HyperellipticFiniteDivisor(F, UP, UPUP, R)ΒΆ
divisor.spad line 633 [edit on github]
F: Field
UPUP: UnivariatePolynomialCategory Fraction UP
R: FunctionFieldCategory(F, UP, UPUP)
This domains implements finite rational divisors on an hyperelliptic 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. The equation of the curve must be y^2 = f(x) and f must have odd degree.
- 0: %
from AbelianMonoid
- *: (Integer, %) -> %
from AbelianGroup
- *: (NonNegativeInteger, %) -> %
from AbelianMonoid
- *: (PositiveInteger, %) -> %
from AbelianSemiGroup
- +: (%, %) -> %
from AbelianSemiGroup
- -: % -> %
from AbelianGroup
- -: (%, %) -> %
from AbelianGroup
- 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)
- 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
- 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)
- zero?: % -> Boolean
from AbelianMonoid
FiniteDivisorCategory(F, UP, UPUP, R)