Change isBlade to work on degenerate metrics

clifford/_multivector.py

@@ -2,6 +2,7 @@
 import math
 from typing import List, Set, Tuple, Union
 import warnings
+import operator
 
 import numpy as np
 
@@ -645,33 +646,45 @@ def isScalar(self) -> bool:
 
         return True
 
-    def isBlade(self) -> bool:
+    def isBlade(self, *, invertible=False) -> bool:
         """Returns true if multivector is a blade.
         """
-        if len(self.grades()) != 1:
+        if len(self.grades()) > 1:
             return False
 
-        return self.isVersor()
+        return self.isVersor(invertible=invertible)
 
-    def isVersor(self) -> bool:
+    def isVersor(self, *, invertible=True) -> bool:
         """Returns true if multivector is a versor.
         From :cite:`ga4cs` section 21.5, definition from 7.6.4
         """
+        if invertible:
+            grade_cmp = operator.eq
+        else:
+            grade_cmp = operator.le  # subset
+
         Vhat = self.gradeInvol()
         Vrev = ~self
-        Vinv = Vrev/(self*Vrev)[()]
+        mag = (self*Vrev)[()]
+        if mag != 0:
+            # not strictly necessary, just scales to make eps appropriate below
+            Vinv = Vrev / mag
+        elif invertible:
+            return False
+        else:
+            Vinv = Vrev
 
         # Test if the versor inverse (~V)/(V * ~V) is truly the inverse of the
         # multivector V
-        if (Vhat*Vinv).grades(eps=0.000001) != {0}:
+        if not grade_cmp((Vhat*Vinv).grades(eps=0.000001), {0}):
             return False
         if not np.sum(np.abs((Vhat*Vinv).value - (Vinv*Vhat).value)) < 0.0001:
             return False
 
         # applying a versor (and hence an invertible blade) to a vector should
         # not change the grade
         if not all(
-            (Vhat*e*Vrev).grades(eps=0.000001) == {1}
+            grade_cmp((Vhat*e*Vrev).grades(eps=0.000001), {1})
             for e in cf.basis_vectors(self.layout).values()
         ):
             return False

clifford/test/test_clifford.py

@@ -631,14 +631,33 @@ def test_categorization(self, g3):
             assert v.isVersor()
 
         neither = [
-            layout.scalar*0,
             1 + e1,
             1 + (e1^e2^e3)
         ]
         for n in neither:
             assert not n.isBlade()
             assert not n.isVersor()
 
+    def test_categorization_null(self, g3c):
+        layout = g3c
+        e1 = layout.blades['e1']
+
+        blades = [
+            layout.scalar*0,
+            layout.einf,
+            layout.eo,
+            e1^layout.eo
+        ]
+        for b in blades:
+            # none of these are invertible
+            assert not b.isBlade(invertible=True)
+            assert not b.isVersor(invertible=True)
+
+            # but if we allow them to be non-invertible, they are blades and
+            # versors
+            assert b.isBlade(invertible=False)
+            assert b.isVersor(invertible=False)
+
     def test_blades_of_grade(self, g3):
         layout = g3
         e1 = layout.blades['e1']

clifford/test/test_degenerate.py

@@ -46,6 +46,15 @@ def POINT(x, y, z):
         L = P1 & P2
         assert L == -(4^e01) + (3^e02) - (1^e12) - (4^e13) + (3^e23)
 
+    def test_is_blade(self):
+        blades = self.layout.blades
+        e0 = blades['e0']
+        e1 = blades['e1']
+
+        for b in [e0, e0^e1]:
+            assert e0.isBlade()
+            assert not e0.isBlade(invertible=True)
+
     def test_no_crash(self):
         """ TODO: This doesn't actually do any asserts! """
         layout = self.layout