gr_generic_chebyshev_t2_fmpz, gr_generic_chebyshev_t_fmpz, gr_generic_chebyshev_u2_fmpz, gr_generic_chebyshev_u_fmpz
Synopsis
#include <flint/gr_special.h>int gr_generic_chebyshev_t2_fmpz(gr_ptr a, gr_ptr b, const fmpz_t n, gr_srcptr x, gr_ctx_t ctx)sourceint gr_generic_chebyshev_u2_fmpz(gr_ptr a, gr_ptr b, const fmpz_t n, gr_srcptr x, gr_ctx_t ctx)sourceChebyshev polynomials T_n(x) and U_n(x) for n \ge 0 by the doubling formulas T_{2k} = 2T_k^2 - 1 and T_{2k+1} = 2 T_k T_{k+1} - x (and analogues for U) along the binary expansion of n, using O(\log n) multiplications. The 2 versions set a to T_n(x) and b to T_{n-1}(x) (respectively U). Negative n gives GR_UNABLE.
Cite this page
The FLINT team, “gr_generic_chebyshev_t2_fmpz, gr_generic_chebyshev_t_fmpz, gr_generic_chebyshev_u2_fmpz, gr_generic_chebyshev_u_fmpz (gr_special.h),” FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev, 2026. https://flintlib.org/doc/gr_special/gr_generic_chebyshev_t2_fmpz.html (generated 2026-10-20).
@misc{flint-doc-gr-special-gr-generic-chebyshev-t2-fmpz,
author = {{The FLINT team}},
title = {{gr\_generic\_chebyshev\_t2\_fmpz, gr\_generic\_chebyshev\_t\_fmpz, gr\_generic\_chebyshev\_u2\_fmpz, gr\_generic\_chebyshev\_u\_fmpz (gr\_special.h)}},
howpublished = {FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev},
year = {2026},
url = {https://flintlib.org/doc/gr_special/gr_generic_chebyshev_t2_fmpz.html},
note = {Generated 2026-10-20}
}