FLINT3.7.0-dev
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_gr_poly_newton_basis_interpolate_exact, gr_poly_newton_basis_interpolate_exact, _gr_poly_newton_basis_interpolate, gr_poly_newton_basis_interpolate

Synopsis#include <flint/gr_poly.h>
int _gr_poly_newton_basis_interpolate_exact(gr_ptr res, gr_srcptr basis, gr_srcptr ys, slong len, gr_ctx_t ctx)source
int gr_poly_newton_basis_interpolate_exact(gr_poly_t res, const gr_vec_t basis, const gr_vec_t ys, gr_ctx_t ctx)source
int _gr_poly_newton_basis_interpolate(gr_ptr res, gr_srcptr basis, gr_srcptr ys, slong len, gr_ctx_t ctx)source
int gr_poly_newton_basis_interpolate(gr_poly_t res, const gr_vec_t basis, const gr_vec_t ys, gr_ctx_t ctx)source

Set res to the Newton basis form of the interpolating polynomial f of length at most len with f(c_i) = y_i for 0 \le i < \mathit{len}, computed by divided differences. The first len points of basis must be pairwise distinct.

The ring is presumed to be an integral domain, which is not checked; over other rings the functions may succeed without the result being an interpolating polynomial. They return GR_DOMAIN or GR_UNABLE if basis has fewer than len points (checked by the non-underscore versions only), if the points are not distinct, or if f has coefficients in the fraction field of R but not in R. The exact versions assume distinct points and coefficients in R, use exact divisions, and may return an arbitrary polynomial otherwise.

Cite this page

The FLINT team, “_gr_poly_newton_basis_interpolate_exact, gr_poly_newton_basis_interpolate_exact, _gr_poly_newton_basis_interpolate, gr_poly_newton_basis_interpolate (gr_poly.h),” FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev, 2026. https://flintlib.org/doc/gr_poly/_gr_poly_newton_basis_interpolate_exact.html (generated 2026-10-20).