i1 : R = QQ[x,y,z]/ideal(x^6-z^6-y^2*z^4);
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i2 : S = integralClosure (R)
o2 = S
o2 : QuotientRing
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The code for this function 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 function
ICfractions(Ring) 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.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>.