Augment kernel basis functionalities

flint-extras/src/nmod_mat_poly.h

@@ -587,7 +587,7 @@ nmod_mat_poly_set_from_poly_mat(nmod_mat_poly_t matp, const nmod_poly_mat_t pmat
  * The functions here compute a `shift`-minimal ordered weak Popov approximant
  * basis for `(pmat,orders)` in the case where `orders` is given by a single
  * integer `orders = (order,...order)`. They iterate from `1` to `order`,
- * computing at each step a basis at order `1` (see @ref mbasis1) and using it
+ * computing at each step a basis at order `1` and using it
  * to update the output `appbas`, the so-called _residual matrix_, and the
  * considered shift. At step `d`, we have `appbas*pmat = 0 mod x^{d-1}`, and we
  * want to update `appbas` so that this becomes zero modulo `x^d`.
@@ -614,8 +614,8 @@ nmod_mat_poly_set_from_poly_mat(nmod_mat_poly_t matp, const nmod_poly_mat_t pmat
  * \todo integrate
  */
 // Complexity: pmat is m x n
-//   - 'order' calls to mbasis1 with dimension m x n, each one gives a
-//   constant matrix K which is generically m-n x m  (may have more rows in
+//   - 'order' calls to constant nullspace with dimension m x n, each one gives
+//   a constant matrix K which is generically m-n x m  (may have more rows in
 //   exceptional cases)
 //   - order products (X Id + K ) * appbas to update the approximant basis
 //   - order computations of "coeff k of appbas*pmat" to find residuals
@@ -639,8 +639,8 @@ nmod_mat_poly_set_from_poly_mat(nmod_mat_poly_t matp, const nmod_poly_mat_t pmat
 // Residual (X^-d appbas*pmat mod X^(order-d)) is continuously updated along
 // the iterations
 // Complexity: pmat is m x n
-//   - 'order' calls to mbasis1 with dimension m x n, each one gives a
-//   constant matrix K which is generically m-n x m  (may have more rows in
+//   - 'order' calls to constant nullspace with dimension m x n, each one gives
+//   a constant matrix K which is generically m-n x m  (may have more rows in
 //   exceptional cases)
 //   - order products (X Id + K ) * appbas to update the approximant basis
 //   - order-1 products (X Id + K ) * (matrix of degree order-ord) to update
@@ -675,7 +675,6 @@ nmod_mat_poly_set_from_poly_mat(nmod_mat_poly_t matp, const nmod_poly_mat_t pmat
 //    // To understand the threshold (cdim > rdim/2 + 1), see the complexities
 //    // mentioned above for these two variants of mbasis
 //}
-// TODO DOC (see @ref mbasis1)
 // TODO resupdate version
 // TODO general version with choice
 void nmod_mat_poly_mbasis(nmod_mat_poly_t appbas,

flint-extras/src/nmod_mat_poly_extra/nmod_mat_poly_mbasis.c

@@ -376,6 +376,3 @@ _PROFILER_REGION_STOP(t_others)
 _MBASIS_PROFILER_OUTPUT
     return;
 }
-
-/* -*- mode: C++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
-// vim:sts=4:sw=4:ts=4:et:sr:cino=>s,f0,{0,g0,(0,\:0,t0,+0,=s

flint-extras/src/nmod_poly_mat_approximant.h

@@ -182,14 +182,13 @@
  * \param[in] order order
  * \param[in] shift shift
  * \param[in] form required form for `appbas` (see #poly_mat_form_t)
- * \param[in] row_wise indicates whether to compute left approximants (working row-wise) or right approximants (working column-wise)
+ * \param[in] orient indicates the orientation (left/right approximants) and the definition of pivots
  * \param[in] randomized if `true`, the algorithm may use a Monte Carlo or Las Vegas verification algorithm
  *
  * \return boolean, result of the verification
  *
- * \todo add parameter row_wise
+ * \todo update documentation
  * \todo support all options, make doc more clear concerning Las Vegas / Monte Carlo
- * \todo WARNING! for the moment, does not really check generation!
  * \todo WARNING! for the moment, hardcoded to check for ordered weak Popov
  */
 int nmod_poly_mat_is_approximant_basis(const nmod_poly_mat_t appbas,
@@ -243,82 +242,16 @@ int nmod_poly_mat_is_approximant_basis(const nmod_poly_mat_t appbas,
 
