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Sheafhom: software for sparse integer matrices. (English) Zbl 1140.13300
Summary: Sheafhom is a free software package for large-scale computations in the category of finitely-generated modules over the integers and related rings. Its front end is a language for problems in algebraic topology and geometry. These problems come down to sparse systems of linear equations over the integers. Sheafhom’s back end solves the sparse systems, with emphasis on avoiding fill-in and integer explosion. We survey and compare algorithms for integer sparse matrices, and we present implementation techniques in Common Lisp. The final section finds the quotient of the free abelian group on 26 letters by sets of words in the dictionary, in the spirit of J.-F. Mestre et al. [Exp. Math. 2, No. 3, 153–155 (1993; Zbl 0818.20033)].
MSC:
13-04 Software, source code, etc. for problems pertaining to commutative algebra
68W30 Symbolic computation and algebraic computation
13P99 Computational aspects and applications of commutative rings
14Q99 Computational aspects in algebraic geometry
14-04 Software, source code, etc. for problems pertaining to algebraic geometry
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