From e6f8dcdfdb13ce0d72f5fe4327de0f150565f432 Mon Sep 17 00:00:00 2001
From: Dimitri LESNOFF <dimitri.lesnoff@lip6.fr>
Date: Thu, 30 Oct 2025 12:05:00 +0100
Subject: [PATCH 01/11] Add _nmod_vec_rand

---
 src/nmod_vec.h          | 2 ++
 src/nmod_vec/randtest.c | 7 +++++++
 2 files changed, 9 insertions(+)

diff --git a/src/nmod_vec.h b/src/nmod_vec.h
index cb44dbd4cb..2c41c3e8b3 100644
--- a/src/nmod_vec.h
+++ b/src/nmod_vec.h
@@ -46,6 +46,8 @@ 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_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/randtest.c b/src/nmod_vec/randtest.c
index 950050f27b..e25d9f55a9 100644
--- a/src/nmod_vec/randtest.c
+++ b/src/nmod_vec/randtest.c
@@ -11,6 +11,13 @@
 
 #include "nmod_vec.h"
 
+void _nmod_vec_rand(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 4ea9a57bea3dc5267d64af160b0d021b44bdd9c8 Mon Sep 17 00:00:00 2001
From: Dimitri LESNOFF <dimitri.lesnoff@lip6.fr>
Date: Wed, 29 Oct 2025 11:55:32 +0100
Subject: [PATCH 02/11] Add nmod_poly rand funcs

---
 doc/source/nmod_poly.rst | 15 +++++++++++++--
 src/nmod_poly.h          |  4 ++++
 src/nmod_poly/randtest.c | 28 ++++++++++++++++++++++++++++
 3 files changed, 45 insertions(+), 2 deletions(-)

diff --git a/doc/source/nmod_poly.rst b/doc/source/nmod_poly.rst
index 3adcc74198..efd505b482 100644
--- a/doc/source/nmod_poly.rst
+++ b/doc/source/nmod_poly.rst
@@ -217,14 +217,25 @@ Assignment and basic manipulation
 Randomization
 --------------------------------------------------------------------------------
 
+.. function:: void nmod_poly_rand(nmod_poly_t poly, flint_rand_t state, slong len)
+
+    Generates a random polynomial with length up to ``len``.
+
+.. function:: void nmod_poly_rand_monic(nmod_poly_t poly, flint_rand_t state, slong len)
+
+    Generates a random monic polynomial with length up to ``len``.
+
+.. function:: void nmod_poly_rand_irreducible(nmod_poly_t poly, flint_rand_t state, slong len)
+
+    Generates a random irreducible polynomial with length up to ``len``.
 
 .. function:: void nmod_poly_randtest(nmod_poly_t poly, flint_rand_t state, slong len)
 
-    Generates a random polynomial with length up to ``len``.
+    Generates a random and sparse with increased probability polynomial with length up to ``len``.
 
 .. function:: void nmod_poly_randtest_monic(nmod_poly_t poly, flint_rand_t state, slong len)
 
-    Generates a random monic polynomial with length ``len``.
+    Generates a random and sparse with increased probability monic polynomial with length ``len``.
 
 .. function:: void nmod_poly_randtest_trinomial(nmod_poly_t poly, flint_rand_t state, slong len)
 
diff --git a/src/nmod_poly.h b/src/nmod_poly.h
index ca86f6f92a..226d0830c0 100644
--- a/src/nmod_poly.h
+++ b/src/nmod_poly.h
@@ -213,6 +213,10 @@ int nmod_poly_is_monic(const nmod_poly_t poly)
 
 /* Randomisation  ************************************************************/
 
+void nmod_poly_rand(nmod_poly_t poly, flint_rand_t state, slong len);
+void nmod_poly_rand_monic(nmod_poly_t poly, flint_rand_t state, slong len);
+void nmod_poly_rand_irreducible(nmod_poly_t poly, flint_rand_t state, slong len);
+
 void nmod_poly_randtest(nmod_poly_t poly, flint_rand_t state, slong len);
 
 NMOD_POLY_INLINE
diff --git a/src/nmod_poly/randtest.c b/src/nmod_poly/randtest.c
index 27eb52160c..cce1ede11a 100644
--- a/src/nmod_poly/randtest.c
+++ b/src/nmod_poly/randtest.c
@@ -14,6 +14,34 @@
 #include "nmod_poly.h"
 #include "nmod_poly_factor.h"
 
+// Rand functions -> random dense polynomials with high probability
+void
+nmod_poly_rand(nmod_poly_t poly, flint_rand_t state, slong len)
+{
+    nmod_poly_fit_length(poly, len);
+    _nmod_vec_rand(poly->coeffs, state, len, poly->mod);
+    poly->length = len;
+    _nmod_poly_normalise(poly);
+}
+
+void
+nmod_poly_rand_monic(nmod_poly_t poly, flint_rand_t state, slong len)
+{
+    nmod_poly_fit_length(poly, len);
+    _nmod_vec_rand(poly->coeffs, state, len - 1, poly->mod);
+    poly->coeffs[len - 1] = 1;
+    poly->length = len;
+}
+
+void
+nmod_poly_rand_irreducible(nmod_poly_t poly, flint_rand_t state, slong len)
+{
+    do {
+        nmod_poly_rand(poly, state, len);
+    } while (nmod_poly_is_zero(poly) || !(nmod_poly_is_irreducible(poly)));
+}
+
+// Randtest functions -> dense/sparse polynomials
 void
 nmod_poly_randtest(nmod_poly_t poly, flint_rand_t state, slong len)
 {

From 4f0ef9b94acc54c8624fd7c21640cd2a5b14c800 Mon Sep 17 00:00:00 2001
From: Dimitri LESNOFF <dimitri.lesnoff@lip6.fr>
Date: Wed, 29 Oct 2025 14:23:14 +0100
Subject: [PATCH 03/11] Add nmod_poly_mat rand funcs

---
 doc/source/nmod_poly_mat.rst |  7 +++++--
 src/nmod_poly_mat.h          |  1 +
 src/nmod_poly_mat/rand.c     | 11 +++++++++++
 3 files changed, 17 insertions(+), 2 deletions(-)

diff --git a/doc/source/nmod_poly_mat.rst b/doc/source/nmod_poly_mat.rst
index 1979f2243b..7f281015b7 100644
--- a/doc/source/nmod_poly_mat.rst
+++ b/doc/source/nmod_poly_mat.rst
@@ -138,10 +138,13 @@ Random matrix generation
 --------------------------------------------------------------------------------
 
 
+.. function:: void nmod_poly_mat_rand(nmod_poly_mat_t mat, flint_rand_t state, slong len)
+
+    Generates a matrix of polynomials with uniformly generated coefficients.
+
 .. function:: void nmod_poly_mat_randtest(nmod_poly_mat_t mat, flint_rand_t state, slong len)
 
-    This is equivalent to applying ``nmod_poly_randtest`` to all entries
-    in the matrix.
+    Generates a matrix of polynomials sparse with an increased probability. It is equivalent to apply ``nmod_poly_randtest`` to all entries in the matrix.
 
