b-pdiv-trivial
▸ function bPdivTrivial
(a: bigint[], b: bigint[], positiveMultiplier?: boolean): object
Defined in euclidean-division-related/bigint/b-pdiv-trivial.ts:42
Performs a trivial pseudo-division and returns the quotient and remainder
of the pseudo division of a/b (a, b both being polynomials) in such a way
that all intermediate calculations and the final result are done in ℤ, i.e.
performs Euclidean (i.e. long) division on the two given polynomials, a/b,
and returns a scaled r and q in the formula a = bq + r, where
degree(r) < degree(b). q is called the quotient and r the remainder.
precondition: the coefficients must be bigints; if they are not they can easily be scaled from floating point numbers to bigints by calling scaleFloatsToBigints or similar before calling this function (recall that all floating point numbers are rational).
precondition: b !== [0], i.e. unequal to the zero polynomial.
see also Polynomial long division
Parameters:
| Name | Type | Default value | Description |
|---|---|---|---|
a | bigint[] | - | the polynomial a in the formula a = bq + r; the polynomial is given with coefficients as a dense array of bigints from highest to lowest power, e.g. [5n,-3n,0n] represents the polynomial 5x^2 - 3x |
b | bigint[] | - | the polynomial b in the formula a = bq + r |
positiveMultiplier | boolean | false | defaults to false - if set to true then the multiplier (of the coefficients of the dividend) leadingCoeff(b)^(deg(a)-deg(b)+1) will be modified to abs(leadingCoeff(b)^(deg(a)-deg(b)+1)) |
Returns: object
| Name | Type |
|---|---|
q | bigint[] |
r | bigint[] |