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RegularChains[ChainTools]

  

IteratedResultant

  

return the iterated resultant of a polynomial with respect to a regular chain

 

Calling Sequence

Parameters

Description

Examples

Calling Sequence

IteratedResultant(p, rc, R)

Parameters

p

-

polynomial of R

rc

-

regular chain of R

R

-

polynomial ring

Description

• 

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 Polynomialv,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.

Examples

withRegularChains:

withChainTools:

RPolynomialRingx,y,t,s

R:=polynomial_ring

(1)

Fx+y2t,t2s

F:=y2t+x,t2s

(2)

pxyt

p:=xyt

(3)

decTriangularizeF,R

dec:=regular_chain

(4)

IteratedResultantp,dec1,R

sy6+s2y2

(5)

See Also

ChainTools

IteratedResultantDim0

IteratedResultantDim1

Polynomial

PolynomialRing

RegularChains

Triangularize

Under

 


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