Ticket #7828: trac_7828-sign.patch

sage/functions/all.py

@@ -60 +60 @@
 from wigner import (wigner_3j, clebsch_gordan, racah, wigner_6j,
                     wigner_9j, gaunt)
 
-from generalized import (dirac_delta, heaviside, unit_step, sgn, 
+from generalized import (dirac_delta, heaviside, unit_step, sgn, sign, 
                          kronecker_delta)
 
 from min_max import max_symbolic, min_symbolic

sage/functions/generalized.py

@@ -402 +402 @@
         sage: sgn(x)
         sgn(x)
 
+    We can also use ``sign``::
+
+        sage: sign(1)
+        1
+        sage: sign(0)
+        0
+        sage: a = AA(-5).nth_root(7)
+        sage: sign(a)
+        -1
+
     REFERENCES:
  
     -  http://en.wikipedia.org/wiki/Sign_function
@@ -449 +459 @@
             0
             sage: sgn(x).subs(x=-1)
             -1
+
+        More tests::
+
+            sage: sign(RR(2))
+            1
+            sage: sign(RDF(2))
+            1
+            sage: sign(AA(-2))
+            -1
+            sage: sign(AA(0))
+            0
         """
+        if hasattr(x,'sign'): # First check if x has a sign method
+            return x.sign()
         try:
             approx_x = ComplexIntervalField()(x)
             if bool(approx_x.imag() == 0):      # x is real
@@ -477 +500 @@
         return 2*dirac_delta(x)
 
 sgn = FunctionSignum()
+sign = sgn
 
 class FunctionKroneckerDelta(BuiltinFunction):
     r"""