It has pattern matching, Groebner basis computations, expression simplification, series expansion, numerical integration, etc.
Deep down every CAS is about manipulating polynomials :)
Deep down every CAS is about manipulating polynomials :)
Maxima is a system for the manipulation of symbolic and numerical expressions, including differentiation, integration, Taylor series, Laplace transforms, ordinary differential equations, systems of linear equations, polynomials, sets, lists, vectors, matrices and tensors.It is not just a matter of whether a feature is there, it needs to be usable in practice. You cannot use Maxima to do computation with large rational polynomials as this paper shows:
https://arxiv.org/pdf/2304.13418
Symbolica is 10 times faster and uses 60 times less memory than Maxima on a medium-sized problem. The larger sized problem does not run with Maxima. Note that this is tested with an older version of Symbolica, the latest version is even faster.
Sith SBCL, open maxima and run:
load("maximalocal.mac");
:lisp (sb-ext:save-lisp-and-die "maxima-optimised" :toplevel #'run :executable t)
Hah...change "Maxima" to "Macsyma" and "Symbolica" to "SMP" and that is close to a slide I remember seeing around 1980 in a presentation by Wolfram and Cole explaining why they had developed a new computer algebra system, SMP, instead of using one of the already available systems.
I don't remember the exact numbers on their slide, but same situation. Existing systems could handle the medium problems that came up in their physics research but were slow and used a lot of memory, and could not do the large problems.