Executable Approximant-Basis Interpolation #
This backend constructs the GS diagonal modular equations, calls an explicit solution-basis context, selects a least shifted-degree solution row, and normalizes the resulting bivariate polynomial.
References #
- [Chowdhury, M. F. I., Jeannerod, C.-P., Neiger, V., Schost, E., and Villard, G., Faster algorithms for multivariate interpolation with multiplicities and simultaneous polynomial approximations][CJNSV15]
def
CompPoly.GuruswamiSudan.ApproximantBasis.normalizeApproximantCandidate?
{F : Type u_1}
[Field F]
[BEq F]
[LawfulBEq F]
[DecidableEq F]
(params : GSInterpParams)
(Q : CBivariate F)
:
Option (CBivariate F)
Normalize a row-derived approximant candidate using the shared interpolation vector policy.
Instances For
def
CompPoly.GuruswamiSudan.ApproximantBasis.approximantBasisPositiveInterpolate
{F : Type u_1}
[Field F]
[BEq F]
[LawfulBEq F]
[DecidableEq F]
(V : CPolynomial.VanishingPolynomialContext F)
(E : CPolynomial.BatchEvalContext F)
(solver : PolynomialMatrix.Approximant.ModularSolutionBasisContext F)
(points : Array (F × F))
(params : GSInterpParams)
:
Option (CBivariate F)
Positive-Y-weight approximant-basis interpolation branch.
Instances For
def
CompPoly.GuruswamiSudan.ApproximantBasis.approximantBasisInterpolate
{F : Type u_1}
[Field F]
[BEq F]
[LawfulBEq F]
[DecidableEq F]
(V : CPolynomial.VanishingPolynomialContext F)
(E : CPolynomial.BatchEvalContext F)
(solver : PolynomialMatrix.Approximant.ModularSolutionBasisContext F)
(points : Array (F × F))
(params : GSInterpParams)
:
Option (CBivariate F)
Approximant-basis interpolation with the shared low-message branch.