From 4cf3226301cf71973aa996401a09979d840d0b5a Mon Sep 17 00:00:00 2001
From: Dimitri LESNOFF <dimitri.lesnoff@lip6.fr>
Date: Mon, 27 Oct 2025 14:48:34 +0100
Subject: [PATCH 01/15] Add a randunif function to src/nmod_vec

---
 src/nmod_vec/{randtest.c => rand.c} | 7 +++++++
 1 file changed, 7 insertions(+)
 rename src/nmod_vec/{randtest.c => rand.c} (84%)

diff --git a/src/nmod_vec/randtest.c b/src/nmod_vec/rand.c
similarity index 84%
rename from src/nmod_vec/randtest.c
rename to src/nmod_vec/rand.c
index 950050f27b..79bde0e242 100644
--- a/src/nmod_vec/randtest.c
+++ b/src/nmod_vec/rand.c
@@ -11,6 +11,13 @@
 
 #include "nmod_vec.h"
 
+void _nmod_vec_randunif(nn_ptr vec, flint_rand_t state, slong len, nmod_t mod)
+{
+    slong i;
+    for (i = 0; i < len; i++)
+        vec[i] = n_randint(state, mod.n);
+}
+
 void _nmod_vec_randtest(nn_ptr vec, flint_rand_t state, slong len, nmod_t mod)
 {
     slong i, sparseness;

From 48d863f0daa9ac68e442e2158d5d382b57dff3ad Mon Sep 17 00:00:00 2001
From: Dimitri LESNOFF <dimitri.lesnoff@lip6.fr>
Date: Mon, 27 Oct 2025 14:51:49 +0100
Subject: [PATCH 02/15] Add randtest to the documentation

---
 doc/source/fmpz.rst | 8 ++++++--
 1 file changed, 6 insertions(+), 2 deletions(-)

diff --git a/doc/source/fmpz.rst b/doc/source/fmpz.rst
index 98ee42436e..db940d802c 100644
--- a/doc/source/fmpz.rst
+++ b/doc/source/fmpz.rst
@@ -255,8 +255,12 @@ should call :func:`flint_rand_clear` to clean up.
 .. function:: void fmpz_randtest_unsigned(fmpz_t f, flint_rand_t state, flint_bitcnt_t bits)
               void fmpz_randtest(fmpz_t f, flint_rand_t state, flint_bitcnt_t bits)
 
-    Generates a random integer whose absolute value has a number of bits which
-    is random from `0` up to ``bits`` inclusive.
+    Generates a random unsigned integer whose absolute value has a number of bits which is random from `0` up to ``bits`` inclusive.
+
+.. function:: void fmpz_randtest(fmpz_t f, flint_rand_t state, flint_bitcnt_t bits)
+              void fmpz_randtest(fmpz_t f, flint_rand_t state, flint_bitcnt_t bits)
+
+    Generates a random signed integer whose absolute value has a number of bits which is random from `0` up to ``bits`` inclusive.
 
 .. function:: void fmpz_randtest_not_zero(fmpz_t f, flint_rand_t state, flint_bitcnt_t bits)
 

From f30cff0c7475ced3a2b70e2897a4fcb139a22113 Mon Sep 17 00:00:00 2001
From: Dimitri LESNOFF <dimitri.lesnoff@lip6.fr>
Date: Mon, 27 Oct 2025 16:09:57 +0100
Subject: [PATCH 03/15] Add fmpz_mod_mat random functions and upgrade
 documentation

---
 doc/source/fmpz_mod_mat.rst  | 13 ++++++++++++-
 doc/source/nmod_mat.rst      |  6 +++++-
 src/fmpz_mat/randtest.c      | 25 +++++++++++++++++++++----
 src/fmpz_mod_mat/randfull.c  | 21 +++++++++++++++++++++
 src/fmpz_mod_mat/randunif.c  | 19 +++++++++++++++++++
 src/nmod_mat/randomisation.c | 10 ++++++++++
 6 files changed, 88 insertions(+), 6 deletions(-)
 create mode 100644 src/fmpz_mod_mat/randfull.c
 create mode 100644 src/fmpz_mod_mat/randunif.c

diff --git a/doc/source/fmpz_mod_mat.rst b/doc/source/fmpz_mod_mat.rst
index e667b240b0..b778926546 100644
--- a/doc/source/fmpz_mod_mat.rst
+++ b/doc/source/fmpz_mod_mat.rst
@@ -95,7 +95,18 @@ Random generation
 .. function:: void fmpz_mod_mat_randtest(fmpz_mod_mat_t mat, flint_rand_t state, const fmpz_mod_ctx_t ctx)
 
     Generate a random matrix with the existing dimensions and entries in
-    `[0, n)` where ``n`` is the modulus.
+    `[0, n)` where ``n`` is the modulus. A sparse matrix is
+    generated with increased probability.
+
+.. function:: void fmpz_mod_mat_randfull(fmpz_mod_mat_t mat, flint_rand_t state, const fmpz_mod_ctx_t ctx)
+
+    Sets the element to random numbers between `1` and `m-1` likely to be close to the modulus
+    of the matrix. This is used to test potential overflow-related bugs.
+
+.. function:: void fmpz_mod_mat_randunif(fmpz_mod_mat_t mat, flint_rand_t state, const fmpz_mod_ctx_t ctx)
+
+    Sets the element to random numbers between `0` and `m-1` likely to be close to the modulus
+    of the matrix. This is used to write benchmarks.
 
