FractionalIdeal(R, F, UP, A)

divisor.spad line 1 [edit on github]

• R: EuclideanDomain

• F: QuotientFieldCategory R

• UP: UnivariatePolynomialCategory F

• A: Join(FramedAlgebra(F, UP), RetractableTo F)

Fractional ideals in a framed algebra.

1: %

from MagmaWithUnit

*: (%, %) -> %

from Magma

/: (%, %) -> %

from Group

=: (%, %) -> Boolean

from BasicType

^: (%, Integer) -> %

from Group

^: (%, NonNegativeInteger) -> %

from MagmaWithUnit

^: (%, PositiveInteger) -> %

from Magma

~=: (%, %) -> Boolean

from BasicType

basis: % -> Vector A

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

coerce: % -> OutputForm

from CoercibleTo OutputForm

commutator: (%, %) -> %

from Group

conjugate: (%, %) -> %

from Group

denom: % -> R

denom(1/d * (f1, ..., fn)) returns d.

ideal: Vector A -> %

ideal([f1, ..., fn]) returns the ideal (f1, ..., fn).

inv: % -> %

from Group

latex: % -> String

from SetCategory

leftPower: (%, NonNegativeInteger) -> %

from MagmaWithUnit

leftPower: (%, PositiveInteger) -> %

from Magma

leftRecip: % -> Union(%, failed)

from MagmaWithUnit

minimize: % -> %

minimize(I) returns a reduced set of generators for I.

norm: % -> F

norm(I) returns the norm of the ideal I.

numer: % -> Vector A

numer(1/d * (f1, ..., fn)) = the vector [f1, ..., fn].

one?: % -> Boolean

from MagmaWithUnit

randomLC: (NonNegativeInteger, Vector A) -> A

randomLC(n, x) should be local but conditional.

recip: % -> Union(%, failed)

from MagmaWithUnit

rightPower: (%, NonNegativeInteger) -> %

from MagmaWithUnit

rightPower: (%, PositiveInteger) -> %

from Magma

rightRecip: % -> Union(%, failed)

from MagmaWithUnit

sample: %

from MagmaWithUnit

BasicType

CoercibleTo OutputForm

Group

Magma

MagmaWithUnit

Monoid

SemiGroup

SetCategory

TwoSidedRecip

unitsKnown