`_nmod_poly_revert_series, nmod_poly_revert_series`

Synopsis#include <flint/nmod_poly.h>

void _nmod_poly_revert_series(nn_ptr Qinv, nn_srcptr Q, slong Qlen, slong n, nmod_t mod)source

void nmod_poly_revert_series(nmod_poly_t Qinv, const nmod_poly_t Q, slong n)source

Set Qinv to the compositional inverse of the power series $Q$ modulo $x^n$ , so that $Q(\mathit{Qinv}(x)) = \mathit{Qinv}(Q(x)) = x \bmod x^n$ . Requires $Q_0 = 0$ and $Q_1$ invertible; the non-underscore version throws FLINT_ERROR otherwise. The underscore version writes $n$ coefficients and does not allow aliasing.

For $n < 2500$ the fast Lagrange inversion of [Joh2015b] is used, which divides by $1, \ldots, n - 1$ ; if one of them is not invertible (small characteristic), and for larger $n$ , Newton iteration with power series composition is used instead.

References#

[Joh2015b] F. Johansson, "A fast algorithm for reversion of power series", Math. Comp. 84 (2015), 475-484, http://doi.org/10.1090/S0025-5718-2014-02857-3

Cite this page

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

@misc{flint-doc-nmod-poly-nmod-poly-revert-series,
  author       = {{The FLINT team}},
  title        = {{\_nmod\_poly\_revert\_series, nmod\_poly\_revert\_series (nmod\_poly.h)}},
  howpublished = {FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev},
  year         = {2026},
  url          = {https://flintlib.org/doc/nmod_poly/_nmod_poly_revert_series.html},
  note         = {Generated 2026-11-02}
}

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