FLINT3.7.0-dev
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fq_embed_mono_to_dual_matrix

Synopsis#include <flint/fq_embed.h>
void fq_embed_mono_to_dual_matrix(fmpz_mod_mat_t res, const fq_ctx_t ctx)source

Sets the d×dd \times d matrix res to the change of basis from the monomial basis 1,x,…,xd−11, x, \ldots, x^{d-1} to its dual basis with respect to the trace form (u,v)↦Tr⁡(uv)(u, v) \mapsto \operatorname{Tr}(uv): the Hankel matrix with entries Tr⁡(xi+j)\operatorname{Tr}(x^{i+j}), computed from the power series expansion of rev⁡(f′)/rev⁡(f)\operatorname{rev}(f')/\operatorname{rev}(f) (Newton's identities). Mapping a coordinate vector of yy by this matrix gives the traces Tr⁡(yxi)\operatorname{Tr}(y x^i).

Cite this page

The FLINT team, “fq_embed_mono_to_dual_matrix (fq_embed.h),” FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev, 2026. https://flintlib.org/doc/fq_embed/fq_embed_mono_to_dual_matrix.html (generated 2026-11-02).