From e0751f16b82305f525c6f385961c673e0347ce05 Mon Sep 17 00:00:00 2001
From: Matthias Gessinger <matthias@gessinger.de>
Date: Fri, 5 Jul 2024 20:20:36 +0200
Subject: [PATCH 1/9] Implement summation of powers of an integer

---
 src/fmpz.h            |  4 +++
 src/fmpz/sum_powers.c | 68 +++++++++++++++++++++++++++++++++++++++++++
 2 files changed, 72 insertions(+)
 create mode 100644 src/fmpz/sum_powers.c

diff --git a/src/fmpz.h b/src/fmpz.h
index 140d0fc299..35c88cb752 100644
--- a/src/fmpz.h
+++ b/src/fmpz.h
@@ -440,6 +440,10 @@ slong fmpz_flog_ui(const fmpz_t x, ulong b);
 double fmpz_get_d_2exp(slong * exp, const fmpz_t f);
 void fmpz_set_d_2exp(fmpz_t f, double m, slong exp);
 
+void fmpz_sum_powers_horner(fmpz_t f, const fmpz_t g, ulong exp);
+void fmpz_sum_powers_div(fmpz_t f, const fmpz_t g, ulong exp);
+void fmpz_sum_powers(fmpz_t f, const fmpz_t g, ulong exp);
+
 #if FLINT_HAVE_FFT_SMALL
 #define MPZ_WANT_FLINT_DIVISION(a, b) (mpz_size(b) >= 1250 && mpz_size(a) - mpz_size(b) >= 1250)
 #else
diff --git a/src/fmpz/sum_powers.c b/src/fmpz/sum_powers.c
new file mode 100644
index 0000000000..6a0401519f
--- /dev/null
+++ b/src/fmpz/sum_powers.c
@@ -0,0 +1,68 @@
+/*
+    Copyright (C) 2024 Matthias Gessinger
+
+    This file is part of FLINT.
+
+    FLINT is free software: you can redistribute it and/or modify it under
+    the terms of the GNU Lesser General Public License (LGPL) as published
+    by the Free Software Foundation; either version 3 of the License, or
+    (at your option) any later version.  See <https://www.gnu.org/licenses/>.
+*/
+
+#include "fmpz.h"
+
+void
+fmpz_sum_powers_horner(fmpz_t f, const fmpz_t g, ulong exp)
+{
+    fmpz_t t;
+    fmpz_init_set_ui(t, 1);
+
+    for (ulong i = 1; i < exp; i++)
+    {
+        fmpz_mul(t, t, g);
+        fmpz_add_ui(t, t, 1);
+    }
+
+    fmpz_swap(f, t);
+    fmpz_clear(t);
+}
+
+void
+fmpz_sum_powers_div(fmpz_t f, const fmpz_t g, ulong exp)
+{
+    fmpz_t t;
+    fmpz_init(t);
+
+    // t = g^(e + 1) - 1
+    fmpz_pow_ui(t, g, exp + 1);
+    fmpz_sub_ui(t, t, 1);
+
+    // f = g - 1
+    fmpz_sub_ui(f, g, 1);
+
+    // f = (g^(e + 1) - 1) / (g - 1)
+    fmpz_tdiv(f, t, g);
+
+    fmpz_clear(t);
+}
+
+void
+fmpz_sum_powers(fmpz_t f, const fmpz_t g, ulong exp)
+{
+    if (exp == 0)
+    {
+        fmpz_zero(f);
+    }
+    else if (exp == 1)
+    {
+        fmpz_add_ui(f, g, 1);
+    }
+    else if (exp <= 100)
+    {
+        _fmpz_sum_powers_horner(f, g, exp);
+    }
+    else
+    {
+        _fmpz_sum_powers_div(f, g, exp);
+    }
+}

From a4d747b76feb614da4f11cccb5d02ab0664463f7 Mon Sep 17 00:00:00 2001
From: Matthias Gessinger <matthias@gessinger.de>
Date: Fri, 5 Jul 2024 21:38:28 +0200
Subject: [PATCH 2/9] Add test for sum of powers

---
 src/fmpz/test/main.c         |  2 +
 src/fmpz/test/t-sum_powers.c | 89 ++++++++++++++++++++++++++++++++++++
 2 files changed, 91 insertions(+)
 create mode 100644 src/fmpz/test/t-sum_powers.c

diff --git a/src/fmpz/test/main.c b/src/fmpz/test/main.c
index 17381eff6d..4ecf5e1362 100644
--- a/src/fmpz/test/main.c
+++ b/src/fmpz/test/main.c
@@ -190,6 +190,7 @@
 #include "t-xgcd_canonical_bezout.c"
 #include "t-xgcd_partial.c"
 #include "t-xor.c"
+#include "t-sum_powers.c"
 
 /* Array of test functions ***************************************************/
 
@@ -360,6 +361,7 @@ test_struct tests[] =
     TEST_FUNCTION(fmpz_xgcd_canonical_bezout),
     TEST_FUNCTION(fmpz_xgcd_partial),
     TEST_FUNCTION(fmpz_xor)
+    TEST_FUNCTION(fmpz_sum_powers)
 };
 
 /* main function *************************************************************/
diff --git a/src/fmpz/test/t-sum_powers.c b/src/fmpz/test/t-sum_powers.c
new file mode 100644
index 0000000000..4b066fa645
--- /dev/null
+++ b/src/fmpz/test/t-sum_powers.c
@@ -0,0 +1,89 @@
+/*
+    Copyright (C) 2024 Matthias Gessinger
+
+    This file is part of FLINT.
+
+    FLINT is free software: you can redistribute it and/or modify it under
+    the terms of the GNU Lesser General Public License (LGPL) as published
+    by the Free Software Foundation; either version 3 of the License, or
+    (at your option) any later version.  See <https://www.gnu.org/licenses/>.
+*/
+
+#include "test_helpers.h"
+#include "ulong_extras.h"
+#include "fmpz.h"
+
+void _sum_powers_naive(fmpz_t f, const fmpz_t g, ulong exp);
+{
+	fmpz_t t;
+	fmpz_init(t);
+
+	fmpz_zero(f);
+
+	for (ulong i = 0; i < exp; i++)
+	{
+		fmpz_pow_ui(t, g, i);
+		fmpz_add(f, f, t);
+	}
+
+	fmpz_clear(t);
+}
+
+TEST_FUNCTION_START(fmpz_sum_powers, state)
+{
+	int i, result;
+
+	for (i = 0; i < 1000 * flint_test_multiplier(); i++)
+	{
+		fmpz_t a, b, c;
+		ulong exp;
+		int aliasing;
+
+		fmpz_init(a);
+		fmpz_init(b);
+		fmpz_init(c);
+
+		fmpz_randtest(a, state, 200);
+		fmpz_randtest(b, state, 200);
+
+		exp = n_randint(state, 1<<10);
+
+		aliasing = n_randint(state, 2);
+
+		if (aliasing == 1)
+		{
+			fmpz_sum_powers(a, a, exp);
+			fmpz_set(b, a);
+		}
+		else
+		{
+			fmpz_sum_powers(b, a, exp);
+		}
+
+		_fmpz_sum_powers_naive(c, a, exp);
+
+		result = fmpz_cmp(c, b);
+
+		if (!result)
+		{
+			flint_printf("FAIL:\n");
+
+			flint_printf("Expected: ");
+			fmpz_print(c);
+			flint_printf("\n");
+
+			flint_printf("Actual: ");
+			fmpz_print(b);
+			flint_printf("\n");
+
+			fflush(stdout);
+			flint_abort();
+		}
+
+		fmpz_clear(a);
+		fmpz_clear(b);
+		fmpz_clear(c);
+	}
+
+	TEST_FUNCTION_END(state);
+}