 
 Windows and concatenation
diff --git a/doc/source/nmod_mat.rst b/doc/source/nmod_mat.rst
index b1da8f22ca..43e2b7164d 100644
--- a/doc/source/nmod_mat.rst
+++ b/doc/source/nmod_mat.rst
@@ -196,9 +196,13 @@ Random matrix generation
 
 .. function:: void nmod_mat_randfull(nmod_mat_t mat, flint_rand_t state)
 
-    Sets the element to random numbers likely to be close to the modulus
+    Sets the element to random numbers between `1` and `m-1` likely to be close to the modulus
     of the matrix. This is used to test potential overflow-related bugs.
 
+.. function:: void nmod_mat_randunif(nmod_mat_t mat, flint_rand_t state)
+
+    Sets the element to uniformly generated random numbers between `0` and `m-1`. This is used for benchmarks.
+
 .. function:: int nmod_mat_randpermdiag(nmod_mat_t mat, flint_rand_t state, nn_srcptr diag, slong n)
 
     Sets ``mat`` to a random permutation of the diagonal matrix
diff --git a/src/fmpz_mat/randtest.c b/src/fmpz_mat/randtest.c
index 1ca4d620b3..1efa3544ea 100644
--- a/src/fmpz_mat/randtest.c
+++ b/src/fmpz_mat/randtest.c
@@ -15,12 +15,29 @@
 void
 fmpz_mat_randtest(fmpz_mat_t mat, flint_rand_t state, flint_bitcnt_t bits)
 {
-    slong r, c, i, j;
+    // Adapted from nmod_vec_randtest
+    slong r, c, i, j=0, len;
+    slong sparseness;
 
     r = mat->r;
     c = mat->c;
+    len = r*c;
 
-    for (i = 0; i < r; i++)
-        for (j = 0; j < c; j++)
-            fmpz_randtest(fmpz_mat_entry(mat, i, j), state, bits);
+    if (n_randint(state, 2))
+    {
+      for (i = 0; i < r; i++)
+          for (j = 0; j < c; j++)
+              fmpz_randtest(fmpz_mat_entry(mat, i, j), state, bits);
+    }
+    else
+    {
+        sparseness = 1 + n_randint(state, FLINT_MAX(2, len));
+        for (i = 0; i < len; i++)
+        {
+            if (n_randint(state, sparseness))
+                *fmpz_mat_entry(mat, i, j) = 0;
+            else
+                fmpz_randtest(fmpz_mat_entry(mat, i, j), state, bits);
+        }
+    }
 }
diff --git a/src/fmpz_mod_mat/randfull.c b/src/fmpz_mod_mat/randfull.c
new file mode 100644
index 0000000000..77b3a72ed3
--- /dev/null
+++ b/src/fmpz_mod_mat/randfull.c
@@ -0,0 +1,21 @@
+#include "fmpz.h"
+#include "fmpz_mod_mat.h"
+
+void fmpz_mod_mat_randfull(fmpz_mod_mat_t mat, flint_rand_t state, const fmpz_mod_ctx_t ctx)
+{
+    fmpz* e;
+    slong i, j, r, c;
+    r = fmpz_mod_mat_nrows(mat, ctx);
+    c = fmpz_mod_mat_nrows(mat, ctx);
+
+    for (i = 0; i < r; i++)
+    {
+        for (j = 0; j < c; j++)
+        {
+            e = fmpz_mod_mat_entry(mat, i, j);
+            fmpz_randm(e, state, ctx->n);
+            if (fmpz_cmp_ui(e, 0))
+                fmpz_one(e);
+        }
+    }
+}
diff --git a/src/fmpz_mod_mat/randunif.c b/src/fmpz_mod_mat/randunif.c
new file mode 100644
index 0000000000..e2182ecfbe
--- /dev/null
+++ b/src/fmpz_mod_mat/randunif.c
@@ -0,0 +1,19 @@
+#include "fmpz.h"
+#include "fmpz_mod_mat.h"
+
+void fmpz_mod_mat_randfull(fmpz_mod_mat_t mat, flint_rand_t state, const fmpz_mod_ctx_t ctx)
+{
+    fmpz* e;
+    slong i, j, r, c;
+    r = fmpz_mod_mat_nrows(mat, ctx);
+    c = fmpz_mod_mat_nrows(mat, ctx);
+
+    for (i = 0; i < r; i++)
+    {
+        for (j = 0; j < c; j++)
+        {
+            e = fmpz_mod_mat_entry(mat, i, j);
+            fmpz_randm(e, state, ctx->n);
+        }
+    }
+}
diff --git a/src/nmod_mat/randomisation.c b/src/nmod_mat/randomisation.c
index 4dfe4bd52d..274842c925 100644
--- a/src/nmod_mat/randomisation.c
+++ b/src/nmod_mat/randomisation.c
@@ -24,6 +24,16 @@ nmod_mat_randfull(nmod_mat_t mat, flint_rand_t state)
             nmod_mat_entry(mat, i, j) = FLINT_MAX(1, n_randint(state, mat->mod.n));
 }
 
