sigma_delta_unable, sigma_delta_commutative, sigma_delta_derivative, sigma_delta_euler_derivative, sigma_delta_forward_shift, sigma_delta_backward_shift, sigma_delta_forward_difference, sigma_delta_backward_difference, sigma_delta_compose, sigma_delta_mahler, sigma_delta_frobenius
#include <flint/gr_ore_poly.h>int sigma_delta_unable(gr_ptr sigma, gr_ptr delta, gr_srcptr a, gr_ore_poly_ctx_struct * ctx)sourceint sigma_delta_commutative(gr_ptr sigma, gr_ptr delta, gr_srcptr a, gr_ore_poly_ctx_struct * ctx)sourceint sigma_delta_derivative(gr_ptr sigma, gr_ptr delta, gr_srcptr a, gr_ore_poly_ctx_struct * ctx)sourceint sigma_delta_euler_derivative(gr_ptr sigma, gr_ptr delta, gr_srcptr a, gr_ore_poly_ctx_struct * ctx)sourceint sigma_delta_forward_shift(gr_ptr sigma, gr_ptr delta, gr_srcptr a, gr_ore_poly_ctx_struct * ctx)sourceint sigma_delta_backward_shift(gr_ptr sigma, gr_ptr delta, gr_srcptr a, gr_ore_poly_ctx_struct * ctx)sourceint sigma_delta_forward_difference(gr_ptr sigma, gr_ptr delta, gr_srcptr a, gr_ore_poly_ctx_struct * ctx)sourceint sigma_delta_backward_difference(gr_ptr sigma, gr_ptr delta, gr_srcptr a, gr_ore_poly_ctx_struct * ctx)sourceint sigma_delta_compose(gr_ptr sigma, gr_ptr delta, gr_srcptr a, gr_ore_poly_ctx_struct * ctx)sourceint sigma_delta_mahler(gr_ptr sigma, gr_ptr delta, gr_srcptr a, gr_ore_poly_ctx_struct * ctx)sourceint sigma_delta_frobenius(gr_ptr sigma, gr_ptr delta, gr_srcptr a, gr_ore_poly_ctx_struct * ctx)sourceThe functions implementing \sigma and \delta for the predefined algebras, with the signature gr_ore_poly_sigma_delta_t. sigma_delta_unable always returns GR_UNABLE; sigma_delta_commutative is the identity and zero; the derivative and Euler derivative versions differentiate a polynomial (with gr_poly_derivative, then a multiplication by x); the shift and difference versions compute Taylor shifts a(x \pm 1) (with gr_poly_taylor_shift) and their differences with a; sigma_delta_compose (used for q-shifts) composes a with the stored \sigma(x) = qx; sigma_delta_mahler substitutes x^b (an inflation); and sigma_delta_frobenius applies gr_fq_frobenius. All except the commutative and Frobenius versions require a base ring of univariate polynomials and return GR_UNABLE otherwise.
The FLINT team, “sigma_delta_unable, sigma_delta_commutative, sigma_delta_derivative, sigma_delta_euler_derivative, sigma_delta_forward_shift, sigma_delta_backward_shift, sigma_delta_forward_difference, sigma_delta_backward_difference, sigma_delta_compose, sigma_delta_mahler, sigma_delta_frobenius (gr_ore_poly.h),” FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev, 2026. https://flintlib.org/doc/gr_ore_poly/sigma_delta_unable.html (generated 2026-10-20).
@misc{flint-doc-gr-ore-poly-sigma-delta-unable,
author = {{The FLINT team}},
title = {{sigma\_delta\_unable, sigma\_delta\_commutative, sigma\_delta\_derivative, sigma\_delta\_euler\_derivative, sigma\_delta\_forward\_shift, sigma\_delta\_backward\_shift, sigma\_delta\_forward\_difference, sigma\_delta\_backward\_difference, sigma\_delta\_compose, sigma\_delta\_mahler, sigma\_delta\_frobenius (gr\_ore\_poly.h)}},
howpublished = {FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev},
year = {2026},
url = {https://flintlib.org/doc/gr_ore_poly/sigma_delta_unable.html},
note = {Generated 2026-10-20}
}