 .. function:: void nmod_poly_mat_randtest_sparse(nmod_poly_mat_t A, flint_rand_t state, slong len, float density)
 
diff --git a/src/nmod_poly_mat.h b/src/nmod_poly_mat.h
index 135cd4d491..a6888d5957 100644
--- a/src/nmod_poly_mat.h
+++ b/src/nmod_poly_mat.h
@@ -141,6 +141,7 @@ void nmod_poly_mat_one(nmod_poly_mat_t mat);
 
 /* Random matrices ***********************************************************/
 
+void nmod_poly_mat_rand(nmod_poly_mat_t A, flint_rand_t state, slong len);
 void nmod_poly_mat_randtest(nmod_poly_mat_t mat, flint_rand_t state,
                                 slong len);
 
diff --git a/src/nmod_poly_mat/rand.c b/src/nmod_poly_mat/rand.c
index 95e28eecd0..5853dc608e 100644
--- a/src/nmod_poly_mat/rand.c
+++ b/src/nmod_poly_mat/rand.c
@@ -12,6 +12,17 @@
 #include "nmod_poly.h"
 #include "nmod_poly_mat.h"
 
+void
+nmod_poly_mat_rand(nmod_poly_mat_t A, flint_rand_t state, slong len)
+{
+    slong i, j;
+
+    for (i = 0; i < A->r; i++)
+        for (j = 0; j < A->c; j++)
+            nmod_poly_rand(nmod_poly_mat_entry(A, i, j), state, len);
+}
+
+
 void
 nmod_poly_mat_randtest(nmod_poly_mat_t A, flint_rand_t state, slong len)
 {

From cacfb536e13a84596b9810046140b9b882fb7dc2 Mon Sep 17 00:00:00 2001
From: Dimitri LESNOFF <dimitri.lesnoff@lip6.fr>
Date: Wed, 29 Oct 2025 15:22:23 +0100
Subject: [PATCH 04/11] Add fmpz_mod_poly_rand, rand_monic, irred funcs

The randtest functions are using `randm` which generates positive coefficients in [0, m) range with m the modulus given by the context.
The documentation told that the coefficients are randomly signed, so I
fixed that.
I introduced a `randm_nonzero` function in fmpz to ensure that
coefficients are nonzero and replaced all occurences of `randm` in
`fmpz_mod_poly_randtest` functions by this new function.
Apart from the `rand` function, this introduces a `rand_monic` and
a `rand_irreducible` function.
---
 doc/source/fmpz.rst          |  4 +++
 doc/source/fmpz_poly.rst     | 18 +++++++++-
 src/fmpz.h                   |  1 +
 src/fmpz/rand.c              |  6 ++++
 src/fmpz_mod_poly.h          |  9 +++++
 src/fmpz_mod_poly/randtest.c | 65 ++++++++++++++++++++++++++++++------
 6 files changed, 92 insertions(+), 11 deletions(-)

diff --git a/doc/source/fmpz.rst b/doc/source/fmpz.rst
index 98ee42436e..b783348777 100644
--- a/doc/source/fmpz.rst
+++ b/doc/source/fmpz.rst
@@ -267,6 +267,10 @@ should call :func:`flint_rand_clear` to clean up.
 
     Generates a random integer in the range `0` to `m - 1` inclusive.
 
+.. function:: void fmpz_randm_nonzero(fmpz_t f, flint_rand_t state, const fmpz_t m)
+
+    Generates a random integer in the range `1` to `m - 1` inclusive.
+
 .. function:: void fmpz_randtest_mod(fmpz_t f, flint_rand_t state, const fmpz_t m)
 
     Generates a random integer in the range `0` to `m - 1` inclusive, with an
diff --git a/doc/source/fmpz_poly.rst b/doc/source/fmpz_poly.rst
index d984d69bed..ce10915764 100644
--- a/doc/source/fmpz_poly.rst
+++ b/doc/source/fmpz_poly.rst
@@ -284,12 +284,28 @@ Assignment and basic manipulation
 Randomisation
 --------------------------------------------------------------------------------
 
+.. function:: void fmpz_mod_poly_rand(fmpz_mod_poly_t f, flint_rand_t state, slong len, const fmpz_mod_ctx_t ctx)
+
+    Sets `f` to a random polynomial with up to the given length and where
+    each coefficient has up to the given number of bits. The coefficients
+    are uniformly generated random numbers in `[0, n)`, where `n` is the modulus given by the context `ctx`.
+
+.. function:: void fmpz_mod_poly_rand_monic(fmpz_mod_poly_t f, flint_rand_t state, slong len, const fmpz_mod_ctx_t ctx)
+
+    Sets `f` to a random monic polynomial with up to the given length and where
+    each coefficient has up to the given number of bits. The coefficients
+    are uniformly generated random numbers in `[0, n)`, where `n` is the modulus given by the context `ctx`.
+
+.. function:: void fmpz_mod_poly_rand_irreducible(fmpz_mod_poly_t f, flint_rand_t state, slong len, const fmpz_mod_ctx_t ctx)
+
+    Sets `f` to a random irreducible polynomial with up to the given length and where each coefficient has up to the given number of bits. The coefficients
+    are uniformly generated random numbers in `[0, n)`, where `n` is the modulus given by the context `ctx`.
 
 .. function:: void fmpz_poly_randtest(fmpz_poly_t f, flint_rand_t state, slong len, flint_bitcnt_t bits)
 
     Sets `f` to a random polynomial with up to the given length and where
     each coefficient has up to the given number of bits. The coefficients
-    are signed randomly.
+    are random numbers in `[1, n)`, where `n` is the modulus given by the context `ctx`.
 
