return the iterated resultant of a polynomial with respect to a regular chain
IteratedResultant(p, rc, R)
polynomial of R
regular chain of R
The command IteratedResultant(p, rc, R) returns the iterated resultant of p with respect to rc.
If p is a constant or all variables in p are free with respect to rc, then p is returned. Otherwise, if v is the largest variable of p algebraic with respect to rc, then IteratedResultant(r, Under(v, rc, R), R) is returned, where r is the resultant of p and the polynomial Polynomial⁡v,rc,R.
This command is part of the RegularChains[ChainTools] package, so it can be used in the form IteratedResultant(..) only after executing the command with(RegularChains[ChainTools]). However, it can always be accessed through the long form of the command by using RegularChains[ChainTools][IteratedResultant](..).
The commands IteratedResultantDim0 and IteratedResultantDim1 provide fast algorithms for computing iterated resultants in prime characteristic and with regular chains in dimensions 0 and 1 respectively.
R ≔ PolynomialRing⁡x,y,t,s
F ≔ x+y2−t,t2−s
p ≔ x⁢y⁢t
dec ≔ Triangularize⁡F,R
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