divisor.spad line 563 [edit on github]
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.
decompose(d) returns [id, f] where d = (id) + div(f).
divisor(a, b) makes the divisor P: (x = a, y = b). Error: if P is singular.
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(g) returns the divisor of the function g.
divisor(h, d, g) returns gcd of divisor of zeros of h and divisor of zeros of d. d must be squarefree. All ramified zeros of d must be contained in zeros of g.
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(I) makes a divisor D from an ideal I.
generator(d) returns f if (f) = d, "failed" if d is not principal. d is assumed to be of degree 0.
generator(d, k, lp) returns f if (f) = d, "failed" if d is not principal. k is sum of orders of d at special places. Special places are places over infinity and over zeros of polynomials in lp. Elements of lp are assumed to be relatively prime.
ideal(D) returns the ideal corresponding to a divisor D.
principal?(D) tests if the argument is the divisor of a function.
reduce(D) converts D to some reduced form (the reduced forms can be different in different implementations).