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The CREAM GAP package computes automorphisms, congruences, endomorphisms andsubalgebras of algebras with an arbitrary number of binary and unaryoperations; it also decides if between two such algebras there exists amonomorphism, an epimorphism, an isomorphism or if one is a divisor of theother. Thus it finds those objects for almost all algebras used in practice(groups, quasigroups in their various signatures, semigroups possibly with manyunary operations, fields, semi-rings, quandles, logic algebras, etc).  As a one-size-fits-all package, it only relies on universal algebra theorems,without taking advantage of specific theorems about, eg, groups or semigroupsto reduce the search space. Canon and Holt produced very fast code to computeautomorphisms of groups that outperform CREAM on orders larger than 128.Similarly, Mitchell et al. take advantage of deep theorems to computeautomorphisms and congruences of completely 0-simple semigroups in a veryefficient manner. However these domains (groups of order above 128 andcompletely 0-simple semigroups) are among the very few examples of GAP codefaster than our general purpose package CREAM. For the overwhelming majority ofother classes of algebras, either ours is the first code computing the abovementioned objects, or the existing algorithms are outperformed by CREAM, insome cases by several orders of magnitude.  To get this performance, CREAM uses a mixture of universal algebra algorithmstogether with GAP coupled with artificial intelligence theorem proving tools(AITP) and very delicate C implementations. As an example of the latter, were-implement Freese's very clever algorithm for computing congruences inuniversal algebras, in a way that outperforms all other known implementations.

CREAM: a Package to Compute [Auto, Endo, Iso, Mono, Epi]-morphisms, Congruences, Divisors and More for Algebras of Type $(2^n,1^n)$