Multivariate powerseries with symbolic coefficients issues

[vbraun]

Multivariate powerseries over SR seem to work, but coercion does not. For example, the coercion from ZZ to QQ works fine:

sage: T.<a,b> = PowerSeriesRing(ZZ,2)
sage: f = 1 + a + b + a*b + T.O(5)
sage: 1/2 * f
1/2 + 1/2*a + 1/2*b + 1/2*a*b + O(a, b)^5

but the same thing fails with SR:

sage: exp(2) * f
---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)

/home/vbraun/opt/sage-4.8.alpha4/devel/sage-main/sage/schemes/generic/<ipython console> in <module>()

/home/vbraun/opt/sage-4.8.alpha4/local/lib/python2.6/site-packages/sage/structure/element.so in sage.structure.element.RingElement.__mul__ (sage/structure/element.c:12158)()

/home/vbraun/opt/sage-4.8.alpha4/local/lib/python2.6/site-packages/sage/structure/coerce.so in sage.structure.coerce.CoercionModel_cache_maps.bin_op (sage/structure/coerce.c:7467)()

TypeError: unsupported operand parent(s) for '*': 'Symbolic Ring' and 'Multivariate Power Series Ring in a, b over Integer Ring'

Also, manually changing the base ring brings out the background polynomial variable:

sage: f.change_ring(SR)
(Tbg*a*b + a + b)*Tbg + 1 + O(a, b)^5

CC: @nilesjohnson

Component: commutative algebra

Keywords: multivariate power series

Issue created by migration from https://trac.sagemath.org/ticket/12240