 .. function:: void fmpz_poly_randtest_unsigned(fmpz_poly_t f, flint_rand_t state, slong len, flint_bitcnt_t bits)
 
diff --git a/src/fmpz.h b/src/fmpz.h
index c8a1c59d43..c3c21a4d42 100644
--- a/src/fmpz.h
+++ b/src/fmpz.h
@@ -112,6 +112,7 @@ int _fmpz_is_canonical(const fmpz_t x);
 void fmpz_randbits_unsigned(fmpz_t f, flint_rand_t state, flint_bitcnt_t bits);
 void fmpz_randbits(fmpz_t f, flint_rand_t state, flint_bitcnt_t bits);
 void fmpz_randm(fmpz_t f, flint_rand_t state, const fmpz_t m);
+void fmpz_randm_nonzero(fmpz_t f, flint_rand_t state, const fmpz_t m);
 void fmpz_randtest(fmpz_t f, flint_rand_t state, flint_bitcnt_t bits);
 void fmpz_randtest_unsigned(fmpz_t f, flint_rand_t state, flint_bitcnt_t bits);
 void fmpz_randtest_not_zero(fmpz_t f, flint_rand_t state, flint_bitcnt_t bits);
diff --git a/src/fmpz/rand.c b/src/fmpz/rand.c
index dfdedce336..b629dd0aa8 100644
--- a/src/fmpz/rand.c
+++ b/src/fmpz/rand.c
@@ -71,6 +71,12 @@ fmpz_randm(fmpz_t f, flint_rand_t state, const fmpz_t m)
     }
 }
 
+void fmpz_randm_nonzero(fmpz_t f, flint_rand_t state, const fmpz_t m) {
+    fmpz_randm(f, state, m);
+    if (fmpz_is_zero(f))
+        fmpz_one(f);
+}
+
 void fmpz_randprime(fmpz_t f, flint_rand_t state, flint_bitcnt_t bits, int proved)
 {
     if (bits <= FLINT_BITS)
diff --git a/src/fmpz_mod_poly.h b/src/fmpz_mod_poly.h
index dc245cd3ae..53b388abbb 100644
--- a/src/fmpz_mod_poly.h
+++ b/src/fmpz_mod_poly.h
@@ -134,6 +134,15 @@ int fmpz_mod_poly_is_canonical(const fmpz_mod_poly_t A, const fmpz_mod_ctx_t ctx
 
 
 /*  Randomisation ************************************************************/
+void fmpz_mod_poly_rand(fmpz_mod_poly_t f, flint_rand_t state,
+                                          slong len, const fmpz_mod_ctx_t ctx);
+
+void fmpz_mod_poly_rand_monic(fmpz_mod_poly_t f,
+                      flint_rand_t state, slong len, const fmpz_mod_ctx_t ctx);
+
+void fmpz_mod_poly_rand_irreducible(fmpz_mod_poly_t f,
+                      flint_rand_t state, slong len, const fmpz_mod_ctx_t ctx);
+
 
 void fmpz_mod_poly_randtest(fmpz_mod_poly_t f, flint_rand_t state,
                                           slong len, const fmpz_mod_ctx_t ctx);
diff --git a/src/fmpz_mod_poly/randtest.c b/src/fmpz_mod_poly/randtest.c
index 97b2830f51..8397a853af 100644
--- a/src/fmpz_mod_poly/randtest.c
+++ b/src/fmpz_mod_poly/randtest.c
@@ -17,7 +17,7 @@
 #include "fmpz_mod_poly.h"
 #include "fmpz_mod_poly_factor.h"
 
-void fmpz_mod_poly_randtest(fmpz_mod_poly_t f, flint_rand_t state, slong len,
+void fmpz_mod_poly_rand(fmpz_mod_poly_t f, flint_rand_t state, slong len,
                                                       const fmpz_mod_ctx_t ctx)
 {
     slong i;
@@ -31,7 +31,7 @@ void fmpz_mod_poly_randtest(fmpz_mod_poly_t f, flint_rand_t state, slong len,
     _fmpz_mod_poly_normalise(f);
 }
 
-void fmpz_mod_poly_randtest_monic(fmpz_mod_poly_t f, flint_rand_t state,
+void fmpz_mod_poly_rand_monic(fmpz_mod_poly_t f, flint_rand_t state,
                                            slong len, const fmpz_mod_ctx_t ctx)
 {
     slong i;
@@ -48,6 +48,51 @@ void fmpz_mod_poly_randtest_monic(fmpz_mod_poly_t f, flint_rand_t state,
     _fmpz_mod_poly_set_length(f, len);
 }
 
+void fmpz_mod_poly_rand_irreducible(fmpz_mod_poly_t f, flint_rand_t state,
+                                           slong len, const fmpz_mod_ctx_t ctx)
+{
+    if (len == 0)
+    {
+        flint_throw(FLINT_ERROR, "Exception (fmpz_mod_poly_randtest_irreducible). len == 0.\n");
+    }
+
+    do {
+        fmpz_mod_poly_rand(f, state, len, ctx);
+    } while (fmpz_mod_poly_is_zero(f, ctx) ||
+             !fmpz_mod_poly_is_irreducible(f, ctx));
+}
+
+void fmpz_mod_poly_randtest(fmpz_mod_poly_t f, flint_rand_t state, slong len,
+                                                      const fmpz_mod_ctx_t ctx)
+{
+    slong i;
+
+    fmpz_mod_poly_fit_length(f, len, ctx);
+
+    for (i = 0; i < len; i++)
+        fmpz_randm_nonzero(f->coeffs + i, state, fmpz_mod_ctx_modulus(ctx));
+
+    _fmpz_mod_poly_set_length(f, len);
+    _fmpz_mod_poly_normalise(f);
+}
+
+void fmpz_mod_poly_randtest_monic(fmpz_mod_poly_t f, flint_rand_t state,
+                                           slong len, const fmpz_mod_ctx_t ctx)
+{
+    slong i;
+
+    FLINT_ASSERT(len > 0);
+
+    fmpz_mod_poly_fit_length(f, len, ctx);
+
+    for (i = 0; i < len - 1; i++)
+        fmpz_randm_nonzero(f->coeffs + i, state, fmpz_mod_ctx_modulus(ctx));
+
+    fmpz_one(f->coeffs + len - 1);
+
+    _fmpz_mod_poly_set_length(f, len);
+}
+
 static void
 fmpz_mod_poly_randtest_monic_sparse(fmpz_mod_poly_t poly, flint_rand_t state,
                             slong len, slong nonzero, const fmpz_mod_ctx_t ctx)
@@ -56,9 +101,9 @@ fmpz_mod_poly_randtest_monic_sparse(fmpz_mod_poly_t poly, flint_rand_t state,
 