+void
+nmod_mat_randunif(nmod_mat_t mat, flint_rand_t state)
+{
+    slong i, j;
+
+    for (i = 0; i < mat->r; i++)
+        for (j = 0; j < mat->c; j++)
+            nmod_mat_entry(mat, i, j) = n_randint(state, mat->mod.n);
+}
+
 void
 nmod_mat_randops(nmod_mat_t mat, flint_rand_t state, slong count)
 {

From 534cd063af053e3579eb1bd6ad3e5c254393382a Mon Sep 17 00:00:00 2001
From: Dimitri LESNOFF <dimitri.lesnoff@lip6.fr>
Date: Mon, 27 Oct 2025 16:47:07 +0100
Subject: [PATCH 04/15] Update headers and documentation

---
 doc/source/nmod_vec.rst     | 5 ++++-
 src/fmpz_mod_mat.h          | 4 ++++
 src/fmpz_mod_mat/randunif.c | 2 +-
 src/nmod_mat.h              | 1 +
 src/nmod_vec.h              | 2 ++
 5 files changed, 12 insertions(+), 2 deletions(-)

diff --git a/doc/source/nmod_vec.rst b/doc/source/nmod_vec.rst
index 55c4e6c14d..d8e187407e 100644
--- a/doc/source/nmod_vec.rst
+++ b/doc/source/nmod_vec.rst
@@ -26,6 +26,10 @@ Random functions
     Sets ``vec`` to a random vector of the given length with entries
     reduced modulo ``mod.n``.
 
+.. function:: void _nmod_vec_randunif(nn_ptr vec, flint_rand_t state, slong len, nmod_t mod)
+
+    Sets ``vec`` to a random vector of the given length with entries uniformly generated between ``0`` and ``mod.n-1`` included.
+
 
 Basic manipulation and comparison
 --------------------------------------------------------------------------------
@@ -224,4 +228,3 @@ performed at the very end of the computation.
     Same specification as ``_nmod_vec_dot_bound_limbs``, but uses the additional
     input ``params`` to reduce the amount of computations; for correctness
     ``params`` must have been computed for the specified ``len`` and ``mod``.
-
diff --git a/src/fmpz_mod_mat.h b/src/fmpz_mod_mat.h
index 9cd599ed69..875357f4bc 100644
--- a/src/fmpz_mod_mat.h
+++ b/src/fmpz_mod_mat.h
@@ -118,6 +118,10 @@ FMPZ_MOD_MAT_INLINE void _fmpz_mod_mat_reduce(fmpz_mod_mat_t mat, const fmpz_mod
 
 void fmpz_mod_mat_randtest(fmpz_mod_mat_t mat, flint_rand_t state, const fmpz_mod_ctx_t ctx);
 
+void fmpz_mod_mat_randfull(fmpz_mod_mat_t mat, flint_rand_t state, const fmpz_mod_ctx_t ctx);
+
+void fmpz_mod_mat_randunif(fmpz_mod_mat_t mat, flint_rand_t state, const fmpz_mod_ctx_t ctx);
+
 void fmpz_mod_mat_randrank(fmpz_mod_mat_t mat, flint_rand_t state, slong rank, const fmpz_mod_ctx_t ctx);
 
 void fmpz_mod_mat_randtril(fmpz_mod_mat_t mat, flint_rand_t state, int unit, const fmpz_mod_ctx_t ctx);
diff --git a/src/fmpz_mod_mat/randunif.c b/src/fmpz_mod_mat/randunif.c
index e2182ecfbe..a689fe151f 100644
--- a/src/fmpz_mod_mat/randunif.c
+++ b/src/fmpz_mod_mat/randunif.c
@@ -1,7 +1,7 @@
 #include "fmpz.h"
 #include "fmpz_mod_mat.h"
 
-void fmpz_mod_mat_randfull(fmpz_mod_mat_t mat, flint_rand_t state, const fmpz_mod_ctx_t ctx)
+void fmpz_mod_mat_randunif(fmpz_mod_mat_t mat, flint_rand_t state, const fmpz_mod_ctx_t ctx)
 {
     fmpz* e;
     slong i, j, r, c;
diff --git a/src/nmod_mat.h b/src/nmod_mat.h
index 7b5dd92771..4eb5f4e039 100644
--- a/src/nmod_mat.h
+++ b/src/nmod_mat.h
@@ -106,6 +106,7 @@ void nmod_mat_concat_vertical(nmod_mat_t res,
 /* Random matrix generation */
 void nmod_mat_randtest(nmod_mat_t mat, flint_rand_t state);
 void nmod_mat_randfull(nmod_mat_t mat, flint_rand_t state);
+void nmod_mat_randunif(nmod_mat_t mat, flint_rand_t state);
 int nmod_mat_randpermdiag(nmod_mat_t mat, flint_rand_t state,
                  nn_srcptr diag, slong n);
 void nmod_mat_randrank(nmod_mat_t, flint_rand_t state, slong rank);
diff --git a/src/nmod_vec.h b/src/nmod_vec.h
index cb44dbd4cb..1389869ccc 100644
--- a/src/nmod_vec.h
+++ b/src/nmod_vec.h
@@ -47,6 +47,8 @@ void _nmod_vec_clear(nn_ptr vec)
 
 void _nmod_vec_randtest(nn_ptr vec, flint_rand_t state, slong len, nmod_t mod);
 