 
 /** @name Approximant basis via linear algebra
- * \anchor mbasis1
+ * \anchor approx_linalg
  *
  *  These functions compute a shifted minimal or shifted Popov approximant
  *  basis using fast linear algebra on constant matrices.
  *
- *  Currently, this is only implemented for the uniform order `(1,...,1)`, following
- *  the algorithm _mbasis_ described in
- *  - P. Giorgi, C.-P. Jeannerod, G. Villard. Proceeding ISSAC 2003,
- *  - P. Giorgi, R. Lebreton. Proceedings ISSAC 2014,
- *  - C.-P. Jeannerod, V. Neiger, G. Villard. Preprint 2018.
- *
- *  The latter reference explicitly shows how to ensure that we obtain the
- *  canonical s-Popov approximant basis.
- *
  *  \todo implement the general Krylov-based approach from JNSV17, which
  *  efficiently solves the problem when the sum of the orders is small
  */
 //@{
 
-/** Computes a shifted Popov approximant basis at order `(1,...,1)` using fast
- * linear algebra on constant matrices. Thus, in this context, the input matrix
- * `pmat` is a constant matrix. This approximant basis consists of two sets of
- * rows:
- * - rows forming a left kernel basis in reduced row echelon form of some
- *   row-permutation of `pmat` (the permutation depends on the shift)
- * - the other rows are coordinate vectors multiplied by the variable `x`;
- *   there is one such row at each index `i` which is not among the pivot
- *   indices of the left kernel basis above.
- *
- * Here the whole approximant basis is stored in the OUT parameter `appbas`.
- *
- * \param[out] appbas polynomial matrix
- * \param[in] pmat constant matrix
- * \param[in] shift shift (vector of integers)
- *
- * \todo modify shift in place
- * \todo does it return Popov? if yes name it popov_mbasis1 and write mbasis1
- * if that makes sense; otherwise write other version popov_mbasis1
- * \todo safety correctness checks
- * \todo is output Popov by this method? check
- * \todo seems that it does not return owP ? (see test_mbasis1.c)
- */
-void mbasis1(nmod_poly_mat_t appbas,
-             slong * res_shift,
-             const nmod_mat_t mat,
-             const slong * shift);
-
-/** Computes a shifted Popov approximant basis at order `(1,...,1)` using fast
- * linear algebra on constant matrices. Thus, in this context, the input matrix
- * `pmat` is a constant matrix. This approximant basis consists of two sets of
- * rows:
- * - rows forming a left kernel basis in reduced row echelon form of some
- *   row-permutation of `pmat` (the permutation depends on the shift)
- * - the other rows are coordinate vectors multiplied by the variable `x`;
- *   there is one such row at each index `i` which is not among the pivot
- *   indices of the left kernel basis above.
- *
- * Here only the first set of rows is stored in the OUT parameter `kerbas`,
- * along with permutation...
- * \todo improve doc, to say exactly what this computes (and what is the return
- * value?)
- *
- * \param[out] kerbas constant matrix
- * \param[in] pmat constant matrix
- * \param[in] shift shift (vector of integers)
- *
- * \todo modify shift in place
- * \todo safety correctness checks
- * \todo is output Popov by this method? check
- */
-slong mbasis1_for_mbasis(nmod_mat_t kerbas,
-                         slong * res_shift,
-                         slong * res_perm,
-                         const nmod_mat_t mat,
-                         const slong * shift);
-
 //@} // doxygen group: Approximant basis via linear algebra
 
 /** @name M-Basis algorithm (uniform approximant order)
@@ -378,14 +311,6 @@ void nmod_poly_mat_mbasis(nmod_poly_mat_t appbas,
  */
 //@{
 
-/** 
- * TODO old doc, to be cleaned (new doc below, maybe not complete enough)
- * F \in K[x]^{nxm} <-> F_prime K^{mxn}[x] FIX and
- * Compute P_{k-1} \in K[x]^{mxm} with the list structured_multiplication_blocks
- * Compute x^{-k} P_{k-1} F mod x iteratively with a naive polynomial multiplication  
- *
- * Use naive polynomial multiplication and list_structured_multiplication_blocks 
- */
 /** Computes a `shift`-ordered weak Popov approximant basis for `(pmat,order)`
  * using the algorithm PM-Basis (see @ref pmbasis) */
 

flint-extras/src/nmod_poly_mat_extra.h

@@ -86,24 +86,4 @@ void nmod_poly_mat_det_iter(nmod_poly_t det, nmod_poly_mat_t mat);
  */
 
 
-/*****************************
-*  Verification algorithms  *
-*****************************/
-
-int nmod_poly_mat_is_approximant_basis(const nmod_poly_mat_t appbas,
-                                       const nmod_poly_mat_t pmat,
-                                       slong order,
-                                       const slong * shift,
-                                       orientation_t orient);
-
-int nmod_poly_mat_is_kernel(const nmod_poly_mat_t ker,
-                            const nmod_poly_mat_t pmat,
-                            const slong * shift,
-                            orientation_t orient);
-
-
-
 #endif // NMOD_POLY_MAT_EXTRA_H
-
-/* -*- mode: C++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
-// vim:sts=4:sw=4:ts=4:et:sr:cino=>s,f0,{0,g0,(0,\:0,t0,+0,=s