From cff75c1fecaa3b12148db851ffbe9c00943cd9c4 Mon Sep 17 00:00:00 2001
From: Benjamin Bertrand <lafrite@poneyworld.net>
Date: Tue, 22 Mar 2016 11:48:29 +0300
Subject: [PATCH] solve eq if know ok

---
 pymath/calculus/equation.py | 80 ++++++++++++++++++++++++++-----------
 1 file changed, 57 insertions(+), 23 deletions(-)

diff --git a/pymath/calculus/equation.py b/pymath/calculus/equation.py
index ffb91e8..b900ff5 100644
--- a/pymath/calculus/equation.py
+++ b/pymath/calculus/equation.py
@@ -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]
                 ):