QEtaAlgebraBasisCategory FΒΆ
qetasamba.spad line 114 [edit on github]
- F: Type 
QEtaAlgebraBasisCategory(F) is a category for a data structure that can be used for reduction modulo an algebra basis (samba basis).
- basis: % -> List F
- basis(x)returns all basis elements.
- coerce: % -> OutputForm
- from CoercibleTo OutputForm 
- initialize: List F -> %
- initialize(m)creates an initial basis.
- multiplier: % -> F
- multiplier(x)returns multiplier element.
- multiplierPower!: (%, NonNegativeInteger) -> F
- multiplierPower!(x,n)returns multiplier element raised to power- n. Since a power of the multiplier is needed several times, this function is mainly here to allow a domain that implements this function to cache the powers.
- numberOfGaps: % -> NonNegativeInteger
- numberOfGaps(x)computes reduce(+, [floor(- x/n) for- xin bas], 0) where t=multiplier(- x), n=qetaGrade(- t) and bas=basis(- x). If #(basis(- x,- i)- =1for all- ifrom 1 to- n-1 then numberOfGaps(- x) is equal to the number of gaps (see Weierstrass Gap Theorem) of the module generated by bas over- C[- t].