From 36be38cb4567bebdca94f1e26a06758c0e376cc4 Mon Sep 17 00:00:00 2001
From: Matthias Gessinger <matthias@gessinger.de>
Date: Fri, 5 Jul 2024 22:43:12 +0200
Subject: [PATCH 3/9] Fix sum_powers after testing

---
 src/fmpz/sum_powers.c               | 94 ++++++++++++++++++-----------
 src/fmpz/test/main.c                |  6 +-
 src/fmpz/test/t-sum_powers.c        | 19 +++---
 src/fmpz/test/t-sum_powers_div.c    | 90 +++++++++++++++++++++++++++
 src/fmpz/test/t-sum_powers_horner.c | 90 +++++++++++++++++++++++++++
 5 files changed, 254 insertions(+), 45 deletions(-)
 create mode 100644 src/fmpz/test/t-sum_powers_div.c
 create mode 100644 src/fmpz/test/t-sum_powers_horner.c

diff --git a/src/fmpz/sum_powers.c b/src/fmpz/sum_powers.c
index 6a0401519f..32df74f6af 100644
--- a/src/fmpz/sum_powers.c
+++ b/src/fmpz/sum_powers.c
@@ -14,55 +14,79 @@
 void
 fmpz_sum_powers_horner(fmpz_t f, const fmpz_t g, ulong exp)
 {
-    fmpz_t t;
-    fmpz_init_set_ui(t, 1);
+	fmpz_t t;
 
-    for (ulong i = 1; i < exp; i++)
-    {
-        fmpz_mul(t, t, g);
-        fmpz_add_ui(t, t, 1);
-    }
+	if (exp == 0 || fmpz_is_zero(g))
+	{
+		fmpz_one(f);
+	}
+	else if (fmpz_is_one(g))
+	{
+		fmpz_set_ui(f, exp + 1);
+	}
+	else
+	{
+		fmpz_init_set_ui(t, 1);
 
-    fmpz_swap(f, t);
-    fmpz_clear(t);
+		for (ulong i = 1; i <= exp; i++)
+		{
+			fmpz_mul(t, t, g);
+			fmpz_add_ui(t, t, 1);
+		}
+
+		fmpz_swap(f, t);
+		fmpz_clear(t);
+	}
 }
 
 void
 fmpz_sum_powers_div(fmpz_t f, const fmpz_t g, ulong exp)
 {
-    fmpz_t t;
-    fmpz_init(t);
+	fmpz_t t;
+
+	if (exp == 0 || fmpz_is_zero(g))
+	{
+		fmpz_one(f);
+	}
+	else if (fmpz_is_one(g))
+	{
+		fmpz_set_ui(f, exp + 1);
+	}
+	else
+	{
+		fmpz_init(t);
 
-    // t = g^(e + 1) - 1
-    fmpz_pow_ui(t, g, exp + 1);
-    fmpz_sub_ui(t, t, 1);
+		// t = g - 1
+		fmpz_sub_ui(t, g, 1);
 
-    // f = g - 1
-    fmpz_sub_ui(f, g, 1);
+		// f = g^(e + 1) - 1
+		fmpz_pow_ui(f, g, exp + 1);
+		fmpz_sub_ui(f, f, 1);
 
-    // f = (g^(e + 1) - 1) / (g - 1)
-    fmpz_tdiv(f, t, g);
+		// f = (g^(e + 1) - 1) / (g - 1)
+		fmpz_tdiv_q(f, f, t);
 
-    fmpz_clear(t);
+		fmpz_clear(t);
+	}
 }
 
 void
 fmpz_sum_powers(fmpz_t f, const fmpz_t g, ulong exp)
 {
-    if (exp == 0)
-    {
-        fmpz_zero(f);
-    }
-    else if (exp == 1)
-    {
-        fmpz_add_ui(f, g, 1);
-    }
-    else if (exp <= 100)
-    {
-        _fmpz_sum_powers_horner(f, g, exp);
-    }
-    else
-    {
-        _fmpz_sum_powers_div(f, g, exp);
-    }
+	if (exp == 0 || fmpz_is_zero(g))
+	{
+		fmpz_one(f);
+	}
+	else if (exp == 1)
+	{
+		fmpz_add_ui(f, g, 1);
+	}
+	else if (exp <= 100)
+	{
+		fmpz_sum_powers_horner(f, g, exp);
+	}
+	else
+	{
+		fmpz_sum_powers_div(f, g, exp);
+	}
 }
diff --git a/src/fmpz/test/main.c b/src/fmpz/test/main.c
index 4ecf5e1362..d2338062a6 100644
--- a/src/fmpz/test/main.c
+++ b/src/fmpz/test/main.c
@@ -190,6 +190,8 @@
 #include "t-xgcd_canonical_bezout.c"
 #include "t-xgcd_partial.c"
 #include "t-xor.c"
+#include "t-sum_powers_horner.c"
+#include "t-sum_powers_div.c"
 #include "t-sum_powers.c"
 
 /* Array of test functions ***************************************************/
@@ -360,7 +362,9 @@ test_struct tests[] =
     TEST_FUNCTION(fmpz_xgcd),
     TEST_FUNCTION(fmpz_xgcd_canonical_bezout),
     TEST_FUNCTION(fmpz_xgcd_partial),
-    TEST_FUNCTION(fmpz_xor)
+    TEST_FUNCTION(fmpz_xor),
+    TEST_FUNCTION(fmpz_sum_powers_horner),
+    TEST_FUNCTION(fmpz_sum_powers_div),
     TEST_FUNCTION(fmpz_sum_powers)
 };
 
diff --git a/src/fmpz/test/t-sum_powers.c b/src/fmpz/test/t-sum_powers.c
index 4b066fa645..7d23402ccb 100644
--- a/src/fmpz/test/t-sum_powers.c
+++ b/src/fmpz/test/t-sum_powers.c
@@ -13,14 +13,14 @@
 #include "ulong_extras.h"
 #include "fmpz.h"
 
-void _sum_powers_naive(fmpz_t f, const fmpz_t g, ulong exp);
+void _fmpz_sum_powers_naive(fmpz_t f, const fmpz_t g, ulong exp)
 {
 	fmpz_t t;
 	fmpz_init(t);
 
 	fmpz_zero(f);
 
