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RegularChains[FastArithmeticTools][NormalizeRegularChainDim0] - normalize a zero-dimensional regular chain
Calling Sequence
NormalizeRegularChainDim0(rc, R)
Parameters
R
-
polynomial ring
rc
a regular chain of R
Description
Returns a normalized regular chain generating the same ideal as rc.
rc is a zero-dimensional non-empty regular chain.
Moreover R must have a prime characteristic such that FFT-based polynomial arithmetic can be used for this actual computation. The higher the degrees of f and rc are, the larger must be such that divides . If the degree of f or rc is too large, then an error is raised.
Examples
We solve a system in 3 variables and 3 unknowns
Its triangular decomposition consists of only one regular chain
Each initial is not equal to 1, hence this regular chain is not normalized
We compute here a regular chain which is normalized and which describes the same solution as the previous one
We check that it is normalized
We check that the two regular chains describe the set of solutions
See Also
NormalForm, NormalFormDim0, NormalizePolynomialDim0, ReduceCoefficientsDim0, RegularChains
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