FiniteDivisorCategory(F, UP, UPUP, R)ΒΆ

divisor.spad line 567

This category describes 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)
decompose(d) returns [id, f] where d = (id) + div(f).
divisor: (F, F) -> %
divisor(a, b) makes the divisor P: (x = a, y = b). Error: if P is singular.
divisor: (F, F, Integer) -> %
divisor(a, b, n) makes the divisor nP where P: (x = a, y = b). P is allowed to be singular if n is a multiple of the rank.
divisor: (R, UP, UP, UP, F) -> %
divisor(h, d, d', g, r) returns the sum of all the finite points where h/d has residue r. h must be integral. d must be squarefree. d' is some derivative of d (not necessarily dd/dx). g = gcd(d, discriminant) contains the ramified zeros of d
divisor: FractionalIdeal(UP, Fraction UP, UPUP, R) -> %
divisor(I) makes a divisor D from an ideal I.
divisor: R -> %
divisor(g) returns the divisor of the function g.
generator: % -> Union(R, failed)
generator(d) returns f if (f) = d, “failed” if d is not principal.
hash: % -> SingleInteger
from SetCategory
hashUpdate!: (HashState, %) -> HashState
from SetCategory
ideal: % -> FractionalIdeal(UP, Fraction UP, UPUP, R)
ideal(D) returns the ideal corresponding to a divisor D.
latex: % -> String
from SetCategory
opposite?: (%, %) -> Boolean
from AbelianMonoid
principal?: % -> Boolean
principal?(D) tests if the argument is the divisor of a function.
reduce: % -> %
reduce(D) converts D to some reduced form (the reduced forms can be differents in different implementations).
sample: %
from AbelianMonoid
subtractIfCan: (%, %) -> Union(%, failed)
from CancellationAbelianMonoid
zero?: % -> Boolean
from AbelianMonoid

AbelianGroup

AbelianMonoid

AbelianSemiGroup

BasicType

CancellationAbelianMonoid

CoercibleTo OutputForm

SetCategory