17624: coerce factorizations to SR

src/sage/symbolic/ring.pyx

@@ -251,6 +251,18 @@ cdef class SymbolicRing(CommutativeRing):
             sage: bool(si == CC.0)
             True
 
+        Polynomial ring element factorizations::
+
+            sage: R.<x> = QQ[]
+            sage: SR(factor(x^2 - 1))
+            (x + 1)*(x - 1)
+            sage: R.<x,y> = QQ[]
+            sage: SR(factor(x^2 - y^2))
+            (x + y)*(x - y)
+            sage: R.<x,y,z> = QQ[]
+            sage: SR(factor(x^2*y^3 + x^2*y^2*z - x*y^3 - x*y^2*z - 2*x*y*z - 2*x*z^2 + 2*y*z + 2*z^2))
+            -(x*y^2 - 2*z)*(x - 1)*(y + z)
+
         """
         cdef GEx exp
 
@@ -271,6 +283,7 @@ cdef class SymbolicRing(CommutativeRing):
 
         from sage.rings.infinity import (infinity, minus_infinity,
                                          unsigned_infinity)
+        from sage.structure.factorization import Factorization
 
         if isinstance(x, (Integer, RealNumber, float, long, complex)):
             GEx_construct_pyobject(exp, x)
@@ -284,6 +297,9 @@ cdef class SymbolicRing(CommutativeRing):
             return new_Expression_from_GEx(self, g_UnsignedInfinity)
         elif isinstance(x, (RingElement, Matrix)):
             GEx_construct_pyobject(exp, x)
+        elif isinstance(x, Factorization):
+            from sage.misc.all import prod
+            return prod([SR(p)**e for p,e in x], SR.one())
         else:
             raise TypeError