33.26 Functions for Quotient Spaces

Computations in quotient spaces usually delegate the work to computations in numerator and denominator.

The following functions are overlaid in the operations record for quotient spaces.

The set theoretic functions

Closure, Elements, IsSubset, Intersection,

and the vector space functions

Base( V ) :

returns the vectors of the canonical basis of V,

Generators( V ) :

returns a list of cosets that generate V,

CanonicalBasis( V ) :

returns the canonical basis of <V> = W / U, this is derived from the canonical basis of W.

SemiEchelonBasis( V )

SemiEchelonBasis( V, vectors ) :

return a semi-echelonized basis of the quotient space V. vectors can be a list of elements of V, or of representatives.

Basis( V )

Basis( V, vectors ) :

return a basis of the quotient space V. vectors can be a list of elements of V, or of representatives.

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