     fmpz_mod_poly_fit_length(poly, len, ctx);
     _fmpz_vec_zero(poly->coeffs, len);
-    fmpz_randm(poly->coeffs + 0, state, fmpz_mod_ctx_modulus(ctx));
+    fmpz_randm_nonzero(poly->coeffs + 0, state, fmpz_mod_ctx_modulus(ctx));
     for (i = 1; i < nonzero; i++)
-       fmpz_randm(poly->coeffs + n_randint(state, len - 1) + 1,
+       fmpz_randm_nonzero(poly->coeffs + n_randint(state, len - 1) + 1,
                                              state, fmpz_mod_ctx_modulus(ctx));
     fmpz_set_ui(poly->coeffs + len - 1, 1);
     _fmpz_mod_poly_set_length(poly, len);
@@ -127,9 +172,9 @@ void fmpz_mod_poly_randtest_trinomial(fmpz_mod_poly_t poly,
     ulong k;
     fmpz_mod_poly_fit_length(poly, len, ctx);
     _fmpz_vec_zero(poly->coeffs, len);
-    fmpz_randm(poly->coeffs, state, fmpz_mod_ctx_modulus(ctx));
+    fmpz_randm_nonzero(poly->coeffs, state, fmpz_mod_ctx_modulus(ctx));
     k = (n_randtest(state) % (len - 2)) + 1;
-    fmpz_randm(poly->coeffs + k, state, fmpz_mod_ctx_modulus(ctx));
+    fmpz_randm_nonzero(poly->coeffs + k, state, fmpz_mod_ctx_modulus(ctx));
     fmpz_one(poly->coeffs + len - 1);
     _fmpz_mod_poly_set_length(poly, len);
 }
@@ -139,10 +184,10 @@ void fmpz_mod_poly_randtest_pentomial(fmpz_mod_poly_t poly,
 {
     fmpz_mod_poly_fit_length(poly, len, ctx);
     _fmpz_vec_zero(poly->coeffs, len);
-    fmpz_randm(poly->coeffs, state, fmpz_mod_ctx_modulus(ctx));
-    fmpz_randm(poly->coeffs + 1, state, fmpz_mod_ctx_modulus(ctx));
-    fmpz_randm(poly->coeffs + 2, state, fmpz_mod_ctx_modulus(ctx));
-    fmpz_randm(poly->coeffs + 3, state, fmpz_mod_ctx_modulus(ctx));
+    fmpz_randm_nonzero(poly->coeffs, state, fmpz_mod_ctx_modulus(ctx));
+    fmpz_randm_nonzero(poly->coeffs + 1, state, fmpz_mod_ctx_modulus(ctx));
+    fmpz_randm_nonzero(poly->coeffs + 2, state, fmpz_mod_ctx_modulus(ctx));
+    fmpz_randm_nonzero(poly->coeffs + 3, state, fmpz_mod_ctx_modulus(ctx));
     fmpz_one(poly->coeffs + len - 1);
     _fmpz_mod_poly_set_length(poly, len);
 }

From bb5d986536e7b567dce420b71e7a63a32fa52819 Mon Sep 17 00:00:00 2001
From: Dimitri LESNOFF <dimitri.lesnoff@lip6.fr>
Date: Wed, 29 Oct 2025 16:37:54 +0100
Subject: [PATCH 05/11] Add fmpz_mod_vec_rand

---
 doc/source/fmpz_mod_vec.rst |  9 ++++++++-
 src/fmpz_mod_vec.h          |  2 ++
 src/fmpz_mod_vec/rand.c     | 10 ++++++++++
 3 files changed, 20 insertions(+), 1 deletion(-)
 create mode 100644 src/fmpz_mod_vec/rand.c

diff --git a/doc/source/fmpz_mod_vec.rst b/doc/source/fmpz_mod_vec.rst
index dd6902b76e..abd08d652a 100644
--- a/doc/source/fmpz_mod_vec.rst
+++ b/doc/source/fmpz_mod_vec.rst
@@ -8,7 +8,7 @@ Conversions
 
 .. function:: void _fmpz_mod_vec_set_fmpz_vec(fmpz * A, const fmpz * B, slong len, const fmpz_mod_ctx_t ctx)
 
-    Set the `fmpz_mod_vec` `(A, len)` to the `fmpz_vec` `(B, len)` after
+    Set the `fmpz_{mod}_{vec}` `(A, len)` to the `fmpz_{vec}` `(B, len)` after
     reduction of each entry modulo the modulus..
 
 Arithmetic
@@ -61,3 +61,10 @@ Multiplication
 .. function:: void _fmpz_mod_vec_mul(fmpz * A, const fmpz * B, const fmpz * C, slong len, const fmpz_mod_ctx_t ctx)
 
     Set `(A, len)` the pointwise multiplication of `(B, len)` and `(C, len)`.
+
+Random functions
+--------------------------------------------------------------------------------
+
+.. function:: void _fmpz_mod_vec_rand(fmpz * A, flint_rand_t state, slong len, const fmpz_mod_ctx_t ctx)
+
+    Sets ``vec`` to a vector of the given length with entries picked uniformly at random in `[0, mod.n)`.
diff --git a/src/fmpz_mod_vec.h b/src/fmpz_mod_vec.h
index 50afb1b88a..3af73e5c4d 100644
--- a/src/fmpz_mod_vec.h
+++ b/src/fmpz_mod_vec.h
@@ -55,6 +55,8 @@ void _fmpz_mod_vec_dot(fmpz_t d, const fmpz * A, const fmpz * B,
 void _fmpz_mod_vec_dot_rev(fmpz_t r, const fmpz * a,
 		          const fmpz * b, slong len, const fmpz_mod_ctx_t ctx);
 
+void _fmpz_mod_vec_rand(fmpz *A, flint_rand_t state, slong len, const fmpz_mod_ctx_t ctx);
+
 #ifdef __cplusplus
 }
 #endif
diff --git a/src/fmpz_mod_vec/rand.c b/src/fmpz_mod_vec/rand.c
new file mode 100644
index 0000000000..70c3549e2d
--- /dev/null
+++ b/src/fmpz_mod_vec/rand.c
@@ -0,0 +1,10 @@
+#include "fmpz.h"
+#include "fmpz_mod.h"
+#include "fmpz_mod_vec.h"
+
+void _fmpz_mod_vec_rand(fmpz *A, flint_rand_t state, slong len, const fmpz_mod_ctx_t ctx)
+{
+    slong i;
+    for (i = 0; i < len; i++)
+        fmpz_randm(A + i, state, fmpz_mod_ctx_modulus(ctx));
+}

From 400598aff3282544f95a69824477d28f68271a9f Mon Sep 17 00:00:00 2001
From: Dimitri LESNOFF <dimitri.lesnoff@lip6.fr>
Date: Wed, 29 Oct 2025 16:39:23 +0100
Subject: [PATCH 06/11] Add a rand function to mpn_mod