+void _nmod_vec_randunif(nn_ptr vec, flint_rand_t state, slong len, nmod_t mod);
+
 NMOD_VEC_INLINE
 void _nmod_vec_zero(nn_ptr vec, slong len)
 {

From 7ab4f133237a5e80bf15f3941555b79a3a3f9900 Mon Sep 17 00:00:00 2001
From: Dimitri LESNOFF <dimitri.lesnoff@lip6.fr>
Date: Mon, 27 Oct 2025 16:54:34 +0100
Subject: [PATCH 05/15] Change randunif to rand

---
 src/fmpz_mod_mat.h           | 2 +-
 src/fmpz_mod_mat/randunif.c  | 2 +-
 src/nmod_mat.h               | 2 +-
 src/nmod_mat/randomisation.c | 2 +-
 src/nmod_vec.h               | 2 +-
 src/nmod_vec/rand.c          | 2 +-
 6 files changed, 6 insertions(+), 6 deletions(-)

diff --git a/src/fmpz_mod_mat.h b/src/fmpz_mod_mat.h
index 875357f4bc..15b871dace 100644
--- a/src/fmpz_mod_mat.h
+++ b/src/fmpz_mod_mat.h
@@ -120,7 +120,7 @@ void fmpz_mod_mat_randtest(fmpz_mod_mat_t mat, flint_rand_t state, const fmpz_mo
 
 void fmpz_mod_mat_randfull(fmpz_mod_mat_t mat, flint_rand_t state, const fmpz_mod_ctx_t ctx);
 
-void fmpz_mod_mat_randunif(fmpz_mod_mat_t mat, flint_rand_t state, const fmpz_mod_ctx_t ctx);
+void fmpz_mod_mat_rand(fmpz_mod_mat_t mat, flint_rand_t state, const fmpz_mod_ctx_t ctx);
 
 void fmpz_mod_mat_randrank(fmpz_mod_mat_t mat, flint_rand_t state, slong rank, const fmpz_mod_ctx_t ctx);
 
diff --git a/src/fmpz_mod_mat/randunif.c b/src/fmpz_mod_mat/randunif.c
index a689fe151f..ddd0e21b82 100644
--- a/src/fmpz_mod_mat/randunif.c
+++ b/src/fmpz_mod_mat/randunif.c
@@ -1,7 +1,7 @@
 #include "fmpz.h"
 #include "fmpz_mod_mat.h"
 
-void fmpz_mod_mat_randunif(fmpz_mod_mat_t mat, flint_rand_t state, const fmpz_mod_ctx_t ctx)
+void fmpz_mod_mat_rand(fmpz_mod_mat_t mat, flint_rand_t state, const fmpz_mod_ctx_t ctx)
 {
     fmpz* e;
     slong i, j, r, c;
diff --git a/src/nmod_mat.h b/src/nmod_mat.h
index 4eb5f4e039..487b02d37c 100644
--- a/src/nmod_mat.h
+++ b/src/nmod_mat.h
@@ -106,7 +106,7 @@ void nmod_mat_concat_vertical(nmod_mat_t res,
 /* Random matrix generation */
 void nmod_mat_randtest(nmod_mat_t mat, flint_rand_t state);
 void nmod_mat_randfull(nmod_mat_t mat, flint_rand_t state);
-void nmod_mat_randunif(nmod_mat_t mat, flint_rand_t state);
+void nmod_mat_rand(nmod_mat_t mat, flint_rand_t state);
 int nmod_mat_randpermdiag(nmod_mat_t mat, flint_rand_t state,
                  nn_srcptr diag, slong n);
 void nmod_mat_randrank(nmod_mat_t, flint_rand_t state, slong rank);
diff --git a/src/nmod_mat/randomisation.c b/src/nmod_mat/randomisation.c
index 274842c925..09846be245 100644
--- a/src/nmod_mat/randomisation.c
+++ b/src/nmod_mat/randomisation.c
@@ -25,7 +25,7 @@ nmod_mat_randfull(nmod_mat_t mat, flint_rand_t state)
 }
 
 void
-nmod_mat_randunif(nmod_mat_t mat, flint_rand_t state)
+nmod_mat_rand(nmod_mat_t mat, flint_rand_t state)
 {
     slong i, j;
 
diff --git a/src/nmod_vec.h b/src/nmod_vec.h
index 1389869ccc..04db64ddba 100644
--- a/src/nmod_vec.h
+++ b/src/nmod_vec.h
@@ -47,7 +47,7 @@ void _nmod_vec_clear(nn_ptr vec)
 
 void _nmod_vec_randtest(nn_ptr vec, flint_rand_t state, slong len, nmod_t mod);
 
