From 65ba8f3f04bbd75a061caa89b4d2389cfca15f23 Mon Sep 17 00:00:00 2001
From: lafrite <lafrite@poneyworld.net>
Date: Sat, 18 Jan 2014 17:08:04 +0100
Subject: [PATCH] formal multiplication done, need to simplify keys

---
 formal.py  | 89 ++++++++++++++++++++++++++++++++++++++----------------
 generic.py | 16 +++++++---
 2 files changed, 74 insertions(+), 31 deletions(-)

diff --git a/formal.py b/formal.py
index ca837c5..861a8bb 100644
--- a/formal.py
+++ b/formal.py
@@ -2,7 +2,7 @@
 # encoding: utf-8
 
 from fraction import Fraction
-from generic import add_in_dict, remove_in_dict
+from generic import add_in_dict, remove_in_dict, convolution_dict
 import re
 
 class FormalExp(object):
@@ -51,20 +51,39 @@ class FormalExp(object):
         m_power = max(power)
         return power[m_power]
 
-    def __add__(self, other):
+    def check_calculous(self, other):
+        """Check if other is a constant and then transform it into a dictionary compatible with FormalExp
+
+        :param other: The thing to compute with the expression
+        :returns: dictionary of this thing
+
+        """
         if type(other) in [int, Fraction]:
-            d = {"":other}
+            return {"":other}
         elif type(other) == FormalExp:
-            d = other._coef
+            return other._coef.copy()
         else:
             raise ValueError("Can't add {type} with FormalExp".format(type=type(other)))
 
+    def const_or_formal(self, d):
+        """Return a constant if there is nothing else, FormalExp otherwise
+
+        :param d: dictionary descripting the expression
+        :returns: a constant or a FormalExp
+
+        """
+        if list(d.keys()) == ['']:
+            return d['']
+        else:
+            return FormalExp(d)
+
+    def __add__(self, other):
+        d = self.check_calculous(other)
+
         d = add_in_dict(self._coef, d)
         d = remove_in_dict(d)
-        if list(d.keys()) == ['']:
-            return [d['']]
-        else:
-            return [FormalExp(d)]
+
+        return [self.const_or_formal(d)]
 
     def __radd__(self, other):
         return self + other
@@ -80,15 +99,35 @@ class FormalExp(object):
         return FormalExp(d)    
 
     def __mul__(self, other):
-        pass
+        d = self.check_calculous(other)
+
+        d = convolution_dict(self._coef, d, op_key = self.op_key)
+        d = remove_in_dict(d)
+
+        return [self.const_or_formal(d)]
+
+    def op_key(self, x,y):
+        """Operation on keys for convolution_dict"""
+        if x == "" or y == "":
+            return x+y
+        else:
+            return x + "*" + y
+
     
     def __rmul__(self, other):
-        pass
+        d = self.check_calculous(other)
+
+        d = convolution_dict(d, self._coef, op_key = self.op_key)
+        d = remove_in_dict(d)
+
+        return [self.const_or_formal(d)]
 
     def __div__(self, other):
+        # Will never be done :D
         pass
     
     def __pow__(self, other):
+        # Will never be done :D quoique
         pass
 
     def __len__(self):
@@ -98,26 +137,24 @@ class FormalExp(object):
         return " + ".join([str(v) + str(k) for k,v in self._coef.items()])
     
 if __name__ == '__main__':
-    #fe1 = FormalExp({"x": 1, "":2})    
-    #print(fe1)
-    #fe2 = FormalExp({"x**12": 5, "":2})    
-    #print(fe2)
-    #fe3 = fe1 + fe2
-    #for s in fe3:
-    #    print(s)
-    #fe4 = fe1 + 2
-    #for s in fe4:
-    #    print(s)
-
-    #print(fe1.master_coef())
-    #print(fe2.master_coef())
-    #print(fe3[0].master_coef())
-    #print(fe4[0].master_coef())
+    fe1 = FormalExp({"x": 1, "":2})    
+    print(fe1)
+    fe2 = FormalExp({"x**12": 5, "":2})    
+    print(fe2)
+    fe3 = fe1 * fe2
+    for s in fe3:
+        print(s)
+    fe4 = fe1 * 2
+    for s in fe4:
+        print(s)
 
     fe = FormalExp(letter = "a")
-    fe_ = -2 + fe
+    fe_ = -2 * fe
     print(fe_[0])
 
+    fe = FormalExp(letter = "a")
+    fe_ = fe * (-2)
+    print(fe_[0])
 
 
 
diff --git a/generic.py b/generic.py
index 5c78ce3..3bb88a3 100644
--- a/generic.py
+++ b/generic.py
@@ -144,6 +144,7 @@ def remove_in_dict(d, value = 0):
     return new_dict
 
 def convolution_dict(D1, D2, op = lambda x,y:x*y,\
+        op_key = lambda x,y: x + y, \
         commutative = True, op_twice = lambda x,y: x + y):
     """Convolution of two dictionaries
 
@@ -170,12 +171,17 @@ def convolution_dict(D1, D2, op = lambda x,y:x*y,\
 
     for k1 in sorted(D1.keys()):
         for k2 in sorted(D2.keys()):
-            if k1+k2 in new_dict.keys():
-                new_dict[k1+k2] = op_twice(new_dict[k1+k2], op(D1[k1],D2[k2]))
-            elif k2+k1 in new_dict.keys() and commutative:
-                new_dict[k2+k1] = op_twice(new_dict[k2+k1], op(D1[k1],D2[k2]))
+            if op_key(k1,k2) in new_dict.keys():
+                key = op_key(k1,k2)
+                new_dict[key] = op_twice(new_dict[key], op(D1[k1],D2[k2]))
+
+            elif op_key(k2,k1) in new_dict.keys() and commutative:
+                key = op_key(k1,k2)
+                new_dict[key] = op_twice(new_dict[key], op(D1[k1],D2[k2]))
+
             else:
-                new_dict[k1+k2] = op(D1[k1],D2[k2])
+                key = op_key(k1,k2)
+                new_dict[key] = op(D1[k1],D2[k2])
 
     return new_dict