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

divisor.spad line 462 [edit on github]

• R : EuclideanDomain
• F : QuotientFieldCategory(R)
• UP : UnivariatePolynomialCategory(F)
• A : FramedAlgebra(F, UP)
• ibasis : Vector(A)

Module representation of fractional ideals.

* : (%, %) -> %

from Magma

1 : () -> %

from MagmaWithUnit

= : (%, %) -> Boolean

from BasicType

^ : (%, NonNegativeInteger) -> %

from MagmaWithUnit

^ : (%, PositiveInteger) -> %

from Magma

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

~= : (%, %) -> Boolean

from BasicType

BasicType

CoercibleTo(OutputForm)

MagmaWithUnit

SemiGroup

Magma

Monoid

SetCategory