Ticket #12511: 12511-I-pow.fixed.patch

sage/rings/number_field/number_field_element.pyx

@@ -50 +50 @@
 from sage.libs.all import pari_gen, pari
 from sage.libs.pari.gen import PariError
 from sage.structure.element cimport Element, generic_power_c
+from sage.structure.element import canonical_coercion
 
 QQ = sage.rings.rational_field.QQ
 ZZ = sage.rings.integer_ring.ZZ
@@ -1621 +1622 @@
             (PY_TYPE_CHECK(exp, Integer) or PY_TYPE_CHECK_EXACT(exp, int) or exp in ZZ)):
             return generic_power_c(base, exp, None)
         else:
+            cbase, cexp = canonical_coercion(base, exp)
+            if not isinstance(cbase, NumberFieldElement):
+                return cbase ** cexp
             from sage.symbolic.power_helper import try_symbolic_power
-            return try_symbolic_power(base, exp)
+            try:
+                return try_symbolic_power(base, exp)
+            except ValueError:
+                if isinstance(exp, Rational):
+                    # pynac can handle this case
+                    return None
+                else:
+                    raise
 
     cdef void _reduce_c_(self):
         """

sage/rings/rational.pyx

@@ -2262 +2262 @@
                 # this is the only sensible answer that avoids rounding and
                 # an infinite recursion.
                 from sage.symbolic.power_helper import try_symbolic_power
-                return try_symbolic_power(self, n)
+                try:
+                    return try_symbolic_power(self, n)
+                except ValueError:
+                    # pynac recognizes this and holds the value
+                    return None
 
             if PY_TYPE_CHECK(n, Element):
                 return (<Element>n)._parent(self)**n

sage/symbolic/expression.pyx

@@ -2625 +2625 @@
             2.3^(x^3 - x^2 + 1/3)
             sage: complex(1,3)^(sqrt(2))
             (1+3j)^sqrt(2)
+        
+        Test complex numeric powers::
+        
+            sage: I^0.5
+            0.707106781186548 + 0.707106781186547*I
+            sage: (I + 1) ^ (0.5 + I)
+            0.400667052375828 + 0.365310866736929*I
+            sage: I^I
+            I^I
+            sage: I^x
+            I^x
+            sage: I^(1/2)
+            sqrt(I)
+            sage: I^(2/3)
+            I^(2/3)
         """
         cdef Expression base, nexp
 

sage/symbolic/power_helper.pyx

@@ -19 +19 @@
     global __pynac_pow
     if __pynac_pow:
         __pynac_pow = False
-        return None
+        raise ValueError("recursion")
     else:
         try:
             __pynac_pow = True