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.
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