Trac #22970: use flint fmpq_mat for rational dense matrices

The flint library has a builtin type for rational matrices:
`fmpq_mat_t`. This ticket proposes to replace the current array of
`mpq_t` wrapped by `Matrix_rational_dense` in favor of `fmpq_mat_t`.

(See also the related #22924 and #22872)

URL: https://trac.sagemath.org/22970
Reported by: vdelecroix
Ticket author(s): Vincent Delecroix
Reviewer(s): Marc Masdeu

src/sage/algebras/quatalg/quaternion_algebra_cython.pyx

@@ -34,6 +34,10 @@ from .quaternion_algebra_element cimport QuaternionAlgebraElement_rational_field
 from sage.libs.gmp.mpz cimport mpz_t, mpz_lcm, mpz_init, mpz_set, mpz_clear, mpz_init_set, mpz_mul, mpz_fdiv_q, mpz_cmp_si
 from sage.libs.gmp.mpq cimport mpq_set_num, mpq_set_den, mpq_canonicalize
 
+from sage.libs.flint.fmpz cimport fmpz_set_mpz
+from sage.libs.flint.fmpq cimport fmpq_canonicalise
+from sage.libs.flint.fmpq_mat cimport fmpq_mat_entry_num, fmpq_mat_entry_den, fmpq_mat_entry
+
 def integral_matrix_and_denom_from_rational_quaternions(v, reverse=False):
     r"""
     Given a list of rational quaternions, return matrix `A` over `\ZZ`
@@ -142,27 +146,28 @@ def rational_matrix_from_rational_quaternions(v, reverse=False):
     if reverse:
         for i in range(n):
             x = v[i]
-            mpq_set_num(A._matrix[n-i-1][3], x.x)
-            mpq_set_num(A._matrix[n-i-1][2], x.y)
-            mpq_set_num(A._matrix[n-i-1][1], x.z)
-            mpq_set_num(A._matrix[n-i-1][0], x.w)
+            fmpz_set_mpz(fmpq_mat_entry_num(A._matrix, n-i-1, 3), x.x)
+            fmpz_set_mpz(fmpq_mat_entry_num(A._matrix, n-i-1, 2), x.y)
+            fmpz_set_mpz(fmpq_mat_entry_num(A._matrix, n-i-1, 1), x.z)
+            fmpz_set_mpz(fmpq_mat_entry_num(A._matrix, n-i-1, 0), x.w)
 
             if mpz_cmp_si(x.d,1):
                 for j in range(4):
-                    mpq_set_den(A._matrix[n-i-1][j], x.d)
-                    mpq_canonicalize(A._matrix[n-i-1][j])
+                    fmpz_set_mpz(fmpq_mat_entry_den(A._matrix, n-i-1, j), x.d)
+                    fmpq_canonicalise(fmpq_mat_entry(A._matrix, n-i-1, j))
     else:
         for i in range(n):
             x = v[i]
-            mpq_set_num(A._matrix[i][0], x.x)
-            mpq_set_num(A._matrix[i][1], x.y)
-            mpq_set_num(A._matrix[i][2], x.z)
-            mpq_set_num(A._matrix[i][3], x.w)
+            fmpz_set_mpz(fmpq_mat_entry_num(A._matrix, i, 0), x.x)
+            fmpz_set_mpz(fmpq_mat_entry_num(A._matrix, i, 1), x.y)
+            fmpz_set_mpz(fmpq_mat_entry_num(A._matrix, i, 2), x.z)
+            fmpz_set_mpz(fmpq_mat_entry_num(A._matrix, i, 3), x.w)
 
             if mpz_cmp_si(x.d,1):
                 for j in range(4):
-                    mpq_set_den(A._matrix[i][j], x.d)
-                    mpq_canonicalize(A._matrix[i][j])
+                    fmpz_set_mpz(fmpq_mat_entry_den(A._matrix, i, j), x.d)
+                    fmpq_canonicalise(fmpq_mat_entry(A._matrix, i, j))
+
     return A
 
 def rational_quaternions_from_integral_matrix_and_denom(A, Matrix_integer_dense H, Integer d, reverse=False):

src/sage/libs/flint/fmpq.pxd

@@ -1,21 +1,74 @@
 # distutils: libraries = flint
 
+from libc.stdio cimport FILE
 from sage.libs.gmp.types cimport mpq_t
-from sage.libs.flint.types cimport fmpq_t
+from sage.libs.flint.types cimport fmpz_t, fmpq_t, flint_rand_t, mp_bitcnt_t, fmpz
+from sage.libs.mpfr cimport mpfr_t, mpfr_rnd_t
 
