Use sympy scalars in more places (#179)

This reduces the chance of obtaining imprecise floating-point numbers when dividing at the call site.

Far from an exhaustive replacement.

Author: eric-wieser

galgebra/deprecated.py

@@ -1,6 +1,6 @@
 import copy
 from itertools import combinations
-from sympy import trigsimp
+from sympy import trigsimp, S
 from . import ga
 from .mv import Mv
 from . import utils
@@ -63,7 +63,7 @@ def ReciprocalFrame(basis, mode='norm'):
     for igrade in index[-2:]:
         grade = []
         for iblade in igrade:
-            blade = Mv(1, 'scalar', ga=GA)
+            blade = Mv(S(1), 'scalar', ga=GA)
             for ibasis in iblade:
                 blade ^= basis[ibasis]
             blade = blade.trigsimp()
@@ -75,7 +75,7 @@ def ReciprocalFrame(basis, mode='norm'):
     duals = copy.copy(MFbasis[-2])
 
     duals.reverse()
-    sgn = 1
+    sgn = S(1)
     rbasis = []
     for dual in duals:
         recpv = (sgn * dual * E).trigsimp()

galgebra/ga.py

@@ -1023,7 +1023,7 @@ def reduce_basis_loop(g, blst):
 
     @staticmethod
     def blade_reduce(lst):
-        sgn = 1
+        sgn = S(1)
         for i in range(1, len(lst)):
             save = lst[i]
             j = i
@@ -1033,7 +1033,7 @@ def blade_reduce(lst):
                 j -= 1
             lst[j] = save
             if lst[j] == lst[j - 1]:
-                return 0, None
+                return S(0), None
         return sgn, lst
 
     def wedge_product_basis_blades(self, blade12):  # blade12 = blade1*blade2
@@ -1045,12 +1045,12 @@ def wedge_product_basis_blades(self, blade12):  # blade12 = blade1*blade2
         index12 = list(index1 + index2)
 
         if len(index12) > self.n:
-            return 0
+            return S(0)
         (sgn, wedge12) = Ga.blade_reduce(index12)
         if sgn != 0:
             return(sgn * self.indexes_to_blades_dict[tuple(wedge12)])
         else:
-            return 0
+            return S(0)
 
     #****** Dot (|) product, reft (<) and right (>) contractions ******#
 
@@ -1089,8 +1089,8 @@ def dot_product_basis_blades(self, blade12, mode):
             return zero
 
         n = len(index)
-        sgn = 1
-        result = 1
+        sgn = S(1)
+        result = S(1)
         ordered = False
         while n > grade:
             ordered = True
@@ -1102,7 +1102,7 @@ def dot_product_basis_blades(self, blade12, mode):
                 if index1 == index2:
                     n -= 2
                     if n < grade:
-                        return 0
+                        return zero
                     result *= self.g[index1, index1]
                     index = index[:i1] + index[i2 + 1:]
                 elif index1 > index2:
@@ -1116,7 +1116,7 @@ def dot_product_basis_blades(self, blade12, mode):
             if ordered:
                 break
         if n > grade:
-            return 0
+            return zero
         else:
             if index == []:
                 return sgn * result