Eliminate special cases from update_and_substitute (#138)

The tables now contain scalars, so this should work for all cases

Note that as a result of this, some multiplications now end up slightly more expanded

Author: eric-wieser

examples/ipython/Terminal.ipynb

@@ -131,11 +131,11 @@
       "[(\u001b[0;34mX\u001b[0m.\u001b[0;34me\u001b[0m), (\u001b[0;34mY\u001b[0m.\u001b[0;34me\u001b[0m),                           1]])\n",
       "(X^Y)**2 = (\u001b[0;34mX\u001b[0m.\u001b[0;34mY\u001b[0m)**2\n",
       "B =  \u001b[0;34mX\u001b[0m^\u001b[0;34mY\u001b[0m - (\u001b[0;34mY\u001b[0m.\u001b[0;34me\u001b[0m)*\u001b[0;34mX\u001b[0m^\u001b[0;34me\u001b[0m + (\u001b[0;34mX\u001b[0m.\u001b[0;34me\u001b[0m)*\u001b[0;34mY\u001b[0m^\u001b[0;34me\u001b[0m\n",
-      "B**2 = 3*(\u001b[0;34mX\u001b[0m.\u001b[0;34mY\u001b[0m)**2 - 2*(\u001b[0;34mX\u001b[0m.\u001b[0;34mY\u001b[0m)*(\u001b[0;34mX\u001b[0m.\u001b[0;34me\u001b[0m)*(\u001b[0;34mY\u001b[0m.\u001b[0;34me\u001b[0m) + 2*(\u001b[0;34mX\u001b[0m.\u001b[0;34mY\u001b[0m)*(\u001b[0;34mX\u001b[0m.\u001b[0;34me\u001b[0m)*\u001b[0;34mY\u001b[0m^\u001b[0;34me\u001b[0m - 2*(\u001b[0;34mX\u001b[0m.\u001b[0;34mY\u001b[0m)*(\u001b[0;34mX\u001b[0m.\u001b[0;34me\u001b[0m)*((\u001b[0;34mY\u001b[0m.\u001b[0;34me\u001b[0m) + \u001b[0;34mY\u001b[0m^\u001b[0;34me\u001b[0m) - 2*(\u001b[0;34mX\u001b[0m.\u001b[0;34mY\u001b[0m)*(\u001b[0;34mY\u001b[0m.\u001b[0;34me\u001b[0m)*\u001b[0;34mX\u001b[0m^\u001b[0;34me\u001b[0m + 2*(\u001b[0;34mX\u001b[0m.\u001b[0;34mY\u001b[0m)*(\u001b[0;34mY\u001b[0m.\u001b[0;34me\u001b[0m)*((\u001b[0;34mX\u001b[0m.\u001b[0;34me\u001b[0m) + \u001b[0;34mX\u001b[0m^\u001b[0;34me\u001b[0m) + 2*(\u001b[0;34mX\u001b[0m.\u001b[0;34mY\u001b[0m)*\u001b[0;34mX\u001b[0m^\u001b[0;34mY\u001b[0m - 2*(\u001b[0;34mX\u001b[0m.\u001b[0;34mY\u001b[0m)*((\u001b[0;34mX\u001b[0m.\u001b[0;34mY\u001b[0m) + \u001b[0;34mX\u001b[0m^\u001b[0;34mY\u001b[0m)\n",
+      "B**2 = (\u001b[0;34mX\u001b[0m.\u001b[0;34mY\u001b[0m)**2 - 2*(\u001b[0;34mX\u001b[0m.\u001b[0;34mY\u001b[0m)*(\u001b[0;34mX\u001b[0m.\u001b[0;34me\u001b[0m)*(\u001b[0;34mY\u001b[0m.\u001b[0;34me\u001b[0m)\n",
       "#L = X^Y^e is a non-euclidian line\n",
       "B = L*e =  \u001b[0;34mX\u001b[0m^\u001b[0;34mY\u001b[0m - (\u001b[0;34mY\u001b[0m.\u001b[0;34me\u001b[0m)*\u001b[0;34mX\u001b[0m^\u001b[0;34me\u001b[0m + (\u001b[0;34mX\u001b[0m.\u001b[0;34me\u001b[0m)*\u001b[0;34mY\u001b[0m^\u001b[0;34me\u001b[0m\n",
       "B*e*B.rev() = (\u001b[0;34mX\u001b[0m.\u001b[0;34mY\u001b[0m)*(-(\u001b[0;34mX\u001b[0m.\u001b[0;34mY\u001b[0m) + 2*(\u001b[0;34mX\u001b[0m.\u001b[0;34me\u001b[0m)*(\u001b[0;34mY\u001b[0m.\u001b[0;34me\u001b[0m))*\u001b[0;34me\u001b[0m\n",
-      "B**2 = (\u001b[0;34mX\u001b[0m.\u001b[0;34mY\u001b[0m)*((\u001b[0;34mX\u001b[0m.\u001b[0;34mY\u001b[0m) - 2*(\u001b[0;34mX\u001b[0m.\u001b[0;34me\u001b[0m)*(\u001b[0;34mY\u001b[0m.\u001b[0;34me\u001b[0m))\n",
+      "B**2 = (\u001b[0;34mX\u001b[0m.\u001b[0;34mY\u001b[0m)**2 - 2*(\u001b[0;34mX\u001b[0m.\u001b[0;34mY\u001b[0m)*(\u001b[0;34mX\u001b[0m.\u001b[0;34me\u001b[0m)*(\u001b[0;34mY\u001b[0m.\u001b[0;34me\u001b[0m)\n",
       "L**2 = (\u001b[0;34mX\u001b[0m.\u001b[0;34mY\u001b[0m)**2 - 2*(\u001b[0;34mX\u001b[0m.\u001b[0;34mY\u001b[0m)*(\u001b[0;34mX\u001b[0m.\u001b[0;34me\u001b[0m)*(\u001b[0;34mY\u001b[0m.\u001b[0;34me\u001b[0m)\n",
       "s = sinh(alpha/2) and c = cosh(alpha/2)\n",
       "exp(alpha*B/(2*|B|)) =  c\n",

