RegularChains
Inverse
inverse of a polynomial with respect to a regular chain
Calling Sequence
Parameters
Description
Examples
Inverse(p, rc, R)
Inverse(p, rc, R, 'normalized'='yes')
R
-
polynomial ring
rc
regular chain of R
p
polynomial of R
'normalized'='yes'
boolean flag (optional)
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](..).
See Also
Chain
ChainTools
Empty
Equations
IsRegular
IsStronglyNormalized
MatrixInverse
NormalForm
NormalizePolynomialDim0
PolynomialRing
RegularizeDim0
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