 cdef extern from "flint/fmpq.h":
-    # Memory management
+    fmpz * fmpq_numref(fmpq_t)
+    fmpz * fmpq_denref(fmpq_t)
     void fmpq_init(fmpq_t)
     void fmpq_clear(fmpq_t)
-
-    # Conversion
-    void fmpq_set_mpq(fmpq_t, const mpq_t)
-    void fmpq_get_mpq(mpq_t, const fmpq_t)
-
-    # Comparison
-    int fmpq_is_zero(const fmpq_t res)
-    int fmpq_is_one(const fmpq_t res)
-    int fmpq_equal(const fmpq_t x, const fmpq_t y)
-    int fmpq_sgn(const fmpq_t)
+    void fmpq_one(fmpq_t)
+    void fmpq_zero(fmpq_t)
+    bint fmpq_is_zero(fmpq_t)
+    bint fmpq_is_one(fmpq_t)
+    int fmpq_sgn(const fmpq_t x)
+    void fmpq_set(fmpq_t dest, const fmpq_t src)
+    void fmpq_swap(fmpq_t op1, fmpq_t op2)
+    void fmpq_neg(fmpq_t dest, const fmpq_t src)
+    void fmpq_abs(fmpq_t dest, const fmpq_t src)
     int fmpq_cmp(const fmpq_t x, const fmpq_t y)
-
+    void fmpq_canonicalise(fmpq_t res)
+    int fmpq_is_canonical(const fmpq_t x)
+    void fmpq_set_si(fmpq_t res, long p, unsigned long q)
+    void fmpq_set_fmpz_frac(fmpq_t res, const fmpz_t p, const fmpz_t q)
+    void fmpq_set_mpq(fmpq_t dest, const mpq_t src)
+    void fmpq_get_mpq(mpq_t dest, const fmpq_t src)
+    int fmpq_get_mpfr(mpfr_t r, const fmpq_t x, mpfr_rnd_t rnd)
+    void flint_mpq_init_set_readonly(mpq_t z, const fmpq_t f)
+    void flint_mpq_clear_readonly(mpq_t z)
+    void fmpq_init_set_readonly(fmpq_t f, const mpq_t z)
+    void fmpq_clear_readonly(fmpq_t f)
+    char * fmpq_get_str(char * str, int b, const fmpq_t x)
+    void fmpq_fprint(FILE * file, const fmpq_t x)
+    void fmpq_print(const fmpq_t x)
+    void fmpq_randtest(fmpq_t res, flint_rand_t state, mp_bitcnt_t bits)
+    void fmpq_randtest_not_zero(fmpq_t res, flint_rand_t state, mp_bitcnt_t bits)
+    void fmpq_randbits(fmpq_t res, flint_rand_t state, mp_bitcnt_t bits)
+    void fmpq_add(fmpq_t res, const fmpq_t op1, const fmpq_t op2)
+    void fmpq_add_si(fmpq_t res, const fmpq_t op1, long c)
+    void fmpq_add_fmpz(fmpq_t res, const fmpq_t op1, const fmpz_t c)
+    void fmpq_sub(fmpq_t res, const fmpq_t op1, const fmpq_t op2)
+    void fmpq_sub_si(fmpq_t res, const fmpq_t op1, long c)
+    void fmpq_sub_fmpz(fmpq_t res, const fmpq_t op1, const fmpz_t c)
+    void fmpq_mul(fmpq_t res, const fmpq_t op1, const fmpq_t op2)
+    void fmpq_mul_fmpz(fmpq_t res, const fmpq_t op, const fmpz_t x)
+    void fmpq_pow_si(fmpq_t rop, const fmpq_t op, long e)
+    void fmpq_addmul(fmpq_t res, const fmpq_t op1, const fmpq_t op2)
+    void fmpq_submul(fmpq_t res, const fmpq_t op1, const fmpq_t op2)
+    void fmpq_inv(fmpq_t dest, const fmpq_t src)
+    void fmpq_div(fmpq_t res, const fmpq_t op1, const fmpq_t op2)
+    void fmpq_div_fmpz(fmpq_t res, const fmpq_t op, const fmpz_t x)
+    void fmpq_mul_2exp(fmpq_t res, const fmpq_t x, mp_bitcnt_t exp)
+    void fmpq_div_2exp(fmpq_t res, const fmpq_t x, mp_bitcnt_t exp)
+    int fmpq_mod_fmpz(fmpz_t res, const fmpq_t x, const fmpz_t mod)
+    void fmpq_gcd(fmpq_t res, const fmpq_t op1, const fmpq_t op2)
+    int fmpq_reconstruct_fmpz(fmpq_t res, const fmpz_t a, const fmpz_t m)
+    int fmpq_reconstruct_fmpz_2(fmpq_t res, const fmpz_t a, const fmpz_t m, const fmpz_t N, const fmpz_t D)
+    mp_bitcnt_t fmpq_height_bits(const fmpq_t x)
+    void fmpq_height(fmpz_t height, const fmpq_t x)
+    void fmpq_next_calkin_wilf(fmpq_t res, const fmpq_t x)
+    void fmpq_next_signed_calkin_wilf(fmpq_t res, const fmpq_t x)
+    void fmpq_next_minimal(fmpq_t res, const fmpq_t x)
+    void fmpq_next_signed_minimal(fmpq_t res, const fmpq_t x)
+    long fmpq_get_cfrac(fmpz * c, fmpq_t rem, const fmpq_t x, long n)
+    void fmpq_set_cfrac(fmpq_t x, const fmpz * c, long n)
+    long fmpq_cfrac_bound(const fmpq_t x)
+    void fmpq_dedekind_sum_naive(fmpq_t s, const fmpz_t h, const fmpz_t k)
+    void fmpq_dedekind_sum_coprime_large(fmpq_t s, const fmpz_t h, const fmpz_t k)
+    double fmpq_dedekind_sum_coprime_d(double h, double k)
+    void fmpq_dedekind_sum_coprime(fmpq_t s, const fmpz_t h, const fmpz_t k)
+    void fmpq_dedekind_sum(fmpq_t s, const fmpz_t h, const fmpz_t k)
+    void fmpq_harmonic_ui(fmpq_t x, unsigned long n)