-	for (ulong i = 0; i < exp; i++)
+	for (ulong i = 0; i <= exp; i++)
 	{
 		fmpz_pow_ui(t, g, i);
 		fmpz_add(f, f, t);
@@ -43,13 +43,16 @@ TEST_FUNCTION_START(fmpz_sum_powers, state)
 		fmpz_init(b);
 		fmpz_init(c);
 
-		fmpz_randtest(a, state, 200);
-		fmpz_randtest(b, state, 200);
+		fmpz_randtest(a, state, 100);
 
-		exp = n_randint(state, 1<<10);
+		exp = n_randint(state, 250);
 
 		aliasing = n_randint(state, 2);
 
+		/* The reference result */
+		_fmpz_sum_powers_naive(c, a, exp);
+
+		/* general function */
 		if (aliasing == 1)
 		{
 			fmpz_sum_powers(a, a, exp);
@@ -60,13 +63,11 @@ TEST_FUNCTION_START(fmpz_sum_powers, state)
 			fmpz_sum_powers(b, a, exp);
 		}
 
-		_fmpz_sum_powers_naive(c, a, exp);
-
-		result = fmpz_cmp(c, b);
+		result = (fmpz_cmp(c, b) == 0);
 
 		if (!result)
 		{
-			flint_printf("FAIL:\n");
+			flint_printf("FAIL in general method:\n");
 
 			flint_printf("Expected: ");
 			fmpz_print(c);
diff --git a/src/fmpz/test/t-sum_powers_div.c b/src/fmpz/test/t-sum_powers_div.c
new file mode 100644
index 0000000000..79c1df8f76
--- /dev/null
+++ b/src/fmpz/test/t-sum_powers_div.c
@@ -0,0 +1,90 @@
+/*
+    Copyright (C) 2024 Matthias Gessinger
+
+    This file is part of FLINT.
+
+    FLINT is free software: you can redistribute it and/or modify it under
+    the terms of the GNU Lesser General Public License (LGPL) as published
+    by the Free Software Foundation; either version 3 of the License, or
+    (at your option) any later version.  See <https://www.gnu.org/licenses/>.
+*/
+
+#include "test_helpers.h"
+#include "ulong_extras.h"
+#include "fmpz.h"
+
+void _fmpz_sum_powers_naive_div(fmpz_t f, const fmpz_t g, ulong exp)
+{
+	fmpz_t t;
+	fmpz_init(t);
+
+	fmpz_zero(f);
+
+	for (ulong i = 0; i <= exp; i++)
+	{
+		fmpz_pow_ui(t, g, i);
+		fmpz_add(f, f, t);
+	}
+
+	fmpz_clear(t);
+}
+
+TEST_FUNCTION_START(fmpz_sum_powers_div, state)
+{
+	int i, result;
+
+	for (i = 0; i < 1000 * flint_test_multiplier(); i++)
+	{
+		fmpz_t a, b, c;
+		ulong exp;
+		int aliasing;
+
+		fmpz_init(a);
+		fmpz_init(b);
+		fmpz_init(c);
+
+		fmpz_randtest(a, state, 100);
+
+		exp = n_randint(state, 250);
+
+		aliasing = n_randint(state, 2);
+
+		/* The reference result */
+		_fmpz_sum_powers_naive_div(c, a, exp);
+
+		/* polynomial division method */
+		if (aliasing == 1)
+		{
+			fmpz_sum_powers_div(a, a, exp);
+			fmpz_set(b, a);
+		}
+		else
+		{
+			fmpz_sum_powers_div(b, a, exp);
+		}
+
+		result = (fmpz_cmp(c, b) == 0);
+
+		if (!result)
+		{
+			flint_printf("FAIL in polynomial division method:\n");
+
+			flint_printf("Expected: ");
+			fmpz_print(c);
+			flint_printf("\n");
+
+			flint_printf("Actual: ");
+			fmpz_print(b);
+			flint_printf("\n");
+
+			fflush(stdout);
+			flint_abort();
+		}
+
+		fmpz_clear(a);
+		fmpz_clear(b);
+		fmpz_clear(c);
+	}
+
+	TEST_FUNCTION_END(state);
+}
diff --git a/src/fmpz/test/t-sum_powers_horner.c b/src/fmpz/test/t-sum_powers_horner.c
new file mode 100644
index 0000000000..7d39f0c70d
--- /dev/null
+++ b/src/fmpz/test/t-sum_powers_horner.c
@@ -0,0 +1,90 @@
+/*
+    Copyright (C) 2024 Matthias Gessinger
+
+    This file is part of FLINT.
+
+    FLINT is free software: you can redistribute it and/or modify it under
+    the terms of the GNU Lesser General Public License (LGPL) as published
+    by the Free Software Foundation; either version 3 of the License, or
+    (at your option) any later version.  See <https://www.gnu.org/licenses/>.
+*/
+
+#include "test_helpers.h"
+#include "ulong_extras.h"
+#include "fmpz.h"
+
+void _fmpz_sum_powers_naive_horner(fmpz_t f, const fmpz_t g, ulong exp)
+{
+	fmpz_t t;
+	fmpz_init(t);
+
+	fmpz_zero(f);
+
+	for (ulong i = 0; i <= exp; i++)
+	{
+		fmpz_pow_ui(t, g, i);
+		fmpz_add(f, f, t);
+	}
+
+	fmpz_clear(t);
+}
+
+TEST_FUNCTION_START(fmpz_sum_powers_horner, state)
+{
+	int i, result;
+
+	for (i = 0; i < 1000 * flint_test_multiplier(); i++)
+	{
+		fmpz_t a, b, c;
+		ulong exp;
+		int aliasing;
+
+		fmpz_init(a);
+		fmpz_init(b);
+		fmpz_init(c);
+
+		fmpz_randtest(a, state, 100);
+
+		exp = n_randint(state, 250);
+
+		aliasing = n_randint(state, 2);
+
+		/* The reference result */
+		_fmpz_sum_powers_naive_horner(c, a, exp);
+
+		/* Horner-style evaluation */
+		if (aliasing == 1)
+		{
+			fmpz_sum_powers_horner(a, a, exp);
+			fmpz_set(b, a);
+		}
+		else
+		{
+			fmpz_sum_powers_horner(b, a, exp);
+		}
+
+		result = (fmpz_cmp(c, b) == 0);
+
+		if (!result)
+		{
+			flint_printf("FAIL in horner evaluation:\n");
+
+			flint_printf("Expected: ");
+			fmpz_print(c);
+			flint_printf("\n");
+
+			flint_printf("Actual: ");
+			fmpz_print(b);
+			flint_printf("\n");
+
+			fflush(stdout);
+			flint_abort();
+		}
+
+		fmpz_clear(a);
+		fmpz_clear(b);
+		fmpz_clear(c);
+	}
+
+	TEST_FUNCTION_END(state);
+}