galgebra/ga.py

@@ -101,16 +101,7 @@ def update_and_substitute(expr1, expr2, mul_dict):
     expr = S(0)
     for (coef1, base1) in zip(coefs1, bases1):
         for (coef2, base2) in zip(coefs2, bases2):
-            #Special cases where base1 and/or base2 is scalar
-            if base1 == 1 and base2 == 1:
-                expr += coef1 * coef2
-            elif base1 == 1:
-                expr += coef1 * coef2 * base2
-            elif base2 == 1:
-                expr += coef1 * coef2 * base1
-            else:
-                key = (base1, base2)
-                expr += coef1 * coef2 * mul_dict[key]
+            expr += coef1 * coef2 * mul_dict[base1, base2]
     return expr
 
 

test/test_test.py

@@ -198,13 +198,13 @@ def test_noneuclidian_distance_calculation(self):
         B = (L*e).expand().blade_rep() # D&L 10.152
         assert str(B) == 'X^Y - (Y.e)*X^e + (X.e)*Y^e'
         Bsq = B*B
-        assert str(Bsq) == '(X.Y)*((X.Y) - 2*(X.e)*(Y.e))'
+        assert str(Bsq) == '(X.Y)**2 - 2*(X.Y)*(X.e)*(Y.e)'
         Bsq = Bsq.scalar()
         assert str(B) == 'X^Y - (Y.e)*X^e + (X.e)*Y^e'
 
         BeBr = B*e*B.rev()
         assert str(BeBr) == '(X.Y)*(-(X.Y) + 2*(X.e)*(Y.e))*e'
-        assert str(B*B) == '(X.Y)*((X.Y) - 2*(X.e)*(Y.e))'
+        assert str(B*B) == '(X.Y)**2 - 2*(X.Y)*(X.e)*(Y.e)'
         assert str(L*L) == '(X.Y)**2 - 2*(X.Y)*(X.e)*(Y.e)' # D&L 10.153
 
         (s,c,Binv,M,S,C,alpha) = symbols('s c (1/B) M S C alpha')