Finitely Presented Associative Algebras (New Version) [HB 73]

In V2.11 finitely-presented (FP) associative algebras are handled by an extension of the commutative algebra machinery to noncommutative data structures and algorithms, where applicable. These include a noncommutative analogue for Gröbner bases.

Features:

• Construction of free algebras over arbitrary fields.
• Arithmetic.
• Mappings into other associative algebras.
• Definition of left, right, two-sided ideals.
• Noncommutative Gröbner bases of ideals, with specialized algorithms for different coefficient fields (fraction-free methods for the rational field and rational function fields).
• Gröbner bases of ideals over finite fields and rationals, using noncommutative extension of the Faugère F4 algorithm.
• Construction of degree-d (truncated) Gröbner bases.
• Normal form of a polynomial with respect to an ideal.
• Construction of FP-algebras as quotient rings.
• Enumeration of the basis of finite-dimensional FP algebras.
• Matrix and structure-constant representations of finite-dimensional FP algebras.
• Construction of a matrix representation (Linton's vector enumerator).