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RegularChains[FastArithmeticTools][ResultantBySpecializationCube] - compute the resultant of two polynomials
Calling Sequence
ResultantBySpecializationCube(f1, f2, v, SCube, R)
Parameters
R
-
polynomial ring
f1
polynomial of R
f2
v
variable of R
SCube
subresultant chain specialization cube
Description
The call ResultantBySpecializationCube(f1, f2, v, SCube, R) returns the resultant of f1 and f2 w.r.t. v. It is computed by interpolating the data in SCube. See the command SubresultantChainSpecializationCube to learn how to build this data-structure.
f1 and f2 must have main variable v and must hold.
R must have a prime characteristic such that FFT-based polynomial arithmetic can be used for this computation. The higher the degrees of f1 and f2 are, the larger must be such that divides . If the degree of f1 or f2 is too large, then an error is raised.
Examples
Define a ring of polynomials.
Define two polynomials of R.
Compute images of the subresultant chain of sufficiently many points in order to interpolate. Multi-dimensional TFT is used to evaluate and interpolate since 1 is passed as fifth argument
Interpolate the resultant from the SCube
Define a regular chain with r2. Note that r2 is not required to be squarefree.
Compute a regular GCD of f1 and f2 modulo rc
See Also
RegularChains, RegularGcd, RegularGcdBySpecializationCube, SubresultantChainSpecializationCube
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