integralBasis -- Compute an integral basis of an algebraic function field.

Synopsis

Usage:

integralBasis(I)
Inputs:
- I, an ideal, in a PolynomialRing R of two variables over QQ, say x,y. defining an affine plane curve which has no singularities at infinity and its projective closure does not contain the point (x:y:z)=(0:1:0).
Outputs:
- a matrix, over frac(R)

Description

Computes an integral basis in CC(x)[y] of the integral closure of CC[x] in CC(x,y). We consider x as transcendental and y as algebraic. The i-th element of the integral basis has degree i as a polynomial in y. Note that the integral basis will have coefficients in QQ.

-- -*- M2-comint -*- {* hash: -1462873685 *}

i1 : R=QQ[x,y]

o1 = R

o1 : PolynomialRing

i2 : I=ideal(y^8-x^3*(1+x)^5)

              8    8     7      6      5     4    3
o2 = ideal(- x  + y  - 5x  - 10x  - 10x  - 5x  - x )

o2 : Ideal of R

Ways to use `integralBasis` :

"integralBasis(Ideal)"

For the programmer

The object integralBasis is a method function.

integralBasis -- Compute an integral basis of an algebraic function field.

Synopsis

Description

Ways to use integralBasis :

For the programmer

Ways to use `integralBasis` :