e-prem-sequence-subresultant
▸ function ePremSequenceSubresultant
(f: number[][], g: number[][], sturm?: boolean): number[][][]
Defined in euclidean-division-related/expansion/e-prem-sequence-subresultant.ts:47
Returns the subresultant pseudo remainder sequence of a/b.
precondition: g !== [], i.e. unequal to the zero polynomial.
precondition: the coefficients must be integer Shewchuk floating point expansions; if they are not they can easily be scaled from floating point numbers to Shewchuk expansions by calling scaleFloatsToInts or similar before calling this function (recall that all floating point numbers are rational).
Intermediate calculations (and the input coefficients) are done in infinite precision up to overlow (meaning integers can be represented exactly up to
2^1024 === 1797...(300 more digits)...37216) and may thus not be applicable to very high degree polynomials (in which case it is better to use bPremSequenceSubresultant)see The subresultant polynomial remainder sequence algorithm by Ruiyuan (Ronnie) Chen, p.10
Parameters:
| Name | Type | Default value | Description |
|---|---|---|---|
f | number[][] | - | the polynomial a in the formula a = bq + r; the polynomial is given with coefficients as a dense array of integer Shewchuk expansions from highest to lowest power, e.g. [[5],[-3],[0]] represents the polynomial 5x^2 - 3x |
g | number[][] | - | the polynomial b in the formula a = bq + r |
sturm | boolean | false | if set to true then calculate a Sturm sequence instead |
Returns: number[][][]