src/sage/libs/flint/fmpq_mat.pxd

@@ -0,0 +1,62 @@
+# distutils: libraries = flint
+
+from sage.libs.flint.types cimport fmpz_t, fmpz, fmpq_t, fmpq, fmpz_mat_t, fmpq_mat_t, flint_rand_t, mp_bitcnt_t
+
+cdef extern from "flint/fmpq_mat.h":
+    fmpq * fmpq_mat_entry(const fmpq_mat_t mat, long i, long j)
+    fmpz * fmpq_mat_entry_num(const fmpq_mat_t mat, long i, long j)
+    fmpz * fmpq_mat_entry_den(const fmpq_mat_t mat, long i, long j)
+    long fmpq_mat_nrows(const fmpq_mat_t mat)
+    long fmpq_mat_ncols(const fmpq_mat_t mat)
+    void fmpq_mat_init(fmpq_mat_t mat, long rows, long cols)
+    void fmpq_mat_clear(fmpq_mat_t mat)
+    void fmpq_mat_swap(fmpq_mat_t mat1, fmpq_mat_t mat2)
+    void fmpq_mat_window_init(fmpq_mat_t window, const fmpq_mat_t mat, long r1, long c1, long r2, long c2)
+    void fmpq_mat_window_clear(fmpq_mat_t window)
+    void fmpq_mat_concat_horizontal(fmpq_mat_t res, const fmpq_mat_t mat1,  const fmpq_mat_t mat2)
+    void fmpq_mat_concat_vertical(fmpq_mat_t res, const fmpq_mat_t mat1,  const fmpq_mat_t mat2)
+    void fmpq_mat_print(const fmpq_mat_t mat)
+    void fmpq_mat_randbits(fmpq_mat_t mat, flint_rand_t state, mp_bitcnt_t bits)
+    void fmpq_mat_randtest(fmpq_mat_t mat, flint_rand_t state, mp_bitcnt_t bits)
+    void fmpq_mat_hilbert_matrix(fmpq_mat_t mat)
+    void fmpq_mat_set(fmpq_mat_t dest, const fmpq_mat_t src)
+    void fmpq_mat_zero(fmpq_mat_t mat)
+    void fmpq_mat_one(fmpq_mat_t mat)
+    void fmpq_mat_transpose(fmpq_mat_t rop, const fmpq_mat_t op)
+    void fmpq_mat_add(fmpq_mat_t mat, const fmpq_mat_t mat1, const fmpq_mat_t mat2)
+    void fmpq_mat_sub(fmpq_mat_t mat, const fmpq_mat_t mat1, const fmpq_mat_t mat2)
+    void fmpq_mat_neg(fmpq_mat_t rop, const fmpq_mat_t op)
+    void fmpq_mat_scalar_mul_fmpz(fmpq_mat_t rop, const fmpq_mat_t op, const fmpz_t x)
+    void fmpq_mat_scalar_div_fmpz(fmpq_mat_t rop, const fmpq_mat_t op, const fmpz_t x)
+    bint fmpq_mat_equal(const fmpq_mat_t mat1, const fmpq_mat_t mat2)
+    bint fmpq_mat_is_integral(const fmpq_mat_t mat)
+    bint fmpq_mat_is_zero(const fmpq_mat_t mat)
+    bint fmpq_mat_is_empty(const fmpq_mat_t mat)
+    bint fmpq_mat_is_square(const fmpq_mat_t mat)
+    int fmpq_mat_get_fmpz_mat(fmpz_mat_t dest, const fmpq_mat_t mat)
+    void fmpq_mat_get_fmpz_mat_entrywise(fmpz_mat_t num, fmpz_mat_t den, const fmpq_mat_t mat)
+    void fmpq_mat_get_fmpz_mat_matwise(fmpz_mat_t num, fmpz_t den, const fmpq_mat_t mat)
