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

View File

@ -4,6 +4,8 @@
from .explicable import Explicable from .explicable import Explicable
from .expression import Expression from .expression import Expression
from .step import Step
from .decorators import no_repetition
from .polynom import Polynom from .polynom import Polynom
from .fraction import Fraction 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 """ 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 = 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 = self.r_exp.simplify()
self.smpl_r_exp.steal_history(self.r_exp)
try: try:
self.smpl_r_exp = self.smpl_l_exp.conv2poly(self.smpl_r_exp) self.smpl_r_exp = self.smpl_l_exp.conv2poly(self.smpl_r_exp)
@ -96,48 +100,75 @@ class Equation(object):
r = self.r_exp, r = self.r_exp,
) )
#@no_repetition(lambda x, y: (x[0] == y[0]) & (x[1] == y[1]))
@no_repetition()
def solve(self): def solve(self):
r"""Solve the equation but yielding each steps r"""Solve the equation but yielding each steps
>>> e = Equation("x + 123 = 0") >>> e = Equation("x + 123 = 0")
>>> for i in e.solve(): >>> for i in e.solve():
... print(i) ... print(" = ".join([str(j) for j in i]))
[< Step ['x', 123, +]>, < Step [0]>] x + 123 = 0
[< Step ['x']>, < Step [-123]>] x + 123 - 123 = 0 - 123
x + 123 - 123 = 0 - 123
x + 123 - 123 = -123
x = -123
>>> e = Equation("2x = x + 2") >>> e = Equation("2x = x + 2")
>>> for i in e.solve(): >>> for i in e.solve():
... print(i) ... print(" = ".join([str(j) for j in i]))
[< Step [2, 'x', *]>, < Step ['x', 2, +]>] 2 x = x + 2
[< Step ['x']>, < Step [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") >>> e = Equation("2x = 1")
>>> for i in e.solve(): >>> for i in e.solve():
... print(i) ... print(" = ".join([str(j) for j in i]))
[< Step [2, 'x', *]>, < Step [1]>] 2 x = 1
[< Step ['x']>, < Step [1, 2, /]>] 2 x \times 2 = 1 \times 2
\frac{ 2 }{ 2 } x = \frac{ 1 }{ 2 }
x = \frac{ 1 }{ 2 }
>>> e = Equation("2x + 1 = 4x + 2") >>> e = Equation("2x + 1 = 4x + 2")
>>> for i in e.solve(): >>> for i in e.solve():
... print(i) ... print(" = ".join([str(j) for j in i]))
[< Step [2, 'x', *, 1, +]>, < Step [4, 'x', *, 2, +]>] 2 x + 1 = 4 x + 2
[< Step [2, 'x', *]>, < Step [4, 'x', *, 1, +]>] 2 x + 1 - 1 = 4 x + 2 - 1
[< Step [-2, 'x', *]>, < Step [1]>] 2 x + 1 - 1 = 4 x + 2 - 1
[< Step ['x']>, < Step [-1, 2, /]>] 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") >>> e = Equation("2x + 3x + 1 = 4x + 2")
>>> for i in e.solve(): >>> for i in e.solve():
... print(i) ... print(" = ".join([str(j) for j in i]))
[< Step [2, 'x', *, 3, 'x', *, +, 1, +]>, < Step [4, 'x', *, 2, +]>] 2 x + 3 x + 1 = 4 x + 2
[< Step [2, 3, +, 'x', *, 1, +]>, < Step [4, 'x', *, 2, +]>] ( 2 + 3 ) x + 1 = 4 x + 2
[< Step [5, 'x', *, 1, +]>, < Step [4, 'x', *, 2, +]>] 5 x + 1 = 4 x + 2
[< Step [5, 'x', *, 1, +, 1, -]>, < Step [4, 'x', *, 2, +, 1, -]>] 5 x + 1 - 1 = 4 x + 2 - 1
[< Step [5, 'x', *]>, < Step [4, 'x', *, 1, +]>] 5 x + 1 - 1 = 4 x + 2 - 1
[< Step ['x']>, < Step [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() yield from self.gene_smpl_steps()
if self.smpl_l_exp._coef[0] != 0: 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], left_poly = self.smpl_l_exp - self.smpl_l_exp._coef[0],
right_poly = self.smpl_r_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 return
try: try:
@ -159,6 +190,7 @@ class Equation(object):
).solve() ).solve()
return return
@no_repetition()
def gene_smpl_steps(self): def gene_smpl_steps(self):
r"""Generate simplification steps of the equation r"""Generate simplification steps of the equation
@ -186,6 +218,8 @@ class Equation(object):
x = \frac{ 5 }{ 3 } x = \frac{ 5 }{ 3 }
""" """
#yield [Step(self.l_exp), Step(self.r_exp)]
for s in Explicable.merge_history( for s in Explicable.merge_history(
[self.smpl_l_exp, self.smpl_r_exp] [self.smpl_l_exp, self.smpl_r_exp]
): ):