Trac #29894: add minimal interface for using ZZ[x]-matrices from flint

So that one may use this later to compute determinants in this case, for
example.

URL: https://trac.sagemath.org/29894
Reported by: chapoton
Ticket author(s): Frédéric Chapoton
Reviewer(s): Travis Scrimshaw

Author: Release Manager

src/sage/libs/flint/flint_wrap.h

@@ -37,6 +37,7 @@
 #include <flint/fmpq_poly.h>
 #include <flint/fmpz.h>
 #include <flint/fmpz_mat.h>
+#include <flint/fmpz_poly_mat.h>
 #include <flint/fmpz_mod_poly.h>
 #include <flint/fmpz_poly.h>
 #include <flint/fmpz_poly_q.h>

src/sage/libs/flint/fmpz_poly_mat.pxd

@@ -0,0 +1,27 @@
+# distutils: libraries = flint
+# distutils: depends = flint/fmpz_poly_mat.h
+
+from sage.libs.flint.types cimport fmpz_poly_mat_t, fmpz_poly_t, fmpz_t, slong, fmpz_mat_t
+
+# flint/fmpz_poly_mat.h
+cdef extern from "flint_wrap.h":
+
+    void fmpz_poly_mat_init(fmpz_poly_mat_t mat, slong rows, slong cols)
+    void fmpz_poly_mat_init_set(fmpz_poly_mat_t mat, const fmpz_poly_mat_t src)
+    void fmpz_poly_mat_clear(fmpz_poly_mat_t mat)
+    fmpz_poly_t fmpz_poly_mat_entry(fmpz_poly_mat_t mat, long i, long j)
+    slong fmpz_poly_mat_nrows(const fmpz_poly_mat_t mat)
+    slong fmpz_poly_mat_ncols(const fmpz_poly_mat_t mat)
+
+    void fmpz_poly_mat_set(fmpz_poly_mat_t mat1, const fmpz_poly_mat_t mat2)
+
+    void fmpz_poly_mat_swap(fmpz_poly_mat_t mat1, fmpz_poly_mat_t mat2)
+
+    void fmpz_poly_mat_transpose(fmpz_poly_mat_t B, const fmpz_poly_mat_t A)
+
+    void fmpz_poly_mat_evaluate_fmpz(fmpz_mat_t B, const fmpz_poly_mat_t A,
+                                                               const fmpz_t x)
+
+    void fmpz_poly_mat_trace(fmpz_poly_t trace, const fmpz_poly_mat_t mat)
+
+    void fmpz_poly_mat_det(fmpz_poly_t det, const fmpz_poly_mat_t A)

src/sage/libs/flint/types.pxd

@@ -79,6 +79,13 @@ cdef extern from "flint_wrap.h":
 
     ctypedef fmpq_mat_struct fmpq_mat_t[1]
 
+# flint/fmpz_poly_mat.h:
+cdef extern from "flint_wrap.h":
+    ctypedef struct fmpz_poly_mat_struct:
+        pass
+
+    ctypedef fmpz_poly_mat_struct fmpz_poly_mat_t[1]
+
 # flint/fmpz_mod_poly.h:
 cdef extern from "flint_wrap.h":
     ctypedef struct fmpz_mod_poly_struct: