FiniteDivisor(F, UP, UPUP, R)

divisor.spad line 807 [edit on github]

• F: Field

• UP: UnivariatePolynomialCategory F

• UPUP: UnivariatePolynomialCategory Fraction UP

• R: FunctionFieldCategory(F, UP, UPUP)

This domains implements finite rational divisors on a curve, that is finite formal sums SUM(n * P) where the n's are integers and the P's are finite rational points on the curve.

0: %

from AbelianMonoid

*: (Integer, %) -> %

from AbelianGroup

*: (NonNegativeInteger, %) -> %

from AbelianMonoid

*: (PositiveInteger, %) -> %

from AbelianSemiGroup

+: (%, %) -> %

from AbelianSemiGroup

-: % -> %

from AbelianGroup

-: (%, %) -> %

from AbelianGroup

=: (%, %) -> Boolean

from BasicType

~=: (%, %) -> Boolean

from BasicType

coerce: % -> OutputForm

from CoercibleTo OutputForm

decompose: % -> Record(id: FractionalIdeal(UP, Fraction UP, UPUP, R), principalPart: R)

from FiniteDivisorCategory(F, UP, UPUP, R)

divisor: (F, F) -> %

from FiniteDivisorCategory(F, UP, UPUP, R)

divisor: (F, F, Integer) -> %

from FiniteDivisorCategory(F, UP, UPUP, R)

divisor: (R, UP, UP) -> %

from FiniteDivisorCategory(F, UP, UPUP, R)

divisor: (R, UP, UP, UP, F) -> %

from FiniteDivisorCategory(F, UP, UPUP, R)

divisor: FractionalIdeal(UP, Fraction UP, UPUP, R) -> %

from FiniteDivisorCategory(F, UP, UPUP, R)

divisor: R -> %

from FiniteDivisorCategory(F, UP, UPUP, R)

finiteBasis: % -> Vector R

finiteBasis(d) returns a basis for d as a module over K[x].

generator: % -> Union(R, failed)

from FiniteDivisorCategory(F, UP, UPUP, R)

generator: (%, Integer, List UP) -> Union(R, failed)

from FiniteDivisorCategory(F, UP, UPUP, R)

ideal: % -> FractionalIdeal(UP, Fraction UP, UPUP, R)

from FiniteDivisorCategory(F, UP, UPUP, R)

latex: % -> String

from SetCategory

lSpaceBasis: % -> Vector R

lSpaceBasis(d) returns a basis for L(d) = {f | (f) >= -d} as a module over K[x].

opposite?: (%, %) -> Boolean

from AbelianMonoid

principal?: % -> Boolean

from FiniteDivisorCategory(F, UP, UPUP, R)

reduce: % -> %

from FiniteDivisorCategory(F, UP, UPUP, R)

sample: %

from AbelianMonoid

subtractIfCan: (%, %) -> Union(%, failed)

from CancellationAbelianMonoid

zero?: % -> Boolean

from AbelianMonoid

AbelianGroup

AbelianMonoid

AbelianSemiGroup

BasicType

CancellationAbelianMonoid

CoercibleTo OutputForm

FiniteDivisorCategory(F, UP, UPUP, R)

SetCategory