9.3 Vector Space Records

A vector space is represented as a GAP record having several entries to hold some necessary information about the vector space.

Basically a vector space record is constructed using the function VectorSpace although one may create such a record by hand. Furthermore vector space records may be returned by functions described here or somewhere else in this manual.

Once a vector space record is created you are free to add components, but you should never alter existing entries, especially generators, field and zero.

The following list mentions all components that are requested for a vector space V.

generators:

a list of elements generating the vector space V.

field:

the field over which the vector space V is written.

zero:

the zero element of the vector space.

isDomain:

always true, because vector spaces are domains.

isVectorSpace:

always true, for obvious reasons.

There are as well some optional components for a vector space record.

base:

a base for V, given as a list of elements of V.

dimension:

the dimension of V which is the length of a base of V.

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