
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>>> e.solution()
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0
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>>> e = Equation("3x = 2x")
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>>> e.solution()
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0
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>>> e = Equation("3x + 1 = 0")
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>>> e.solution()
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< Fraction -1 / 3>
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>>> e = Equation("6x + 2 = 0")
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>>> e.solution()
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< Fraction -1 / 3>
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"""
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num = self.smpl_r_exp._coef[0] - self.smpl_l_exp._coef[0]
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try:
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denom = self.smpl_l_exp._coef[1]
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except IndexError:
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denom = 0
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try:
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denom -= self.smpl_r_exp._coef[1]
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except IndexError:
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pass
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if denom == 0 and num == 0:
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raise EquationError("All number are solution")
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elif denom == 0:
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raise NoSolutionError("This equation has no solution")
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return Fraction(num, denom).simplify()
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def is_solution(self, num):
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""" Tell if a number is a solution.
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:param num: the number to test
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>>> e = Equation("2x + 1 = x + 2")
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>>> e.is_solution(2)
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False
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>>> e.is_solution(1)
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True
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>>> e = Equation("3x = 2x")
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>>> e.is_solution(1)
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False
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>>> e.is_solution(0)
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True
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>>> e = Equation("3x + 1 = 0")
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>>> e.is_solution(0)
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False
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>>> e.is_solution(Fraction(-1, 3))
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True
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>>> e.is_solution(Fraction(-2, 6))
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True
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"""
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l_part = self.smpl_l_exp.replace_letter(num).simplify()
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r_part = self.smpl_r_exp.replace_letter(num).simplify()
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return l_part == r_part
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class EquationError(Exception):
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pass
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class NoSolutionError(EquationError):
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pass
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# -----------------------------
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# Reglages pour 'vim'
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# vim:set autoindent expandtab tabstop=4 shiftwidth=4:
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# cursor: 16 del
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