---
 doc/source/mpn_mod.rst |  1 +
 src/mpn_mod/ring.c     | 12 ++++++++++++
 2 files changed, 13 insertions(+)

diff --git a/doc/source/mpn_mod.rst b/doc/source/mpn_mod.rst
index 7e6ec0fbbf..b3a6857272 100644
--- a/doc/source/mpn_mod.rst
+++ b/doc/source/mpn_mod.rst
@@ -109,6 +109,7 @@ Basic operations and arithmetic
               int mpn_mod_set_mpn(nn_ptr res, nn_srcptr x, slong xn, gr_ctx_t ctx)
               int mpn_mod_set_fmpz(nn_ptr res, const fmpz_t x, gr_ctx_t ctx)
               int mpn_mod_set_other(nn_ptr res, gr_ptr v, gr_ctx_t v_ctx, gr_ctx_t ctx)
+              int mpn_mod_rand(nn_ptr res, flint_rand_t state, gr_ctx_t ctx)
               int mpn_mod_randtest(nn_ptr res, flint_rand_t state, gr_ctx_t ctx)
               int mpn_mod_write(gr_stream_t out, nn_srcptr x, gr_ctx_t ctx)
               int mpn_mod_get_fmpz(fmpz_t res, nn_srcptr x, gr_ctx_t ctx)
diff --git a/src/mpn_mod/ring.c b/src/mpn_mod/ring.c
index e822705371..5a0baae9b6 100644
--- a/src/mpn_mod/ring.c
+++ b/src/mpn_mod/ring.c
@@ -202,6 +202,18 @@ mpn_mod_set_other(nn_ptr res, gr_ptr v, gr_ctx_t v_ctx, gr_ctx_t ctx)
     return gr_generic_set_other(res, v, v_ctx, ctx);
 }
 
+int
+mpn_mod_rand(nn_ptr res, flint_rand_t state, gr_ctx_t ctx)
+{
+    fmpz_t t;
+    fmpz_init(t);
+    fmpz_set_ui_array(t, MPN_MOD_CTX_MODULUS(ctx), MPN_MOD_CTX_NLIMBS(ctx));
+    fmpz_randm(t, state, t);
+    GR_IGNORE(mpn_mod_set_fmpz(res, t, ctx));
+    fmpz_clear(t);
+    return GR_SUCCESS;
+}
+
 int
 mpn_mod_randtest(nn_ptr res, flint_rand_t state, gr_ctx_t ctx)
 {

From 9060505154313a2d1705504e14168d6d827d6cad Mon Sep 17 00:00:00 2001
From: Dimitri LESNOFF <dimitri.lesnoff@lip6.fr>
Date: Wed, 29 Oct 2025 17:39:36 +0100
Subject: [PATCH 07/11] Add mpn_mod_vec_rand func

---
 src/mpn_mod.h     |  2 ++
 src/mpn_mod/vec.c | 13 +++++++++++++
 2 files changed, 15 insertions(+)

diff --git a/src/mpn_mod.h b/src/mpn_mod.h
index 8af7008d00..01adc4f8b5 100644
--- a/src/mpn_mod.h
+++ b/src/mpn_mod.h
@@ -67,6 +67,7 @@ mpn_mod_ctx_set_is_field(gr_ctx_t ctx, truth_t is_field)
 
 int gr_ctx_init_mpn_mod(gr_ctx_t ctx, const fmpz_t n);
 int _gr_ctx_init_mpn_mod(gr_ctx_t ctx, nn_srcptr n, slong nlimbs);
+int mpn_mod_rand(nn_ptr res, flint_rand_t state, gr_ctx_t ctx);
 void gr_ctx_init_mpn_mod_randtest(gr_ctx_t ctx, flint_rand_t state);
 
 int mpn_mod_ctx_write(gr_stream_t out, gr_ctx_t ctx);
@@ -191,6 +192,7 @@ int mpn_mod_div(nn_ptr res, nn_srcptr x, nn_srcptr y, gr_ctx_t ctx);
 int _mpn_mod_vec_zero(nn_ptr res, slong len, gr_ctx_t ctx);
 int _mpn_mod_vec_clear(nn_ptr FLINT_UNUSED(res), slong FLINT_UNUSED(len), gr_ctx_t FLINT_UNUSED(ctx));
 int _mpn_mod_vec_set(nn_ptr res, nn_srcptr x, slong len, gr_ctx_t ctx);
+int _mpn_mod_vec_rand(nn_ptr res, flint_rand_t state, slong len, gr_ctx_t ctx);
 void _mpn_mod_vec_swap(nn_ptr vec1, nn_ptr vec2, slong len, gr_ctx_t ctx);
 int _mpn_mod_vec_neg(nn_ptr res, nn_srcptr x, slong len, gr_ctx_t ctx);
 int _mpn_mod_vec_add(nn_ptr res, nn_srcptr x, nn_srcptr y, slong len, gr_ctx_t ctx);
diff --git a/src/mpn_mod/vec.c b/src/mpn_mod/vec.c
index a01c42b9ea..4d3d8d5286 100644
--- a/src/mpn_mod/vec.c
+++ b/src/mpn_mod/vec.c
@@ -32,6 +32,19 @@ _mpn_mod_vec_set(nn_ptr res, nn_srcptr x, slong len, gr_ctx_t ctx)
     return GR_SUCCESS;
 }
 
+int
+_mpn_mod_vec_rand(nn_ptr res, flint_rand_t state, slong len, gr_ctx_t ctx)
+{
+    slong n = MPN_MOD_CTX_NLIMBS(ctx);
+    slong i;
+
+    for (i = 0; i < len; i++)
+        if (mpn_mod_rand(res + i * n, state, ctx) != GR_SUCCESS)
+            return GR_UNABLE;
+
+    return GR_SUCCESS;
+}
+
 void
 _mpn_mod_vec_swap(nn_ptr vec1, nn_ptr vec2, slong len, gr_ctx_t ctx)
 {

From 59f5c7d794c80911c7cab49f0cf1001fa13a2bf0 Mon Sep 17 00:00:00 2001
From: Dimitri LESNOFF <dimitri.lesnoff@lip6.fr>
Date: Wed, 29 Oct 2025 19:13:29 +0100
Subject: [PATCH 08/11] Revert "Add fmpz_mod_vec_rand"

I added _fmpz_mod_vec_rand with the intent to use it in
_mpn_mod_vec_rand but did not use it in the end.

This reverts commit f98e52c300d6b6f0a3a54792c4744450dc05f712.
---
 doc/source/fmpz_mod_vec.rst |  9 +--------
 src/fmpz_mod_vec.h          |  2 --
 src/fmpz_mod_vec/rand.c     | 10 ----------
 3 files changed, 1 insertion(+), 20 deletions(-)
 delete mode 100644 src/fmpz_mod_vec/rand.c

diff --git a/doc/source/fmpz_mod_vec.rst b/doc/source/fmpz_mod_vec.rst
index abd08d652a..dd6902b76e 100644
--- a/doc/source/fmpz_mod_vec.rst
+++ b/doc/source/fmpz_mod_vec.rst
@@ -8,7 +8,7 @@ Conversions
 
 .. function:: void _fmpz_mod_vec_set_fmpz_vec(fmpz * A, const fmpz * B, slong len, const fmpz_mod_ctx_t ctx)
 
-    Set the `fmpz_{mod}_{vec}` `(A, len)` to the `fmpz_{vec}` `(B, len)` after
+    Set the `fmpz_mod_vec` `(A, len)` to the `fmpz_vec` `(B, len)` after
     reduction of each entry modulo the modulus..
 