From 48ef3d3fe1d6f723f10b1643560b3787e064e4e0 Mon Sep 17 00:00:00 2001
From: Matthias Gessinger <matthias@gessinger.de>
Date: Fri, 5 Jul 2024 23:46:59 +0200
Subject: [PATCH 4/9] Add fmpz_sum_divisors and tests

---
 src/fmpz.h                     |  11 +--
 src/fmpz/sum_divisors.c        |  75 +++++++++++++++++++++
 src/fmpz/sum_powers.c          | 114 +++++++++++++++----------------
 src/fmpz/test/main.c           |   4 +-
 src/fmpz/test/t-sum_divisors.c | 120 +++++++++++++++++++++++++++++++++
 5 files changed, 262 insertions(+), 62 deletions(-)
 create mode 100644 src/fmpz/sum_divisors.c
 create mode 100644 src/fmpz/test/t-sum_divisors.c

diff --git a/src/fmpz.h b/src/fmpz.h
index 35c88cb752..52a5b6c711 100644
--- a/src/fmpz.h
+++ b/src/fmpz.h
@@ -378,6 +378,13 @@ void fmpz_pow_ui(fmpz_t f, const fmpz_t g, ulong exp);
 void fmpz_ui_pow_ui(fmpz_t x, ulong b, ulong e);
 int fmpz_pow_fmpz(fmpz_t a, const fmpz_t b, const fmpz_t e);
 
+void fmpz_sum_powers(fmpz_t f, const fmpz_t g, ulong exp);
+void fmpz_sum_powers_horner(fmpz_t f, const fmpz_t g, ulong exp);
+void fmpz_sum_powers_div(fmpz_t f, const fmpz_t g, ulong exp);
+
+void fmpz_sum_divisors(fmpz_t f, const fmpz_t g);
+void fmpz_sum_divisors_proper(fmpz_t f, const fmpz_t g);
+
 void fmpz_sqrt(fmpz_t f, const fmpz_t g);
 void fmpz_sqrtrem(fmpz_t f, fmpz_t r, const fmpz_t g);
 
@@ -440,10 +447,6 @@ slong fmpz_flog_ui(const fmpz_t x, ulong b);
 double fmpz_get_d_2exp(slong * exp, const fmpz_t f);
 void fmpz_set_d_2exp(fmpz_t f, double m, slong exp);
 
-void fmpz_sum_powers_horner(fmpz_t f, const fmpz_t g, ulong exp);
-void fmpz_sum_powers_div(fmpz_t f, const fmpz_t g, ulong exp);
-void fmpz_sum_powers(fmpz_t f, const fmpz_t g, ulong exp);
-
 #if FLINT_HAVE_FFT_SMALL
 #define MPZ_WANT_FLINT_DIVISION(a, b) (mpz_size(b) >= 1250 && mpz_size(a) - mpz_size(b) >= 1250)
 #else
diff --git a/src/fmpz/sum_divisors.c b/src/fmpz/sum_divisors.c
new file mode 100644
index 0000000000..c3465f91d3
--- /dev/null
+++ b/src/fmpz/sum_divisors.c
@@ -0,0 +1,75 @@
+/*
+    Copyright (C) 2024 Matthias Gessinger
+
+    This file is part of FLINT.
+
+    FLINT is free software: you can redistribute it and/or modify it under
+    the terms of the GNU Lesser General Public License (LGPL) as published
+    by the Free Software Foundation; either version 3 of the License, or
+    (at your option) any later version.  See <https://www.gnu.org/licenses/>.
+*/
+
+#include "fmpz.h"
+#include "fmpz_factor.h"
+
+void
+fmpz_sum_divisors(fmpz_t f, const fmpz_t g)
+{
+    fmpz_factor_t factors;
+    fmpz * temp;
+    ulong exp;
+    ulong i;
+
+    fmpz * p;
+
+    if (fmpz_is_zero(g) || fmpz_is_pm1(g))
+    {
+        fmpz_set(f, g);
+    }
+    else
+    {
+        fmpz_factor_init(factors);
+
+        fmpz_factor(factors, g);
+        i = 0;
+
+        temp = factors->p + i;
+        exp = factors->exp[i];
+
+        fmpz_sum_powers(temp, temp, exp);
+
+        for (i = 1; i < factors->num; i++)
+        {
+            p = factors->p + i;
+            exp = factors->exp[i];
+
+            fmpz_sum_powers(p, p, exp);
+
+            fmpz_mul(temp, temp, p);
+        }
+
+        if (factors->sign == -1)
+        {
+            fmpz_neg(f, temp);
+        }
+        else
+        {
+            fmpz_swap(f, temp);
+        }
+
+        fmpz_factor_clear(factors);
+    }
+}
+
+void
+fmpz_sum_divisors_proper(fmpz_t f, const fmpz_t g)
+{
+	fmpz_t temp;
+	fmpz_init(temp);
+
+	fmpz_sum_divisors(temp, g);
+
+	fmpz_sub(f, temp, g);
+
+	fmpz_clear(temp);
+}
diff --git a/src/fmpz/sum_powers.c b/src/fmpz/sum_powers.c
index 32df74f6af..50f71611b2 100644
--- a/src/fmpz/sum_powers.c
+++ b/src/fmpz/sum_powers.c
@@ -14,79 +14,79 @@
 void
 fmpz_sum_powers_horner(fmpz_t f, const fmpz_t g, ulong exp)
 {
-	fmpz_t t;
+    fmpz_t t;
 
-	if (exp == 0 || fmpz_is_zero(g))
-	{
-		fmpz_one(f);
-	}
-	else if (fmpz_is_one(g))
-	{
-		fmpz_set_ui(f, exp + 1);
-	}
-	else
-	{
-		fmpz_init_set_ui(t, 1);
+    if (exp == 0 || fmpz_is_zero(g))
+    {
+        fmpz_one(f);
+    }
+    else if (fmpz_is_one(g))
+    {
+        fmpz_set_ui(f, exp + 1);
+    }
+    else
+    {
+        fmpz_init_set_ui(t, 1);
 
-		for (ulong i = 1; i <= exp; i++)
-		{
-			fmpz_mul(t, t, g);
-			fmpz_add_ui(t, t, 1);
-		}
+        for (ulong i = 1; i <= exp; i++)
+        {
+            fmpz_mul(t, t, g);
+            fmpz_add_ui(t, t, 1);
+        }
 
-		fmpz_swap(f, t);
-		fmpz_clear(t);
-	}
+        fmpz_swap(f, t);
+        fmpz_clear(t);
+    }
 }
 
 void
 fmpz_sum_powers_div(fmpz_t f, const fmpz_t g, ulong exp)
 {
-	fmpz_t t;
+    fmpz_t t;
 
