HyperellipticFiniteDivisor(F, UP, UPUP, R)
divisor.spad line 630
[edit on github]
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.
- * : (Integer, %) -> %
- from AbelianGroup
- * : (NonNegativeInteger, %) -> %
- from AbelianMonoid
- * : (PositiveInteger, %) -> %
- from AbelianSemiGroup
- + : (%, %) -> %
- from AbelianSemiGroup
- - : % -> %
- from AbelianGroup
- - : (%, %) -> %
- from AbelianGroup
- 0 : () -> %
- from AbelianMonoid
- = : (%, %) -> 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 -> %
- 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)
- 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")
- from CancellationAbelianMonoid
- zero? : % -> Boolean
- from AbelianMonoid
- ~= : (%, %) -> Boolean
- from BasicType
SetCategory
CoercibleTo(OutputForm)
AbelianMonoid
AbelianSemiGroup
BasicType
FiniteDivisorCategory(F, UP, UPUP, R)
CancellationAbelianMonoid
AbelianGroup