FractionalIdeal(R, F, UP, A)

divisor.spad line 1 [edit on github]

Fractional ideals in a framed algebra.

* : (%, %) -> %
from Magma
/ : (%, %) -> %
from Group
1 : () -> %
from MagmaWithUnit
= : (%, %) -> Boolean
from BasicType
^ : (%, Integer) -> %
from Group
^ : (%, NonNegativeInteger) -> %
from MagmaWithUnit
^ : (%, PositiveInteger) -> %
from Magma
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
~= : (%, %) -> Boolean
from BasicType

SetCategory

MagmaWithUnit

CoercibleTo(OutputForm)

Group

SemiGroup

TwoSidedRecip

unitsKnown

Magma

Monoid

BasicType