-	if (exp == 0 || fmpz_is_zero(g))
-	{
-		fmpz_one(f);
-	}
-	else if (fmpz_is_one(g))
-	{
-		fmpz_set_ui(f, exp + 1);
-	}
-	else
-	{
-		fmpz_init(t);
+    if (exp == 0 || fmpz_is_zero(g))
+    {
+        fmpz_one(f);
+    }
+    else if (fmpz_is_one(g))
+    {
+        fmpz_set_ui(f, exp + 1);
+    }
+    else
+    {
+        fmpz_init(t);
 
-		// t = g - 1
-		fmpz_sub_ui(t, g, 1);
+        /* t = g - 1 */
+        fmpz_sub_ui(t, g, 1);
 
-		// f = g^(e + 1) - 1
-		fmpz_pow_ui(f, g, exp + 1);
-		fmpz_sub_ui(f, f, 1);
+        /* f = g^(e + 1) - 1 */
+        fmpz_pow_ui(f, g, exp + 1);
+        fmpz_sub_ui(f, f, 1);
 
-		// f = (g^(e + 1) - 1) / (g - 1)
-		fmpz_tdiv_q(f, f, t);
+        /* f = (g^(e + 1) - 1) / (g - 1) */
+        fmpz_tdiv_q(f, f, t);
 
-		fmpz_clear(t);
-	}
+        fmpz_clear(t);
+    }
 }
 
 void
 fmpz_sum_powers(fmpz_t f, const fmpz_t g, ulong exp)
 {
-	if (exp == 0 || fmpz_is_zero(g))
-	{
-		fmpz_one(f);
-	}
-	else if (exp == 1)
-	{
-		fmpz_add_ui(f, g, 1);
-	}
-	else if (exp <= 100)
-	{
-		fmpz_sum_powers_horner(f, g, exp);
-	}
-	else
-	{
-		fmpz_sum_powers_div(f, g, exp);
-	}
+    if (exp == 0 || fmpz_is_zero(g))
+    {
+        fmpz_one(f);
+    }
+    else if (exp == 1)
+    {
+        fmpz_add_ui(f, g, 1);
+    }
+    else if (exp <= 100)
+    {
+        fmpz_sum_powers_horner(f, g, exp);
+    }
+    else
+    {
+        fmpz_sum_powers_div(f, g, exp);
+    }
 }
diff --git a/src/fmpz/test/main.c b/src/fmpz/test/main.c
index d2338062a6..c6a4b8b0a4 100644
--- a/src/fmpz/test/main.c
+++ b/src/fmpz/test/main.c
@@ -193,6 +193,7 @@
 #include "t-sum_powers_horner.c"
 #include "t-sum_powers_div.c"
 #include "t-sum_powers.c"
+#include "t-sum_divisors.c"
 
 /* Array of test functions ***************************************************/
 
@@ -365,7 +366,8 @@ test_struct tests[] =
     TEST_FUNCTION(fmpz_xor),
     TEST_FUNCTION(fmpz_sum_powers_horner),
     TEST_FUNCTION(fmpz_sum_powers_div),
-    TEST_FUNCTION(fmpz_sum_powers)
+    TEST_FUNCTION(fmpz_sum_powers),
+    TEST_FUNCTION(fmpz_sum_divisors)
 };
 
 /* main function *************************************************************/
diff --git a/src/fmpz/test/t-sum_divisors.c b/src/fmpz/test/t-sum_divisors.c
new file mode 100644
index 0000000000..536d2f613a
--- /dev/null
+++ b/src/fmpz/test/t-sum_divisors.c
@@ -0,0 +1,120 @@
+/*
+    Copyright (C) 2024 Matthias Gessinger
+
+    This file is part of FLINT.
+
+    FLINT is free software: you can redistribute it and/or modify it under
+    the terms of the GNU Lesser General Public License (LGPL) as published
+    by the Free Software Foundation; either version 3 of the License, or
+    (at your option) any later version.  See <https://www.gnu.org/licenses/>.
+*/
+
+#include "test_helpers.h"
+#include "ulong_extras.h"
+#include "fmpz.h"
+
+void _fmpz_sum_divisors_naive(fmpz_t f, fmpz_t g)
+{
+	fmpz_t sqrt, temp1, temp2, temp3, out;
+
+	fmpz_init(sqrt);
+	fmpz_init(temp1);
+	fmpz_init(temp2);
+	fmpz_init(temp3);
+	fmpz_init(out);
+
+	int is_neg = fmpz_cmp_ui(g, 0) < 1;
+
+	fmpz_abs(f, g);
+	fmpz_sqrt(sqrt, f);
+
+	fmpz_set_si(temp1, 1);
+	while (fmpz_cmp(temp1, sqrt) != 1)
+	{
+		fmpz_tdiv_qr(temp3, temp2, f, temp1);
+
+		if (fmpz_is_zero(temp2))
+		{
+			fmpz_add(out, out, temp3);
+
+			if (fmpz_cmp(temp1, temp3) != 0)
+			{
+				fmpz_add(out, out, temp1);
+			}
+		}
+
+		fmpz_add_si(temp1, temp1, 1);
+	}
+
+	if (is_neg)
+	{
+		fmpz_neg(f, out);
+	}
+	else
+	{
+		fmpz_set(f, out);
+	}
+
+	fmpz_clear(out);
+	fmpz_clear(temp1);
+	fmpz_clear(temp2);
+	fmpz_clear(temp3);
+	fmpz_clear(sqrt);
+}
+
+TEST_FUNCTION_START(fmpz_sum_divisors, state)
+{
+	int i, result;
+
+	for (i = 0; i < 1000 * flint_test_multiplier(); i++)
+	{
+		fmpz_t a, b, c;
+		int aliasing;
+
+		fmpz_init(a);
+		fmpz_init(b);
+		fmpz_init(c);
+
+		fmpz_randtest(a, state, 32);
+
+		aliasing = n_randint(state, 2);
+
+		/* The reference result */
+		_fmpz_sum_divisors_naive(c, a);
+
+		/* general function */
+		if (aliasing == 1)
+		{
+			fmpz_sum_divisors(a, a);
+			fmpz_set(b, a);
+		}
+		else
+		{
+			fmpz_sum_divisors(b, a);
+		}
+
+		result = (fmpz_cmp(c, b) == 0);
+
+		if (!result)
+		{
+			flint_printf("FAIL:\n");
+
+			flint_printf("Expected: ");
+			fmpz_print(c);
+			flint_printf("\n");
+
+			flint_printf("Actual: ");
+			fmpz_print(b);
+			flint_printf("\n");
+
+			fflush(stdout);
+			flint_abort();
+		}
+
+		fmpz_clear(a);
+		fmpz_clear(b);
+		fmpz_clear(c);
+	}
+
+	TEST_FUNCTION_END(state);
+}

From 0f8c263e703c74e769ebfa584d6aaed6d4d41336 Mon Sep 17 00:00:00 2001
From: Matthias Gessinger <matthias@gessinger.de>
Date: Sat, 6 Jul 2024 09:18:47 +0200
Subject: [PATCH 5/9] Add documentation

---
 doc/source/fmpz.rst | 23 +++++++++++++++++++++++
 1 file changed, 23 insertions(+)

diff --git a/doc/source/fmpz.rst b/doc/source/fmpz.rst
index fdae8a70cc..2732961a13 100644
--- a/doc/source/fmpz.rst
+++ b/doc/source/fmpz.rst
@@ -959,6 +959,29 @@ Basic arithmetic
 
     Assumes that `m \neq 0`, raises an ``abort`` signal otherwise.
 