 Arithmetic
@@ -61,10 +61,3 @@ Multiplication
 .. function:: void _fmpz_mod_vec_mul(fmpz * A, const fmpz * B, const fmpz * C, slong len, const fmpz_mod_ctx_t ctx)
 
     Set `(A, len)` the pointwise multiplication of `(B, len)` and `(C, len)`.
-
-Random functions
---------------------------------------------------------------------------------
-
-.. function:: void _fmpz_mod_vec_rand(fmpz * A, flint_rand_t state, slong len, const fmpz_mod_ctx_t ctx)
-
-    Sets ``vec`` to a vector of the given length with entries picked uniformly at random in `[0, mod.n)`.
diff --git a/src/fmpz_mod_vec.h b/src/fmpz_mod_vec.h
index 3af73e5c4d..50afb1b88a 100644
--- a/src/fmpz_mod_vec.h
+++ b/src/fmpz_mod_vec.h
@@ -55,8 +55,6 @@ void _fmpz_mod_vec_dot(fmpz_t d, const fmpz * A, const fmpz * B,
 void _fmpz_mod_vec_dot_rev(fmpz_t r, const fmpz * a,
 		          const fmpz * b, slong len, const fmpz_mod_ctx_t ctx);
 
-void _fmpz_mod_vec_rand(fmpz *A, flint_rand_t state, slong len, const fmpz_mod_ctx_t ctx);
-
 #ifdef __cplusplus
 }
 #endif
diff --git a/src/fmpz_mod_vec/rand.c b/src/fmpz_mod_vec/rand.c
deleted file mode 100644
index 70c3549e2d..0000000000
--- a/src/fmpz_mod_vec/rand.c
+++ /dev/null
@@ -1,10 +0,0 @@
-#include "fmpz.h"
-#include "fmpz_mod.h"
-#include "fmpz_mod_vec.h"
-
-void _fmpz_mod_vec_rand(fmpz *A, flint_rand_t state, slong len, const fmpz_mod_ctx_t ctx)
-{
-    slong i;
-    for (i = 0; i < len; i++)
-        fmpz_randm(A + i, state, fmpz_mod_ctx_modulus(ctx));
-}

From eafe4cf4bf11d5b62f4ec58747729db6d06bb021 Mon Sep 17 00:00:00 2001
From: Dimitri LESNOFF <dimitri.lesnoff@lip6.fr>
Date: Mon, 3 Nov 2025 14:45:44 +0100
Subject: [PATCH 09/11] Replace randm_non_zero by randtest calls

---
 src/fmpz_mod_poly/randtest.c | 41 ++++++++++++++++++++++++------------
 1 file changed, 27 insertions(+), 14 deletions(-)

diff --git a/src/fmpz_mod_poly/randtest.c b/src/fmpz_mod_poly/randtest.c
index 8397a853af..2048568979 100644
--- a/src/fmpz_mod_poly/randtest.c
+++ b/src/fmpz_mod_poly/randtest.c
@@ -69,8 +69,10 @@ void fmpz_mod_poly_randtest(fmpz_mod_poly_t f, flint_rand_t state, slong len,
 
     fmpz_mod_poly_fit_length(f, len, ctx);
 
-    for (i = 0; i < len; i++)
-        fmpz_randm_nonzero(f->coeffs + i, state, fmpz_mod_ctx_modulus(ctx));
+    for (i = 0; i < len; i++) {
+        fmpz_randtest_unsigned(f->coeffs + i, state, fmpz_bits(fmpz_mod_ctx_modulus(ctx) + 1));
+        fmpz_mod(f->coeffs + i, f->coeffs + i, fmpz_mod_ctx_modulus(ctx));
+    }
 
     _fmpz_mod_poly_set_length(f, len);
     _fmpz_mod_poly_normalise(f);
@@ -85,8 +87,10 @@ void fmpz_mod_poly_randtest_monic(fmpz_mod_poly_t f, flint_rand_t state,
 
     fmpz_mod_poly_fit_length(f, len, ctx);
 
-    for (i = 0; i < len - 1; i++)
-        fmpz_randm_nonzero(f->coeffs + i, state, fmpz_mod_ctx_modulus(ctx));
+    for (i = 0; i < len - 1; i++) {
+        fmpz_randtest_unsigned(f->coeffs + i, state, fmpz_bits(fmpz_mod_ctx_modulus(ctx) + 1));
+        fmpz_mod(f->coeffs + i, f->coeffs + i, fmpz_mod_ctx_modulus(ctx));
+    }
 
     fmpz_one(f->coeffs + len - 1);
 
@@ -101,10 +105,13 @@ fmpz_mod_poly_randtest_monic_sparse(fmpz_mod_poly_t poly, flint_rand_t state,
 
