38.28 Algebra Records

Algebras and their subalgebras are represented by records. Once an algebra record is created you may add record components to it but you must not alter information already present.

Algebra records must always contain the components isDomain and isAlgebra. Subalgebras contain an additional component parent. The components generators, zero and one are not necessarily contained.

The contents of important record components of an algebra A is described below.

The category components are

isDomain:

is true.

isAlgebra:

is true.

isUnitalAlgebra:

is present (and then true) if A is a unital algebra.

The identification components are

field:

is the coefficient field of A.

generators:

is a list of algebra generators. Duplicate generators are allowed, also the algebra zero may be among the generators. Note that once created this entry must never be changed, as most of the other entries depend on generators. If generators is not bound it can be computed using Generators.

parent:

if present this contains the algebra record of the parent algebra of a subalgebra A, otherwise A itself is a parent algebra.

zero:

is the additive neutral element of A, can be computed using Zero.

The component operations contains the operations record of A. This will usually be one of AlgebraOps, UnitalAlgebraOps, or a record for more specific algebras.

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