-void _nmod_vec_randunif(nn_ptr vec, flint_rand_t state, slong len, nmod_t mod);
+void _nmod_vec_rand(nn_ptr vec, flint_rand_t state, slong len, nmod_t mod);
 
 NMOD_VEC_INLINE
 void _nmod_vec_zero(nn_ptr vec, slong len)
diff --git a/src/nmod_vec/rand.c b/src/nmod_vec/rand.c
index 79bde0e242..e25d9f55a9 100644
--- a/src/nmod_vec/rand.c
+++ b/src/nmod_vec/rand.c
@@ -11,7 +11,7 @@
 
 #include "nmod_vec.h"
 
-void _nmod_vec_randunif(nn_ptr vec, flint_rand_t state, slong len, nmod_t mod)
+void _nmod_vec_rand(nn_ptr vec, flint_rand_t state, slong len, nmod_t mod)
 {
     slong i;
     for (i = 0; i < len; i++)

From 1fb1e3ec75218eae59c8b9e2bf2842a2526499dd Mon Sep 17 00:00:00 2001
From: Dimitri LESNOFF <dimitri.lesnoff@lip6.fr>
Date: Mon, 27 Oct 2025 17:32:06 +0100
Subject: [PATCH 06/15] randunif->rand: Change file name

---
 src/fmpz_mod_mat/{randunif.c => rand.c} | 0
 1 file changed, 0 insertions(+), 0 deletions(-)
 rename src/fmpz_mod_mat/{randunif.c => rand.c} (100%)

diff --git a/src/fmpz_mod_mat/randunif.c b/src/fmpz_mod_mat/rand.c
similarity index 100%
rename from src/fmpz_mod_mat/randunif.c
rename to src/fmpz_mod_mat/rand.c

From c245cdcc6728289cc39ea88cf9ba80e32373e0e9 Mon Sep 17 00:00:00 2001
From: Dimitri LESNOFF <dimitri.lesnoff@lip6.fr>
Date: Mon, 27 Oct 2025 17:37:21 +0100
Subject: [PATCH 07/15] Uses fmpz_zero instead of dereferencing

---
 src/fmpz_mat/randtest.c | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/src/fmpz_mat/randtest.c b/src/fmpz_mat/randtest.c
index 1efa3544ea..86cfdbcddc 100644
--- a/src/fmpz_mat/randtest.c
+++ b/src/fmpz_mat/randtest.c
@@ -35,7 +35,7 @@ fmpz_mat_randtest(fmpz_mat_t mat, flint_rand_t state, flint_bitcnt_t bits)
         for (i = 0; i < len; i++)
         {
             if (n_randint(state, sparseness))
-                *fmpz_mat_entry(mat, i, j) = 0;
+                fmpz_zero(fmpz_mat_entry(mat, i, j));
             else
                 fmpz_randtest(fmpz_mat_entry(mat, i, j), state, bits);
         }

From 2ff76f1f87cda2f559fd34397f928ee7f01acf38 Mon Sep 17 00:00:00 2001
From: Dimitri Lesnoff <54949944+dlesnoff@users.noreply.github.com>
Date: Tue, 28 Oct 2025 10:40:15 +0100
Subject: [PATCH 08/15] Add documentation suggestions

Co-authored-by: Vincent Neiger <vneiger@users.noreply.github.com>
---
 doc/source/fmpz_mod_mat.rst | 8 ++++----
 doc/source/nmod_mat.rst     | 4 ++--
 doc/source/nmod_vec.rst     | 2 +-
 3 files changed, 7 insertions(+), 7 deletions(-)

diff --git a/doc/source/fmpz_mod_mat.rst b/doc/source/fmpz_mod_mat.rst
index b778926546..9d3a9d8b40 100644
--- a/doc/source/fmpz_mod_mat.rst
+++ b/doc/source/fmpz_mod_mat.rst
@@ -100,13 +100,13 @@ Random generation
 
 .. function:: void fmpz_mod_mat_randfull(fmpz_mod_mat_t mat, flint_rand_t state, const fmpz_mod_ctx_t ctx)
 
-    Sets the element to random numbers between `1` and `m-1` likely to be close to the modulus
+    Sets the element to random numbers in `[0, n)`, likely to be close to the modulus ``n``
     of the matrix. This is used to test potential overflow-related bugs.
 
-.. function:: void fmpz_mod_mat_randunif(fmpz_mod_mat_t mat, flint_rand_t state, const fmpz_mod_ctx_t ctx)
+.. function:: void fmpz_mod_mat_rand(fmpz_mod_mat_t mat, flint_rand_t state, const fmpz_mod_ctx_t ctx)
 
-    Sets the element to random numbers between `0` and `m-1` likely to be close to the modulus
-    of the matrix. This is used to write benchmarks.
+    Sets the element to random numbers in `[0, n)`, likely to be close to the modulus ``n``
+    of the matrix.
 