     fmpz_mod_poly_fit_length(poly, len, ctx);
     _fmpz_vec_zero(poly->coeffs, len);
-    fmpz_randm_nonzero(poly->coeffs + 0, state, fmpz_mod_ctx_modulus(ctx));
-    for (i = 1; i < nonzero; i++)
-       fmpz_randm_nonzero(poly->coeffs + n_randint(state, len - 1) + 1,
-                                             state, fmpz_mod_ctx_modulus(ctx));
+    fmpz_randtest_unsigned(poly->coeffs + 0, state, fmpz_bits(fmpz_mod_ctx_modulus(ctx) + 1));
+    fmpz_mod(poly->coeffs + 0, poly->coeffs + 0, fmpz_mod_ctx_modulus(ctx));
+    for (i = 1; i < nonzero; i++) {
+       ulong random_idx = n_randint(state, len - 1);
+       fmpz_randtest_unsigned(poly->coeffs + random_idx + 1, state, fmpz_bits(fmpz_mod_ctx_modulus(ctx) + 1));
+       fmpz_mod(poly->coeffs + random_idx + 1, poly->coeffs + random_idx + 1, fmpz_bits(fmpz_mod_ctx_modulus(ctx)));
+    }
     fmpz_set_ui(poly->coeffs + len - 1, 1);
     _fmpz_mod_poly_set_length(poly, len);
 }
@@ -172,9 +179,11 @@ void fmpz_mod_poly_randtest_trinomial(fmpz_mod_poly_t poly,
     ulong k;
     fmpz_mod_poly_fit_length(poly, len, ctx);
     _fmpz_vec_zero(poly->coeffs, len);
-    fmpz_randm_nonzero(poly->coeffs, state, fmpz_mod_ctx_modulus(ctx));
+    fmpz_randtest_unsigned(poly->coeffs, state, fmpz_bits(fmpz_mod_ctx_modulus(ctx) + 1));
+    fmpz_mod(poly->coeffs, poly->coeffs, fmpz_mod_ctx_modulus(ctx));
     k = (n_randtest(state) % (len - 2)) + 1;
-    fmpz_randm_nonzero(poly->coeffs + k, state, fmpz_mod_ctx_modulus(ctx));
+    fmpz_randtest_unsigned(poly->coeffs + k, state, fmpz_bits(fmpz_mod_ctx_modulus(ctx) + 1));
+    fmpz_mod(poly->coeffs + k, poly->coeffs + k, fmpz_mod_ctx_modulus(ctx));
     fmpz_one(poly->coeffs + len - 1);
     _fmpz_mod_poly_set_length(poly, len);
 }
@@ -184,10 +193,14 @@ void fmpz_mod_poly_randtest_pentomial(fmpz_mod_poly_t poly,
 {
     fmpz_mod_poly_fit_length(poly, len, ctx);
     _fmpz_vec_zero(poly->coeffs, len);
-    fmpz_randm_nonzero(poly->coeffs, state, fmpz_mod_ctx_modulus(ctx));
-    fmpz_randm_nonzero(poly->coeffs + 1, state, fmpz_mod_ctx_modulus(ctx));
-    fmpz_randm_nonzero(poly->coeffs + 2, state, fmpz_mod_ctx_modulus(ctx));
-    fmpz_randm_nonzero(poly->coeffs + 3, state, fmpz_mod_ctx_modulus(ctx));
+    fmpz_randtest_unsigned(poly->coeffs, state, fmpz_bits(fmpz_mod_ctx_modulus(ctx) + 1));
+    fmpz_mod(poly->coeffs, poly->coeffs, fmpz_mod_ctx_modulus(ctx));
+    fmpz_randtest_unsigned(poly->coeffs + 1, state, fmpz_bits(fmpz_mod_ctx_modulus(ctx) + 1));
+    fmpz_mod(poly->coeffs + 1, poly->coeffs + 1, fmpz_mod_ctx_modulus(ctx));
+    fmpz_randtest_unsigned(poly->coeffs + 2, state, fmpz_bits(fmpz_mod_ctx_modulus(ctx) + 1));
+    fmpz_mod(poly->coeffs + 2, poly->coeffs + 2, fmpz_mod_ctx_modulus(ctx));
+    fmpz_randtest_unsigned(poly->coeffs + 3, state, fmpz_bits(fmpz_mod_ctx_modulus(ctx) + 1));
+    fmpz_mod(poly->coeffs + 3, poly->coeffs + 3, fmpz_mod_ctx_modulus(ctx));
     fmpz_one(poly->coeffs + len - 1);
     _fmpz_mod_poly_set_length(poly, len);
 }

From 4dff27e1a3f8af7d63ac5e3097099b3040951d23 Mon Sep 17 00:00:00 2001
From: Dimitri LESNOFF <dimitri.lesnoff@lip6.fr>
Date: Mon, 3 Nov 2025 16:17:26 +0100
Subject: [PATCH 10/11] Fix documentation of mpn_mod

---
 doc/source/mpn_mod.rst | 6 +++++-
 src/mpn_mod.h          | 2 +-
 2 files changed, 6 insertions(+), 2 deletions(-)

diff --git a/doc/source/mpn_mod.rst b/doc/source/mpn_mod.rst
index b3a6857272..85dc3b75a8 100644
--- a/doc/source/mpn_mod.rst
+++ b/doc/source/mpn_mod.rst
@@ -94,6 +94,11 @@ Context objects
 Basic operations and arithmetic
 -------------------------------------------------------------------------------
 
+
+.. function:: int mpn_mod_rand(nn_ptr res, flint_rand_t state, gr_ctx_t ctx)
+
+   Generates a coefficient uniformly between `0` and `MPN_MOD_CTX_MODULUS(ctx)` exclusive.
+
 .. function:: int mpn_mod_ctx_write(gr_stream_t out, gr_ctx_t ctx)
               void mpn_mod_ctx_clear(gr_ctx_t ctx)
               truth_t mpn_mod_ctx_is_field(gr_ctx_t ctx)
@@ -109,7 +114,6 @@ Basic operations and arithmetic
               int mpn_mod_set_mpn(nn_ptr res, nn_srcptr x, slong xn, gr_ctx_t ctx)
               int mpn_mod_set_fmpz(nn_ptr res, const fmpz_t x, gr_ctx_t ctx)
               int mpn_mod_set_other(nn_ptr res, gr_ptr v, gr_ctx_t v_ctx, gr_ctx_t ctx)
-              int mpn_mod_rand(nn_ptr res, flint_rand_t state, gr_ctx_t ctx)
               int mpn_mod_randtest(nn_ptr res, flint_rand_t state, gr_ctx_t ctx)
               int mpn_mod_write(gr_stream_t out, nn_srcptr x, gr_ctx_t ctx)
               int mpn_mod_get_fmpz(fmpz_t res, nn_srcptr x, gr_ctx_t ctx)
diff --git a/src/mpn_mod.h b/src/mpn_mod.h
index 01adc4f8b5..8c0c5e7f65 100644
--- a/src/mpn_mod.h
+++ b/src/mpn_mod.h
@@ -67,7 +67,6 @@ mpn_mod_ctx_set_is_field(gr_ctx_t ctx, truth_t is_field)
 
 int gr_ctx_init_mpn_mod(gr_ctx_t ctx, const fmpz_t n);
 int _gr_ctx_init_mpn_mod(gr_ctx_t ctx, nn_srcptr n, slong nlimbs);
-int mpn_mod_rand(nn_ptr res, flint_rand_t state, gr_ctx_t ctx);
 void gr_ctx_init_mpn_mod_randtest(gr_ctx_t ctx, flint_rand_t state);
 
 int mpn_mod_ctx_write(gr_stream_t out, gr_ctx_t ctx);
@@ -127,6 +126,7 @@ int mpn_mod_neg_one(nn_ptr res, gr_ctx_t ctx);
 int mpn_mod_set_mpn(nn_ptr res, nn_srcptr x, slong xn, gr_ctx_t ctx);
 int mpn_mod_set_fmpz(nn_ptr res, const fmpz_t x, gr_ctx_t ctx);
 int mpn_mod_set_other(nn_ptr res, gr_ptr v, gr_ctx_t v_ctx, gr_ctx_t ctx);
+int mpn_mod_rand(nn_ptr res, flint_rand_t state, gr_ctx_t ctx);
 int mpn_mod_randtest(nn_ptr res, flint_rand_t state, gr_ctx_t ctx);
 int mpn_mod_write(gr_stream_t out, nn_srcptr x, gr_ctx_t ctx);
 