+.. function:: void fmpz_sum_powers_horner(fmpz_t f, const fmpz_t g, ulong e)
+
+.. function:: void fmpz_sum_powers_div(fmpz_t f, const fmpz_t g, ulong e)
+
+.. function:: void fmpz_sum_powers(fmpz_t f, const fmpz_t g, ulong e)
+
+   Sets `f` to the sum of powers of g, starting at `g^0 = 1` up to and
+   including `p^e`.
+
+   The `horner` method uses a horner-style method to evaluate the sum.
+
+   The `div` method uses polynomial division to evaluate the sum with a
+   single exponentiation and a single division.
+
+.. function:: void fmpz_sum_divisors(fmpz_t f, const fmpz_t g)
+
+   Sets `f` to the sum of divisors of `g`, including 1 and `g` itself.
+
+.. function:: void fmpz_sum_divisors_proper(fmpz_t f, const fmpz_t g)
+
+   Sets `f` to the sum of proper divisors of `g`, including 1 but excluding
+   `g` itself.
+
 .. function:: slong fmpz_clog(const fmpz_t x, const fmpz_t b)
               slong fmpz_clog_ui(const fmpz_t x, ulong b)
 

From 7d627bbb1f3982dd83f6fdb511461740563fc15a Mon Sep 17 00:00:00 2001
From: Matthias Gessinger <matthias@gessinger.de>
Date: Sat, 6 Jul 2024 09:40:19 +0200
Subject: [PATCH 6/9] Add example program to compute aliquot sequence

---
 AUTHORS            |  2 ++
 examples/aliquot.c | 47 ++++++++++++++++++++++++++++++++++++++++++++++
 2 files changed, 49 insertions(+)
 create mode 100644 examples/aliquot.c

diff --git a/AUTHORS b/AUTHORS
index 9da22903ae..484cf66ca2 100644
--- a/AUTHORS
+++ b/AUTHORS
@@ -446,6 +446,8 @@ David Berghaus
 Matthias Gessinger
 
   Graeffe transforms.
+  Sums of powers and sums of divisors of integers.
+  Aliquot sequences.
 
 Erik Postma
 
diff --git a/examples/aliquot.c b/examples/aliquot.c
new file mode 100644
index 0000000000..53229bd8b5
--- /dev/null
+++ b/examples/aliquot.c
@@ -0,0 +1,47 @@
+/*
+    Copyright (C) 2024 Matthias Gessinger
+
+    This file is part of FLINT.
+
+    FLINT is free software: you can redistribute it and/or modify it under
+    the terms of the GNU Lesser General Public License (LGPL) as published
+    by the Free Software Foundation; either version 3 of the License, or
+    (at your option) any later version.  See <https://www.gnu.org/licenses/>.
+*/
+
+#include <flint/fmpz.h>
+#include <flint/profiler.h>
+
+int
+main(int argc, char * argv[])
+{
+	fmpz_t n;
+	ulong num_iterations = 0;
+
+	fmpz_init_set_si(n, 138);
+
+	flint_printf("Computing aliquot sequence\n");
+	flint_printf("%3wu : ", 0);
+	fmpz_print(n);
+	flint_printf("\n");
+
+	TIMEIT_ONCE_START
+
+	while (!fmpz_is_one(n))
+	{
+		fmpz_sum_divisors_proper(n, n);
+		num_iterations++;
+
+		flint_printf("%3wu : ", num_iterations);
+		fmpz_print(n);
+		flint_printf("\n");
+	}
+
+	flint_printf("Sequence terminated after %wu iterations.\n", num_iterations);
+
+	TIMEIT_ONCE_STOP
+	SHOW_MEMORY_USAGE
+
+	fmpz_clear(n);
+	return 0;
+}

From 639dfd9255f63a4e8ba769a88a0b23b254eaff29 Mon Sep 17 00:00:00 2001
From: Matthias Gessinger <matthias@gessinger.de>
Date: Sat, 6 Jul 2024 09:48:36 +0200
Subject: [PATCH 7/9] Fix formatting

---
 examples/aliquot.c                  |  42 ++++++------
 src/fmpz/sum_divisors.c             |  10 +--
 src/fmpz/test/t-sum_powers.c        | 102 ++++++++++++++--------------
 src/fmpz/test/t-sum_powers_div.c    | 102 ++++++++++++++--------------
 src/fmpz/test/t-sum_powers_horner.c | 102 ++++++++++++++--------------
 5 files changed, 179 insertions(+), 179 deletions(-)

diff --git a/examples/aliquot.c b/examples/aliquot.c
index 53229bd8b5..c467591319 100644
--- a/examples/aliquot.c
+++ b/examples/aliquot.c
@@ -15,33 +15,33 @@
 int
 main(int argc, char * argv[])
 {
-	fmpz_t n;
-	ulong num_iterations = 0;
+    fmpz_t n;
+    ulong num_iterations = 0;
 
-	fmpz_init_set_si(n, 138);
+    fmpz_init_set_si(n, 138);
 
-	flint_printf("Computing aliquot sequence\n");
-	flint_printf("%3wu : ", 0);
-	fmpz_print(n);
-	flint_printf("\n");
+    flint_printf("Computing aliquot sequence\n");
+    flint_printf("%3wu : ", 0);
+    fmpz_print(n);
+    flint_printf("\n");
 
-	TIMEIT_ONCE_START
+    TIMEIT_ONCE_START
 
-	while (!fmpz_is_one(n))
-	{
-		fmpz_sum_divisors_proper(n, n);
-		num_iterations++;
+    while (!fmpz_is_one(n))
+    {
+        fmpz_sum_divisors_proper(n, n);
+        num_iterations++;
 
-		flint_printf("%3wu : ", num_iterations);
-		fmpz_print(n);
-		flint_printf("\n");
-	}
+        flint_printf("%3wu : ", num_iterations);
+        fmpz_print(n);
+        flint_printf("\n");
+    }
 
-	flint_printf("Sequence terminated after %wu iterations.\n", num_iterations);
+    flint_printf("Sequence terminated after %wu iterations.\n", num_iterations);
 
-	TIMEIT_ONCE_STOP
-	SHOW_MEMORY_USAGE
+    TIMEIT_ONCE_STOP
+    SHOW_MEMORY_USAGE
 
-	fmpz_clear(n);
-	return 0;
+    fmpz_clear(n);
+    return 0;
 }
diff --git a/src/fmpz/sum_divisors.c b/src/fmpz/sum_divisors.c
index c3465f91d3..de286e302d 100644
--- a/src/fmpz/sum_divisors.c
+++ b/src/fmpz/sum_divisors.c
@@ -64,12 +64,12 @@ fmpz_sum_divisors(fmpz_t f, const fmpz_t g)
 void
 fmpz_sum_divisors_proper(fmpz_t f, const fmpz_t g)
 {
-	fmpz_t temp;
-	fmpz_init(temp);
+    fmpz_t temp;
+    fmpz_init(temp);
 