 
 Windows and concatenation
diff --git a/doc/source/nmod_mat.rst b/doc/source/nmod_mat.rst
index 43e2b7164d..33dced7c27 100644
--- a/doc/source/nmod_mat.rst
+++ b/doc/source/nmod_mat.rst
@@ -196,12 +196,12 @@ Random matrix generation
 
 .. function:: void nmod_mat_randfull(nmod_mat_t mat, flint_rand_t state)
 
-    Sets the element to random numbers between `1` and `m-1` likely to be close to the modulus
+    Sets the element to random numbers in `[0, n)`, likely to be close to the modulus ``n``
     of the matrix. This is used to test potential overflow-related bugs.
 
 .. function:: void nmod_mat_randunif(nmod_mat_t mat, flint_rand_t state)
 
-    Sets the element to uniformly generated random numbers between `0` and `m-1`. This is used for benchmarks.
+    Sets the element to uniformly generated random numbers in `[0, n)`, where `n` is the modulus of the matrix.
 
 .. function:: int nmod_mat_randpermdiag(nmod_mat_t mat, flint_rand_t state, nn_srcptr diag, slong n)
 
diff --git a/doc/source/nmod_vec.rst b/doc/source/nmod_vec.rst
index d8e187407e..e311d33c6f 100644
--- a/doc/source/nmod_vec.rst
+++ b/doc/source/nmod_vec.rst
@@ -28,7 +28,7 @@ Random functions
 
 .. function:: void _nmod_vec_randunif(nn_ptr vec, flint_rand_t state, slong len, nmod_t mod)
 
-    Sets ``vec`` to a random vector of the given length with entries uniformly generated between ``0`` and ``mod.n-1`` included.
+    Sets ``vec`` to a vector of the given length with entries picked uniformly at random in `[0, mod.n)`.
 
 
 Basic manipulation and comparison

From 1baa250f74b3234d9d553e8e17e1b39740690c3d Mon Sep 17 00:00:00 2001
From: Dimitri LESNOFF <dimitri.lesnoff@lip6.fr>
Date: Tue, 28 Oct 2025 10:54:11 +0100
Subject: [PATCH 09/15] Fix loops in random generation

---
 src/fmpz_mat/randtest.c | 14 ++++++++------
 1 file changed, 8 insertions(+), 6 deletions(-)

diff --git a/src/fmpz_mat/randtest.c b/src/fmpz_mat/randtest.c
index 86cfdbcddc..bd02c21e4e 100644
--- a/src/fmpz_mat/randtest.c
+++ b/src/fmpz_mat/randtest.c
@@ -16,7 +16,7 @@ void
 fmpz_mat_randtest(fmpz_mat_t mat, flint_rand_t state, flint_bitcnt_t bits)
 {
     // Adapted from nmod_vec_randtest
-    slong r, c, i, j=0, len;
+    slong r, c, i, j, len;
     slong sparseness;
 
     r = mat->r;
@@ -32,12 +32,14 @@ fmpz_mat_randtest(fmpz_mat_t mat, flint_rand_t state, flint_bitcnt_t bits)
     else
     {
         sparseness = 1 + n_randint(state, FLINT_MAX(2, len));
-        for (i = 0; i < len; i++)
+        for (i = 0; i < r; i++)
         {
-            if (n_randint(state, sparseness))
-                fmpz_zero(fmpz_mat_entry(mat, i, j));
-            else
-                fmpz_randtest(fmpz_mat_entry(mat, i, j), state, bits);
+            for (j = 0; j < c; j++) {
+                if (n_randint(state, sparseness))
+                    fmpz_zero(fmpz_mat_entry(mat, i, j));
+                else
+                    fmpz_randtest(fmpz_mat_entry(mat, i, j), state, bits);
+            }
         }
     }
 }

From 3ce0ff0af416b85b68c5b8e0e67c5ef4599e6350 Mon Sep 17 00:00:00 2001
From: Dimitri LESNOFF <dimitri.lesnoff@lip6.fr>
Date: Tue, 28 Oct 2025 11:18:44 +0100
Subject: [PATCH 10/15] Fix documentation

---
 doc/source/fmpz.rst | 7 +------
 1 file changed, 1 insertion(+), 6 deletions(-)

diff --git a/doc/source/fmpz.rst b/doc/source/fmpz.rst
index db940d802c..00824c4a52 100644
--- a/doc/source/fmpz.rst
+++ b/doc/source/fmpz.rst
@@ -255,12 +255,7 @@ should call :func:`flint_rand_clear` to clean up.
 .. function:: void fmpz_randtest_unsigned(fmpz_t f, flint_rand_t state, flint_bitcnt_t bits)
               void fmpz_randtest(fmpz_t f, flint_rand_t state, flint_bitcnt_t bits)
 
-    Generates a random unsigned integer whose absolute value has a number of bits which is random from `0` up to ``bits`` inclusive.
-
-.. function:: void fmpz_randtest(fmpz_t f, flint_rand_t state, flint_bitcnt_t bits)
-              void fmpz_randtest(fmpz_t f, flint_rand_t state, flint_bitcnt_t bits)
-
-    Generates a random signed integer whose absolute value has a number of bits which is random from `0` up to ``bits`` inclusive.
+    Generates a random (unsigned) integer whose absolute value has a number of bits which is random from `0` up to ``bits`` inclusive.
 