+    void fmpq_mat_get_fmpz_mat_rowwise(fmpz_mat_t num, fmpz * den, const fmpq_mat_t mat)
+    void fmpq_mat_get_fmpz_mat_colwise(fmpz_mat_t num, fmpz * den, const fmpq_mat_t mat)
+    void fmpq_mat_get_fmpz_mat_rowwise_2(fmpz_mat_t num, fmpz_mat_t num2, fmpz * den, const fmpq_mat_t mat, const fmpq_mat_t mat2)
+    void fmpq_mat_get_fmpz_mat_mod_fmpz(fmpz_mat_t dest, const fmpq_mat_t mat, const fmpz_t mod)
+    void fmpq_mat_set_fmpz_mat(fmpq_mat_t dest, const fmpz_mat_t src)
+    void fmpq_mat_set_fmpz_mat_div_fmpz(fmpq_mat_t X, const fmpz_mat_t Xmod, const fmpz_t div)
+    int fmpq_mat_set_fmpz_mat_mod_fmpz(fmpq_mat_t X, const fmpz_mat_t Xmod, const fmpz_t mod)
+    void fmpq_mat_mul_direct(fmpq_mat_t C, const fmpq_mat_t A, const fmpq_mat_t B)
+    void fmpq_mat_mul_cleared(fmpq_mat_t C, const fmpq_mat_t A, const fmpq_mat_t B)
+    void fmpq_mat_mul(fmpq_mat_t C, const fmpq_mat_t A, const fmpq_mat_t B)
+    void fmpq_mat_mul_fmpz_mat(fmpq_mat_t C, const fmpq_mat_t A, const fmpz_mat_t B)
+    void fmpq_mat_mul_r_fmpz_mat(fmpq_mat_t C, const fmpz_mat_t A, const fmpq_mat_t B)
+    void fmpq_mat_trace(fmpq_t trace, const fmpq_mat_t mat)
+    void fmpq_mat_det(fmpq_t det, const fmpq_mat_t mat)
+    int fmpq_mat_solve_fraction_free(fmpq_mat_t X, const fmpq_mat_t A, const fmpq_mat_t B)
+    int fmpq_mat_solve_dixon(fmpq_mat_t X, const fmpq_mat_t A, const fmpq_mat_t B)
+    int fmpq_mat_solve_fmpz_mat(fmpq_mat_t X, const fmpz_mat_t A, const fmpz_mat_t B)
+    int fmpq_mat_inv(fmpq_mat_t B, const fmpq_mat_t A)
+    int fmpq_mat_pivot(long * perm, fmpq_mat_t mat, long r, long c)
+    long fmpq_mat_rref_classical(fmpq_mat_t B, const fmpq_mat_t A)
+    long fmpq_mat_rref_fraction_free(fmpq_mat_t B, const fmpq_mat_t A)
+    long fmpq_mat_rref(fmpq_mat_t B, const fmpq_mat_t A)
+    void fmpq_mat_gso(fmpq_mat_t B, const fmpq_mat_t A)
+

src/sage/libs/flint/fmpz.pxd

@@ -184,3 +184,7 @@ cdef extern from "flint/fmpz.h":
     void fmpz_bin_uiui(fmpz_t, ulong, ulong)
     void fmpz_rfac_ui(fmpz_t, fmpz_t, ulong)
     void fmpz_rfac_uiui(fmpz_t, ulong, ulong)
+
+    # Random Generators
+    void fmpz_randbits(fmpz_t f, flint_rand_t state, mp_bitcnt_t bits)
+    void fmpz_randm(fmpz_t f, flint_rand_t state, const fmpz_t m)

src/sage/libs/flint/types.pxd

@@ -47,12 +47,19 @@ cdef extern from "flint/fmpz.h":
 
     ctypedef fmpz_preinvn_struct[1] fmpz_preinvn_t
 
+
 cdef extern from "flint/fmpz_mat.h":
     ctypedef struct fmpz_mat_struct:
         pass
 
     ctypedef fmpz_mat_struct fmpz_mat_t[1]
 
