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1 Introduction
 1.1 Nilpotent associative algebras and canonical forms

1 Introduction

This package contains implementations of the algorithms described in [EM17]. Namely it contains a descendants algorithm for nilpotent associative algebras and a method to calculate the roots of maximal descendant trees in the coclass graph associated to the nilpotent associative F-algebras of coclass r. The implementation relies on the ModIsom package, especially the representation of nilpotent associative F-algebras by canonical forms, see [Eic11] for details.

1.1 Nilpotent associative algebras and canonical forms

For convenience a lot of the functions in this package are implemented for canonical forms and for nilpotent associative algebras. Only the functions taking canonical forms as input are documented. The corresponding functions for nilpotent associative algebras are named similar to the ones for canonical forms, replacing CanoForm by NAAlg. One can convert between the two types using the following functions.

1.1-1 NAAlgByCanoForm
‣ NAAlgByCanoForm( C )( operation )

Converts a canonical form C to a nilpotent associative algebra.

1.1-2 CanoFormByNAAlg
‣ CanoFormByNAAlg( A )( operation )

Converts a nilpotent associative algebra A to a canonical form.

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