 .. function:: void fmpz_randtest_not_zero(fmpz_t f, flint_rand_t state, flint_bitcnt_t bits)
 

From 9a63870fa2332f3c02c2b5bcb7c25e7e4f226958 Mon Sep 17 00:00:00 2001
From: Dimitri LESNOFF <dimitri.lesnoff@lip6.fr>
Date: Tue, 28 Oct 2025 11:32:17 +0100
Subject: [PATCH 11/15] Uses vec internally

---
 src/nmod_mat/randomisation.c | 5 ++---
 1 file changed, 2 insertions(+), 3 deletions(-)

diff --git a/src/nmod_mat/randomisation.c b/src/nmod_mat/randomisation.c
index 09846be245..155ed6c4cc 100644
--- a/src/nmod_mat/randomisation.c
+++ b/src/nmod_mat/randomisation.c
@@ -17,11 +17,10 @@
 void
 nmod_mat_randfull(nmod_mat_t mat, flint_rand_t state)
 {
-    slong i, j;
+    slong i;
 
     for (i = 0; i < mat->r; i++)
-        for (j = 0; j < mat->c; j++)
-            nmod_mat_entry(mat, i, j) = FLINT_MAX(1, n_randint(state, mat->mod.n));
+        _nmod_vec_rand(nmod_mat_row_ptr(mat, i), state, mat->c, mat->mod);
 }
 
 void

From ed77486530958f120f9138e9e47683dec8595989 Mon Sep 17 00:00:00 2001
From: Dimitri LESNOFF <dimitri.lesnoff@lip6.fr>
Date: Tue, 28 Oct 2025 11:35:37 +0100
Subject: [PATCH 12/15] Adds a function to get the modulus

---
 doc/source/nmod_mat.rst |  6 +++++-
 src/nmod_mat.h          | 11 +++++++++++
 2 files changed, 16 insertions(+), 1 deletion(-)

diff --git a/doc/source/nmod_mat.rst b/doc/source/nmod_mat.rst
index 33dced7c27..a37307ff62 100644
--- a/doc/source/nmod_mat.rst
+++ b/doc/source/nmod_mat.rst
@@ -76,7 +76,11 @@ Memory management
     Swaps two matrices by swapping the individual entries rather than swapping
     the contents of the structs.
 
-.. function:: void nmod_mat_set_mod(nmod_mat_t mat, ulong n);
+.. function:: nmod_t nmod_mat_mod(const nmod_mat_t mat)
+
+    Returns the modulus of a matrix.
+
+.. function:: void nmod_mat_set_mod(nmod_mat_t mat, ulong n)
 
     Sets the modulus of an already initialized matrix ``mat`` to be `n`. Row
     and column dimensions are unchanged, and allocated memory is unaffected.
diff --git a/src/nmod_mat.h b/src/nmod_mat.h
index 487b02d37c..c6a5412b3e 100644
--- a/src/nmod_mat.h
+++ b/src/nmod_mat.h
@@ -40,6 +40,11 @@ ulong * nmod_mat_entry_ptr(const nmod_mat_t mat, slong i, slong j)
    return &nmod_mat_entry(mat, i, j);
 }
 
+NMOD_MAT_INLINE
+ulong * nmod_mat_row_ptr(const nmod_mat_t mat, slong i)
+{
+   return &nmod_mat_entry(mat, i, 0);
+}
 /* See inlines.c */
 
 NMOD_MAT_INLINE
@@ -56,6 +61,12 @@ slong nmod_mat_ncols(const nmod_mat_t mat)
 
 void nmod_mat_set_mod(nmod_mat_t mat, ulong n);
 
+NMOD_MAT_INLINE
+nmod_t nmod_mat_mod(const nmod_mat_t mat)
+{
+   return mat->mod;
+}
+
 /* Memory management */
 void nmod_mat_init(nmod_mat_t mat, slong rows, slong cols, ulong n);
 void nmod_mat_init_set(nmod_mat_t mat, const nmod_mat_t src);

From 5440826508ce7a5d39bae42027a2b51e1f4fab9d Mon Sep 17 00:00:00 2001
From: Dimitri Lesnoff <54949944+dlesnoff@users.noreply.github.com>
Date: Tue, 28 Oct 2025 14:20:10 +0100
Subject: [PATCH 13/15] Apply suggestions from code review

Co-authored-by: Vincent Neiger <vneiger@users.noreply.github.com>
---
 doc/source/nmod_mat.rst | 2 +-
 doc/source/nmod_vec.rst | 2 +-
 2 files changed, 2 insertions(+), 2 deletions(-)

diff --git a/doc/source/nmod_mat.rst b/doc/source/nmod_mat.rst
index a37307ff62..44579a4273 100644
--- a/doc/source/nmod_mat.rst
+++ b/doc/source/nmod_mat.rst
@@ -203,7 +203,7 @@ Random matrix generation
     Sets the element to random numbers in `[0, n)`, likely to be close to the modulus ``n``
     of the matrix. This is used to test potential overflow-related bugs.
 