+cdef extern from "flint/fmpq_mat.h":
+    ctypedef struct fmpq_mat_struct:
+        pass
+
+    ctypedef fmpq_mat_struct fmpq_mat_t[1]
+
 cdef extern from "flint/fmpz_mod_poly.h":
     ctypedef struct fmpz_mod_poly_struct:
         pass

src/sage/libs/gmp/randomize.pxd

@@ -18,13 +18,23 @@ cdef inline void mpq_randomize_entry(mpq_t x, mpz_t num_bound, mpz_t den_bound):
         mpz_mul_si(mpq_numref(x), mpq_numref(x), -1)
     mpq_canonicalize(x)
 
+cdef inline void mpq_randomize_entry_nonzero(mpq_t x, mpz_t num_bound, mpz_t den_bound):
+    mpq_randomize_entry(x, num_bound, den_bound)
+    while mpq_sgn(x) == 0:
+        mpq_randomize_entry(x, num_bound, den_bound)
+
 cdef inline void mpq_randomize_entry_as_int(mpq_t x, mpz_t bound):
     cdef randstate rstate = current_randstate()
     mpz_urandomm(mpq_numref(x), rstate.gmp_state, bound)
     mpz_set_si(mpq_denref(x), 1)
     if rstate.c_random() % 2:
         mpz_mul_si(mpq_numref(x), mpq_numref(x), -1)
 
+cdef inline void mpq_randomize_entry_as_int_nonzero(mpq_t x, mpz_t bound):
+    mpq_randomize_entry_as_int(x, bound)
+    while mpq_sgn(x) == 0:
+        mpq_randomize_entry_as_int(x, bound)
+
 cdef inline void mpq_randomize_entry_recip_uniform(mpq_t x):
     cdef randstate rstate = current_randstate()
     # Numerator is selected the same way as ZZ.random_element();
@@ -39,3 +49,8 @@ cdef inline void mpq_randomize_entry_recip_uniform(mpq_t x):
     if den == 0: den = 1
     mpz_set_si(mpq_denref(x), SAGE_RAND_MAX / den)
     mpq_canonicalize(x)
+
+cdef inline void mpq_randomize_entry_recip_uniform_nonzero(mpq_t x):
+    mpq_randomize_entry_recip_uniform_nonzero(x)
+    while mpq_sgn(x) == 0:
+        mpq_randomize_entry_recip_uniform_nonzero(x)

src/sage/libs/pari/convert_flint.pxd

@@ -1,8 +1,13 @@
 from cypari2.types cimport GEN
 from cypari2.gen cimport Gen
-from sage.libs.flint.types cimport fmpz_t, fmpz_mat_t
+from sage.libs.flint.types cimport fmpz_t, fmpz_mat_t, fmpq_t, fmpq_mat_t
 
 cdef GEN _new_GEN_from_fmpz_t(fmpz_t value)
-cdef GEN _new_GEN_from_fmpz_mat_t(fmpz_mat_t B, Py_ssize_t nr, Py_ssize_t nc)
-cdef GEN _new_GEN_from_fmpz_mat_t_rotate90(fmpz_mat_t B, Py_ssize_t nr, Py_ssize_t nc)
-cdef Gen integer_matrix(fmpz_mat_t B, Py_ssize_t nr, Py_ssize_t nc, bint permute_for_hnf)
+cdef GEN _new_GEN_from_fmpz_mat_t(fmpz_mat_t B)
+cdef GEN _new_GEN_from_fmpz_mat_t_rotate90(fmpz_mat_t B)
+cdef Gen integer_matrix(fmpz_mat_t B, bint rotate)
+
+cdef GEN _new_GEN_from_fmpq_t(fmpq_t value)
+cdef GEN _new_GEN_from_fmpq_mat_t(fmpq_mat_t B)
+cdef GEN _new_GEN_from_fmpq_mat_t_rotate90(fmpq_mat_t B)
+cdef Gen rational_matrix(fmpq_mat_t B, bint rotate)