[Axiom-mail] A question about Axiom capabilities

[Mike Valenzuela]

Hello, I'm investigating several CA systems currently and I am wondering if Axiom has certain capabilities.

Specifically:

(A) Differentiation through indefinite sums with respect to indexed/subscripted variables. E.g., D( sum(p[i]*x[i],i)^2, j ) --> 2* p[j] * sum(p[i]*x[i],i)

(B) Matrix Calculus. E.g., 
  D( sum( p[k] * multivariate_normal(mu[k], Sigma[k]), k), Sigma[j] ) -->  Some large awful thing defined in equation 373 from the Matrix Cookbook, Version: November 14, 2008.

As I do some work with random variables and certainty equivalents, it would be nice to find a CAS that allows me to easily double check my math.