-.. function:: void nmod_mat_randunif(nmod_mat_t mat, flint_rand_t state)
+.. function:: void nmod_mat_rand(nmod_mat_t mat, flint_rand_t state)
 
     Sets the element to uniformly generated random numbers in `[0, n)`, where `n` is the modulus of the matrix.
 
diff --git a/doc/source/nmod_vec.rst b/doc/source/nmod_vec.rst
index e311d33c6f..2388f506e6 100644
--- a/doc/source/nmod_vec.rst
+++ b/doc/source/nmod_vec.rst
@@ -26,7 +26,7 @@ Random functions
     Sets ``vec`` to a random vector of the given length with entries
     reduced modulo ``mod.n``.
 
-.. function:: void _nmod_vec_randunif(nn_ptr vec, flint_rand_t state, slong len, nmod_t mod)
+.. function:: void _nmod_vec_rand(nn_ptr vec, flint_rand_t state, slong len, nmod_t mod)
 
     Sets ``vec`` to a vector of the given length with entries picked uniformly at random in `[0, mod.n)`.
 

From 8b583924713ec81969db466b241ace15efa18c2c Mon Sep 17 00:00:00 2001
From: Dimitri LESNOFF <dimitri.lesnoff@lip6.fr>
Date: Tue, 28 Oct 2025 14:23:38 +0100
Subject: [PATCH 14/15] Apply suggestion for nmod_mat_rand(full)

Co-authored-by: vneiger <vincent.neiger@lip6.fr>
---
 src/nmod_mat/randomisation.c | 11 ++++-------
 1 file changed, 4 insertions(+), 7 deletions(-)

diff --git a/src/nmod_mat/randomisation.c b/src/nmod_mat/randomisation.c
index 155ed6c4cc..fe70b721d0 100644
--- a/src/nmod_mat/randomisation.c
+++ b/src/nmod_mat/randomisation.c
@@ -17,20 +17,17 @@
 void
 nmod_mat_randfull(nmod_mat_t mat, flint_rand_t state)
 {
-    slong i;
+    slong i, j;
 
     for (i = 0; i < mat->r; i++)
-        _nmod_vec_rand(nmod_mat_row_ptr(mat, i), state, mat->c, mat->mod);
+        for (j = 0; j < mat->c; j++)
+            nmod_mat_entry(mat, i, j) = FLINT_MAX(1, n_randint(state, mat->mod.n));
 }
 
 void
 nmod_mat_rand(nmod_mat_t mat, flint_rand_t state)
 {
-    slong i, j;
-
-    for (i = 0; i < mat->r; i++)
-        for (j = 0; j < mat->c; j++)
-            nmod_mat_entry(mat, i, j) = n_randint(state, mat->mod.n);
+    _nmod_vec_rand(mat->entries, state, mat->r*mat->c, mat->mod);
 }
 
 void

From 4afd8c062f51c3b6f5a2be1805b93e96aeb8ecab Mon Sep 17 00:00:00 2001
From: Dimitri LESNOFF <dimitri.lesnoff@lip6.fr>
Date: Tue, 28 Oct 2025 16:07:10 +0100
Subject: [PATCH 15/15] Make looping over matrices compatible with stride

---
 src/nmod_mat/randomisation.c | 8 ++++++--
 1 file changed, 6 insertions(+), 2 deletions(-)

diff --git a/src/nmod_mat/randomisation.c b/src/nmod_mat/randomisation.c
index fe70b721d0..52e9a99c81 100644
--- a/src/nmod_mat/randomisation.c
+++ b/src/nmod_mat/randomisation.c
@@ -27,7 +27,9 @@ nmod_mat_randfull(nmod_mat_t mat, flint_rand_t state)
 void
 nmod_mat_rand(nmod_mat_t mat, flint_rand_t state)
 {
-    _nmod_vec_rand(mat->entries, state, mat->r*mat->c, mat->mod);
+    slong i;
+    for (i = 0; i < mat->r; i++)
+        _nmod_vec_rand(nmod_mat_row_ptr(mat, i), state, mat->c, mat->mod);
 }
 
 void
@@ -129,7 +131,9 @@ nmod_mat_randrank(nmod_mat_t mat, flint_rand_t state, slong rank)
 void
 nmod_mat_randtest(nmod_mat_t mat, flint_rand_t state)
 {
-    _nmod_vec_randtest(mat->entries, state, mat->r * mat->c, mat->mod);
+    slong i;
+    for (i = 0; i < mat->r; i++)
+        _nmod_vec_randtest(nmod_mat_row_ptr(mat, i), state, mat->c, mat->mod);
 }
 
 void