# HyperellipticFiniteDivisor(F, UP, UPUP, R)ΒΆ

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
=: (%, %) -> 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, 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)
hash: % -> SingleInteger
from SetCategory
hashUpdate!: (HashState, %) -> HashState
from SetCategory
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)
from CancellationAbelianMonoid
zero?: % -> Boolean
from AbelianMonoid

AbelianGroup

AbelianMonoid

AbelianSemiGroup

BasicType

CancellationAbelianMonoid

FiniteDivisorCategory(F, UP, UPUP, R)

SetCategory