The function call ExtendedRegularGcd(p1, p2, v, rc, R) returns a list of pairs  where , ,  are polynomials of R and  is a regular chain of R.

For each pair, the polynomial  is a GCD of p1 and p2 modulo the saturated ideal of .

For each pair, the polynomials , ,  satisfy  modulo the saturated ideal of .

For each pair, the leading coefficient of the polynomial  with respect to v is regular modulo the saturated ideal of .

The returned regular chains  form a triangular decomposition of rc (in the sense of Kalkbrener).

If 'normalized'='yes' is present, the returned regular chains are normalized.

If 'normalized'='strongly' is present, the returned regular chains are strongly normalized.

If 'normalized'='yes' is present, rc must be normalized.

If 'normalized'='strongly' is present, rc must be strongly normalized.

v must be the common main variable of p1 and p2

The initials of p1 and p2 must be regular with respect to rc.

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

Moreno Maza, M. "On triangular decompositions of algebraic varieties" Technical Report 4/99, NAG, UK, Presented at the MEGA-2000 Conference, Bath, UK. Available at http://www.csd.uwo.ca/~moreno.