-	fmpz_sum_divisors(temp, g);
+    fmpz_sum_divisors(temp, g);
 
-	fmpz_sub(f, temp, g);
+    fmpz_sub(f, temp, g);
 
-	fmpz_clear(temp);
+    fmpz_clear(temp);
 }
diff --git a/src/fmpz/test/t-sum_powers.c b/src/fmpz/test/t-sum_powers.c
index 7d23402ccb..fcb3accde6 100644
--- a/src/fmpz/test/t-sum_powers.c
+++ b/src/fmpz/test/t-sum_powers.c
@@ -15,76 +15,76 @@
 
 void _fmpz_sum_powers_naive(fmpz_t f, const fmpz_t g, ulong exp)
 {
-	fmpz_t t;
-	fmpz_init(t);
+    fmpz_t t;
+    fmpz_init(t);
 
-	fmpz_zero(f);
+    fmpz_zero(f);
 
-	for (ulong i = 0; i <= exp; i++)
-	{
-		fmpz_pow_ui(t, g, i);
-		fmpz_add(f, f, t);
-	}
+    for (ulong i = 0; i <= exp; i++)
+    {
+        fmpz_pow_ui(t, g, i);
+        fmpz_add(f, f, t);
+    }
 
-	fmpz_clear(t);
+    fmpz_clear(t);
 }
 
 TEST_FUNCTION_START(fmpz_sum_powers, state)
 {
-	int i, result;
+    int i, result;
 
-	for (i = 0; i < 1000 * flint_test_multiplier(); i++)
-	{
-		fmpz_t a, b, c;
-		ulong exp;
-		int aliasing;
+    for (i = 0; i < 1000 * flint_test_multiplier(); i++)
+    {
+        fmpz_t a, b, c;
+        ulong exp;
+        int aliasing;
 
-		fmpz_init(a);
-		fmpz_init(b);
-		fmpz_init(c);
+        fmpz_init(a);
+        fmpz_init(b);
+        fmpz_init(c);
 
-		fmpz_randtest(a, state, 100);
+        fmpz_randtest(a, state, 100);
 
-		exp = n_randint(state, 250);
+        exp = n_randint(state, 250);
 
-		aliasing = n_randint(state, 2);
+        aliasing = n_randint(state, 2);
 
-		/* The reference result */
-		_fmpz_sum_powers_naive(c, a, exp);
+        /* The reference result */
+        _fmpz_sum_powers_naive(c, a, exp);
 
-		/* general function */
-		if (aliasing == 1)
-		{
-			fmpz_sum_powers(a, a, exp);
-			fmpz_set(b, a);
-		}
-		else
-		{
-			fmpz_sum_powers(b, a, exp);
-		}
+        /* general function */
+        if (aliasing == 1)
+        {
+            fmpz_sum_powers(a, a, exp);
+            fmpz_set(b, a);
+        }
+        else
+        {
+            fmpz_sum_powers(b, a, exp);
+        }
 
-		result = (fmpz_cmp(c, b) == 0);
+        result = (fmpz_cmp(c, b) == 0);
 
-		if (!result)
-		{
-			flint_printf("FAIL in general method:\n");
+        if (!result)
+        {
+            flint_printf("FAIL:\n");
 
-			flint_printf("Expected: ");
-			fmpz_print(c);
-			flint_printf("\n");
+            flint_printf("Expected: ");
+            fmpz_print(c);
+            flint_printf("\n");
 
-			flint_printf("Actual: ");
-			fmpz_print(b);
-			flint_printf("\n");
+            flint_printf("Actual: ");
+            fmpz_print(b);
+            flint_printf("\n");
 
-			fflush(stdout);
-			flint_abort();
-		}
+            fflush(stdout);
+            flint_abort();
+        }
 
-		fmpz_clear(a);
-		fmpz_clear(b);
-		fmpz_clear(c);
-	}
+        fmpz_clear(a);
+        fmpz_clear(b);
+        fmpz_clear(c);
+    }
 
-	TEST_FUNCTION_END(state);
+    TEST_FUNCTION_END(state);
 }
diff --git a/src/fmpz/test/t-sum_powers_div.c b/src/fmpz/test/t-sum_powers_div.c
index 79c1df8f76..38e1728888 100644
--- a/src/fmpz/test/t-sum_powers_div.c
+++ b/src/fmpz/test/t-sum_powers_div.c
@@ -15,76 +15,76 @@
 
 void _fmpz_sum_powers_naive_div(fmpz_t f, const fmpz_t g, ulong exp)
 {
-	fmpz_t t;
-	fmpz_init(t);
+    fmpz_t t;
+    fmpz_init(t);
 
-	fmpz_zero(f);
+    fmpz_zero(f);
 
-	for (ulong i = 0; i <= exp; i++)
-	{
-		fmpz_pow_ui(t, g, i);
-		fmpz_add(f, f, t);
-	}
+    for (ulong i = 0; i <= exp; i++)
+    {
+        fmpz_pow_ui(t, g, i);
+        fmpz_add(f, f, t);
+    }
 
-	fmpz_clear(t);
+    fmpz_clear(t);
 }
 
 TEST_FUNCTION_START(fmpz_sum_powers_div, state)
 {
-	int i, result;
+    int i, result;
 
-	for (i = 0; i < 1000 * flint_test_multiplier(); i++)
-	{
-		fmpz_t a, b, c;
-		ulong exp;
-		int aliasing;
+    for (i = 0; i < 1000 * flint_test_multiplier(); i++)
+    {
+        fmpz_t a, b, c;
+        ulong exp;
+        int aliasing;
 
-		fmpz_init(a);
-		fmpz_init(b);
-		fmpz_init(c);
+        fmpz_init(a);
+        fmpz_init(b);
+        fmpz_init(c);
 
-		fmpz_randtest(a, state, 100);
+        fmpz_randtest(a, state, 100);
 
-		exp = n_randint(state, 250);
+        exp = n_randint(state, 250);
 
-		aliasing = n_randint(state, 2);
+        aliasing = n_randint(state, 2);
 
-		/* The reference result */
-		_fmpz_sum_powers_naive_div(c, a, exp);
+        /* The reference result */
+        _fmpz_sum_powers_naive_div(c, a, exp);
 
-		/* polynomial division method */
-		if (aliasing == 1)
-		{
-			fmpz_sum_powers_div(a, a, exp);
-			fmpz_set(b, a);
-		}
-		else
-		{
-			fmpz_sum_powers_div(b, a, exp);
-		}
+        /* polynomial division method */
+        if (aliasing == 1)
+        {
+            fmpz_sum_powers_div(a, a, exp);
+            fmpz_set(b, a);
+        }
+        else
+        {
+            fmpz_sum_powers_div(b, a, exp);
+        }
 
