Mapytex/pymath/calculus/equation.py

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#!/usr/bin/env python
# encoding: utf-8
from .explicable import Explicable
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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"""
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@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))
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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 }
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"""
for s in Explicable.merge_history(
[self.smpl_l_exp, self.smpl_r_exp]
):
yield s
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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'
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# cursor: 16 del