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solve eq if know ok

This commit is contained in:
Benjamin Bertrand 2016-03-22 11:48:29 +03:00
parent 1b6bd56f8a
commit cff75c1fec
1 changed files with 57 additions and 23 deletions
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80
pymath/calculus/equation.py
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@ -4,6 +4,8 @@
from .explicable import Explicable
from .expression import Expression
from .step import Step
from .decorators import no_repetition
from .polynom import Polynom
from .fraction import Fraction
@ -71,7 +73,9 @@ class Equation(object):
""" 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_l_exp.steal_history(self.l_exp)
self.smpl_r_exp = self.r_exp.simplify()
self.smpl_r_exp.steal_history(self.r_exp)
try:
self.smpl_r_exp = self.smpl_l_exp.conv2poly(self.smpl_r_exp)
@ -96,48 +100,75 @@ class Equation(object):
r = self.r_exp,
)
#@no_repetition(lambda x, y: (x[0] == y[0]) & (x[1] == y[1]))
@no_repetition()
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]>]
... print(" = ".join([str(j) for j in i]))
x + 123 = 0
x + 123 - 123 = 0 - 123
x + 123 - 123 = 0 - 123
x + 123 - 123 = -123
x = -123
>>> e = Equation("2x = x + 2")
>>> for i in e.solve():
... print(i)
[< Step [2, 'x', *]>, < Step ['x', 2, +]>]
[< Step ['x']>, < Step [2]>]
... print(" = ".join([str(j) for j in i]))
2 x = x + 2
2 x - x = x + 2 - x
2 x - x = x + 2 - x
( 2 - 1 ) x = x - x + 2
x = ( 1 - 1 ) x + 2
x = 2
>>> e = Equation("2x = 1")
>>> for i in e.solve():
... print(i)
[< Step [2, 'x', *]>, < Step [1]>]
[< Step ['x']>, < Step [1, 2, /]>]
... print(" = ".join([str(j) for j in i]))
2 x = 1
2 x \times 2 = 1 \times 2
\frac{ 2 }{ 2 } x = \frac{ 1 }{ 2 }
x = \frac{ 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, /]>]
... print(" = ".join([str(j) for j in i]))
2 x + 1 = 4 x + 2
2 x + 1 - 1 = 4 x + 2 - 1
2 x + 1 - 1 = 4 x + 2 - 1
2 x + 1 - 1 = 4 x + 2 - 1
2 x = 4 x + 1
2 x - 4 x = 4 x + 1 - 4 x
2 x - 4 x = 4 x + 1 - 4 x
( 2 - 4 ) x = 4 x - 4 x + 1
-2 x = ( 4 - 4 ) x + 1
-2 x = 1
-2 x \times ( -2 ) = 1 \times ( -2 )
\frac{ -2 }{ -2 } x = \frac{ 1 }{ -2 }
x = \frac{ -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]>]
... 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
5 x + 1 - 1 = 4 x + 2 - 1
5 x + 1 - 1 = 4 x + 2 - 1
5 x + 1 - 1 = 4 x + 2 - 1
5 x = 4 x + 1
5 x - 4 x = 4 x + 1 - 4 x
5 x - 4 x = 4 x + 1 - 4 x
( 5 - 4 ) x = 4 x - 4 x + 1
x = ( 4 - 4 ) x + 1
x = 1
"""
yield from self.gene_smpl_steps()
if self.smpl_l_exp._coef[0] != 0:
yield from Equation(
eq = 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()
)
yield from eq.solve()
return
try:
@ -159,6 +190,7 @@ class Equation(object):
).solve()
return
@no_repetition()
def gene_smpl_steps(self):
r"""Generate simplification steps of the equation
@ -186,6 +218,8 @@ class Equation(object):
x = \frac{ 5 }{ 3 }
"""
#yield [Step(self.l_exp), Step(self.r_exp)]
for s in Explicable.merge_history(
[self.smpl_l_exp, self.smpl_r_exp]
):