FractionalIdealAsModule(R, F, UP, A, ibasis)

divisor.spad line 463 [edit on github]

• R: EuclideanDomain

• F: QuotientFieldCategory R

• UP: UnivariatePolynomialCategory F

• A: FramedAlgebra(F, UP)

• ibasis: Vector A

Module representation of fractional ideals.

1: %

from MagmaWithUnit

*: (%, %) -> %

from Magma

=: (%, %) -> Boolean

from BasicType

^: (%, NonNegativeInteger) -> %

from MagmaWithUnit

^: (%, PositiveInteger) -> %

from Magma

~=: (%, %) -> Boolean

from BasicType

basis: % -> Vector A

basis((f1, ..., fn)) = the vector [f1, ..., fn].

coerce: % -> OutputForm

from CoercibleTo OutputForm

latex: % -> String

from SetCategory

leftPower: (%, NonNegativeInteger) -> %

from MagmaWithUnit

leftPower: (%, PositiveInteger) -> %

from Magma

leftRecip: % -> Union(%, failed)

from MagmaWithUnit

module: FractionalIdeal(R, F, UP, A) -> % if A has RetractableTo F

module(I) returns I viewed has a module over R.

module: Vector A -> %

module([f1, ..., fn]) = the module generated by (f1, ..., fn) over R.

norm: % -> F

norm(f) returns the norm of the module f.

one?: % -> Boolean

from MagmaWithUnit

recip: % -> Union(%, failed)

from MagmaWithUnit

rightPower: (%, NonNegativeInteger) -> %

from MagmaWithUnit

rightPower: (%, PositiveInteger) -> %

from Magma

rightRecip: % -> Union(%, failed)

from MagmaWithUnit

sample: %

from MagmaWithUnit

BasicType

CoercibleTo OutputForm

Magma

MagmaWithUnit

Monoid

SemiGroup

SetCategory