From 716a13e00f8d41c9c2da7ba9bc7cc9c5283dfc1b Mon Sep 17 00:00:00 2001
From: Dimitri LESNOFF <dimitri.lesnoff@lip6.fr>
Date: Mon, 3 Nov 2025 17:15:40 +0100
Subject: [PATCH 11/11] Remove +1 to uint pointers

---
 src/fmpz_mod_poly/randtest.c | 20 ++++++++++----------
 1 file changed, 10 insertions(+), 10 deletions(-)

diff --git a/src/fmpz_mod_poly/randtest.c b/src/fmpz_mod_poly/randtest.c
index 2048568979..e722dba9e8 100644
--- a/src/fmpz_mod_poly/randtest.c
+++ b/src/fmpz_mod_poly/randtest.c
@@ -70,7 +70,7 @@ void fmpz_mod_poly_randtest(fmpz_mod_poly_t f, flint_rand_t state, slong len,
     fmpz_mod_poly_fit_length(f, len, ctx);
 
     for (i = 0; i < len; i++) {
-        fmpz_randtest_unsigned(f->coeffs + i, state, fmpz_bits(fmpz_mod_ctx_modulus(ctx) + 1));
+        fmpz_randtest_unsigned(f->coeffs + i, state, fmpz_bits(fmpz_mod_ctx_modulus(ctx)));
         fmpz_mod(f->coeffs + i, f->coeffs + i, fmpz_mod_ctx_modulus(ctx));
     }
 
@@ -88,7 +88,7 @@ void fmpz_mod_poly_randtest_monic(fmpz_mod_poly_t f, flint_rand_t state,
     fmpz_mod_poly_fit_length(f, len, ctx);
 
     for (i = 0; i < len - 1; i++) {
-        fmpz_randtest_unsigned(f->coeffs + i, state, fmpz_bits(fmpz_mod_ctx_modulus(ctx) + 1));
+        fmpz_randtest_unsigned(f->coeffs + i, state, fmpz_bits(fmpz_mod_ctx_modulus(ctx)));
         fmpz_mod(f->coeffs + i, f->coeffs + i, fmpz_mod_ctx_modulus(ctx));
     }
 
@@ -105,11 +105,11 @@ fmpz_mod_poly_randtest_monic_sparse(fmpz_mod_poly_t poly, flint_rand_t state,
 
     fmpz_mod_poly_fit_length(poly, len, ctx);
     _fmpz_vec_zero(poly->coeffs, len);
-    fmpz_randtest_unsigned(poly->coeffs + 0, state, fmpz_bits(fmpz_mod_ctx_modulus(ctx) + 1));
+    fmpz_randtest_unsigned(poly->coeffs + 0, state, fmpz_bits(fmpz_mod_ctx_modulus(ctx)));
     fmpz_mod(poly->coeffs + 0, poly->coeffs + 0, fmpz_mod_ctx_modulus(ctx));
     for (i = 1; i < nonzero; i++) {
        ulong random_idx = n_randint(state, len - 1);
-       fmpz_randtest_unsigned(poly->coeffs + random_idx + 1, state, fmpz_bits(fmpz_mod_ctx_modulus(ctx) + 1));
+       fmpz_randtest_unsigned(poly->coeffs + random_idx + 1, state, fmpz_bits(fmpz_mod_ctx_modulus(ctx)));
        fmpz_mod(poly->coeffs + random_idx + 1, poly->coeffs + random_idx + 1, fmpz_bits(fmpz_mod_ctx_modulus(ctx)));
     }
     fmpz_set_ui(poly->coeffs + len - 1, 1);
@@ -179,10 +179,10 @@ void fmpz_mod_poly_randtest_trinomial(fmpz_mod_poly_t poly,
     ulong k;
     fmpz_mod_poly_fit_length(poly, len, ctx);
     _fmpz_vec_zero(poly->coeffs, len);
-    fmpz_randtest_unsigned(poly->coeffs, state, fmpz_bits(fmpz_mod_ctx_modulus(ctx) + 1));
+    fmpz_randtest_unsigned(poly->coeffs, state, fmpz_bits(fmpz_mod_ctx_modulus(ctx)));
     fmpz_mod(poly->coeffs, poly->coeffs, fmpz_mod_ctx_modulus(ctx));
     k = (n_randtest(state) % (len - 2)) + 1;
-    fmpz_randtest_unsigned(poly->coeffs + k, state, fmpz_bits(fmpz_mod_ctx_modulus(ctx) + 1));
+    fmpz_randtest_unsigned(poly->coeffs + k, state, fmpz_bits(fmpz_mod_ctx_modulus(ctx)));
     fmpz_mod(poly->coeffs + k, poly->coeffs + k, fmpz_mod_ctx_modulus(ctx));
     fmpz_one(poly->coeffs + len - 1);
     _fmpz_mod_poly_set_length(poly, len);
@@ -193,13 +193,13 @@ void fmpz_mod_poly_randtest_pentomial(fmpz_mod_poly_t poly,
 {
     fmpz_mod_poly_fit_length(poly, len, ctx);
     _fmpz_vec_zero(poly->coeffs, len);
-    fmpz_randtest_unsigned(poly->coeffs, state, fmpz_bits(fmpz_mod_ctx_modulus(ctx) + 1));
+    fmpz_randtest_unsigned(poly->coeffs, state, fmpz_bits(fmpz_mod_ctx_modulus(ctx)));
     fmpz_mod(poly->coeffs, poly->coeffs, fmpz_mod_ctx_modulus(ctx));
-    fmpz_randtest_unsigned(poly->coeffs + 1, state, fmpz_bits(fmpz_mod_ctx_modulus(ctx) + 1));
+    fmpz_randtest_unsigned(poly->coeffs + 1, state, fmpz_bits(fmpz_mod_ctx_modulus(ctx)));
     fmpz_mod(poly->coeffs + 1, poly->coeffs + 1, fmpz_mod_ctx_modulus(ctx));
-    fmpz_randtest_unsigned(poly->coeffs + 2, state, fmpz_bits(fmpz_mod_ctx_modulus(ctx) + 1));
+    fmpz_randtest_unsigned(poly->coeffs + 2, state, fmpz_bits(fmpz_mod_ctx_modulus(ctx)));
     fmpz_mod(poly->coeffs + 2, poly->coeffs + 2, fmpz_mod_ctx_modulus(ctx));
-    fmpz_randtest_unsigned(poly->coeffs + 3, state, fmpz_bits(fmpz_mod_ctx_modulus(ctx) + 1));
+    fmpz_randtest_unsigned(poly->coeffs + 3, state, fmpz_bits(fmpz_mod_ctx_modulus(ctx)));
     fmpz_mod(poly->coeffs + 3, poly->coeffs + 3, fmpz_mod_ctx_modulus(ctx));
     fmpz_one(poly->coeffs + len - 1);
     _fmpz_mod_poly_set_length(poly, len);