The function call Inverse(p, rc, R) returns a list . The list   consists of pairs  such that  equals  modulo the saturated ideal of , where  is regular with respect to . The list  is a list of regular chains  such that p is a zero-divisor modulo . In addition, the set of all regular chains occurring in  and  is a triangular decomposition of rc. To be precise, they form a decomposition of rc in the sense of Kalkbrener.

If  is passed, then the regular chain rc must be normalized. In addition, all the returned regular chains will be normalized.

If the regular chain rc is normalized but  is not passed, then there is no guarantee that the returned regular chains will be normalized.

For zero-dimensional regular chains in prime characteristic, the commands RegularizeDim0 and NormalizePolynomialDim0 can be combined to obtain the same specification as the command Inverse  while gaining the advantages of  modular techniques and asymptotically fast polynomial arithmetic.

This command is part of the RegularChains package, so it can be used in the form Inverse(..) only after executing the command with(RegularChains). However, it can always be accessed through the long form of the command by using RegularChains[Inverse](..).