integralClosure Ring -- compute the integral closure of a ring

integralClosure Ring -- compute the integral closure of a ring

Synopsis:

Usage: S = integralClosure (R)

Function: integralClosure -- compute the integral closure of a ring

Input:

R, an instance of class Ring: a reduced ring

Output:

S, an instance of class Ring: The integral closure of Rin its total ring of fractions given as a quotient ring using new variables are indexed variables using w.

Optional arguments :

integralClosure(..., Variable => ...) -- Sets the name of the indexed variables introduced in computing the integral closure of a reduced ring.

i1 : R = QQ[x,y,z]/ideal(x^6-z^6-y^2*z^4);

i2 : S = integralClosure (R)



o2 = S



o2 : QuotientRing

The function integralClosure was written so that certain information can be retrieved if desired. The information of largest interest is the fractions that correspond to the added variables in this description of the integral closure. Unfortunately, all of the added features currently only work on affine domains. The map and the corresponding fractions are obtained as a matrix using the functionICfractions R where R is an affine domain. This function can be run without first using integralClosure. The natrual map from R into its integral closure is obtained using the function ICmap and the conductor of the integral closure of R into R is found using conductor (ICmap R). Note that both ICfractions and ICmap take the input ring R as input rather than the output of integralClosure in this way you can use these functions without running integralClosure.

See also:

conductor

The function integralClosure is based on Theo De Jong's paper, An Algorithm for Computing the Integral Closure, J. Symbolic Computation, (1998) 26, 273-277. This implementation is written and maintained by Amelia Taylor, ataylor@math.rutgers.edu.