-		result = (fmpz_cmp(c, b) == 0);
+        result = (fmpz_cmp(c, b) == 0);
 
-		if (!result)
-		{
-			flint_printf("FAIL in polynomial division method:\n");
+        if (!result)
+        {
+            flint_printf("FAIL:\n");
 
-			flint_printf("Expected: ");
-			fmpz_print(c);
-			flint_printf("\n");
+            flint_printf("Expected: ");
+            fmpz_print(c);
+            flint_printf("\n");
 
-			flint_printf("Actual: ");
-			fmpz_print(b);
-			flint_printf("\n");
+            flint_printf("Actual: ");
+            fmpz_print(b);
+            flint_printf("\n");
 
-			fflush(stdout);
-			flint_abort();
-		}
+            fflush(stdout);
+            flint_abort();
+        }
 
-		fmpz_clear(a);
-		fmpz_clear(b);
-		fmpz_clear(c);
-	}
+        fmpz_clear(a);
+        fmpz_clear(b);
+        fmpz_clear(c);
+    }
 
-	TEST_FUNCTION_END(state);
+    TEST_FUNCTION_END(state);
 }
diff --git a/src/fmpz/test/t-sum_powers_horner.c b/src/fmpz/test/t-sum_powers_horner.c
index 7d39f0c70d..8a61de4d77 100644
--- a/src/fmpz/test/t-sum_powers_horner.c
+++ b/src/fmpz/test/t-sum_powers_horner.c
@@ -15,76 +15,76 @@
 
 void _fmpz_sum_powers_naive_horner(fmpz_t f, const fmpz_t g, ulong exp)
 {
-	fmpz_t t;
-	fmpz_init(t);
+    fmpz_t t;
+    fmpz_init(t);
 
-	fmpz_zero(f);
+    fmpz_zero(f);
 
-	for (ulong i = 0; i <= exp; i++)
-	{
-		fmpz_pow_ui(t, g, i);
-		fmpz_add(f, f, t);
-	}
+    for (ulong i = 0; i <= exp; i++)
+    {
+        fmpz_pow_ui(t, g, i);
+        fmpz_add(f, f, t);
+    }
 
-	fmpz_clear(t);
+    fmpz_clear(t);
 }
 
 TEST_FUNCTION_START(fmpz_sum_powers_horner, state)
 {
-	int i, result;
+    int i, result;
 
-	for (i = 0; i < 1000 * flint_test_multiplier(); i++)
-	{
-		fmpz_t a, b, c;
-		ulong exp;
-		int aliasing;
+    for (i = 0; i < 1000 * flint_test_multiplier(); i++)
+    {
+        fmpz_t a, b, c;
+        ulong exp;
+        int aliasing;
 
-		fmpz_init(a);
-		fmpz_init(b);
-		fmpz_init(c);
+        fmpz_init(a);
+        fmpz_init(b);
+        fmpz_init(c);
 
-		fmpz_randtest(a, state, 100);
+        fmpz_randtest(a, state, 100);
 
-		exp = n_randint(state, 250);
+        exp = n_randint(state, 250);
 
-		aliasing = n_randint(state, 2);
+        aliasing = n_randint(state, 2);
 
-		/* The reference result */
-		_fmpz_sum_powers_naive_horner(c, a, exp);
+        /* The reference result */
+        _fmpz_sum_powers_naive_horner(c, a, exp);
 
-		/* Horner-style evaluation */
-		if (aliasing == 1)
-		{
-			fmpz_sum_powers_horner(a, a, exp);
-			fmpz_set(b, a);
-		}
-		else
-		{
-			fmpz_sum_powers_horner(b, a, exp);
-		}
+        /* Horner-style evaluation */
+        if (aliasing == 1)
+        {
+            fmpz_sum_powers_horner(a, a, exp);
+            fmpz_set(b, a);
+        }
+        else
+        {
+            fmpz_sum_powers_horner(b, a, exp);
+        }
 
-		result = (fmpz_cmp(c, b) == 0);
+        result = (fmpz_cmp(c, b) == 0);
 
-		if (!result)
-		{
-			flint_printf("FAIL in horner evaluation:\n");
+        if (!result)
+        {
+            flint_printf("FAIL:\n");
 
-			flint_printf("Expected: ");
-			fmpz_print(c);
-			flint_printf("\n");
+            flint_printf("Expected: ");
+            fmpz_print(c);
+            flint_printf("\n");
 
-			flint_printf("Actual: ");
-			fmpz_print(b);
-			flint_printf("\n");
+            flint_printf("Actual: ");
+            fmpz_print(b);
+            flint_printf("\n");
 
-			fflush(stdout);
-			flint_abort();
-		}
+            fflush(stdout);
+            flint_abort();
+        }
 
-		fmpz_clear(a);
-		fmpz_clear(b);
-		fmpz_clear(c);
-	}
+        fmpz_clear(a);
+        fmpz_clear(b);
+        fmpz_clear(c);
+    }
 
-	TEST_FUNCTION_END(state);
+    TEST_FUNCTION_END(state);
 }

From 92c40aba3977889e12970a02beb016d15ad869f3 Mon Sep 17 00:00:00 2001
From: Matthias Gessinger <matthias@gessinger.de>
Date: Sat, 6 Jul 2024 13:30:00 +0200
Subject: [PATCH 8/9] Style fixes

---
 doc/source/fmpz.rst  |  5 +++--
 src/fmpz/test/main.c | 18 +++++++++---------
 2 files changed, 12 insertions(+), 11 deletions(-)

diff --git a/doc/source/fmpz.rst b/doc/source/fmpz.rst
index 2732961a13..34e06f3f5f 100644
--- a/doc/source/fmpz.rst
+++ b/doc/source/fmpz.rst
@@ -965,10 +965,11 @@ Basic arithmetic
 
 .. function:: void fmpz_sum_powers(fmpz_t f, const fmpz_t g, ulong e)
 
-   Sets `f` to the sum of powers of g, starting at `g^0 = 1` up to and
+   Sets `f` to the sum of powers of `g`, starting at `g^0 = 1` up to and
    including `p^e`.
 
-   The `horner` method uses a horner-style method to evaluate the sum.
+   The `horner` method uses a horner-style method to evaluate the sum
+   iteratively.
 
    The `div` method uses polynomial division to evaluate the sum with a
    single exponentiation and a single division.
diff --git a/src/fmpz/test/main.c b/src/fmpz/test/main.c
index c6a4b8b0a4..09b0569e11 100644
--- a/src/fmpz/test/main.c
+++ b/src/fmpz/test/main.c
@@ -176,6 +176,10 @@
 #include "t-submul.c"
 #include "t-submul_si.c"
 #include "t-submul_ui.c"
+#include "t-sum_powers_horner.c"
+#include "t-sum_powers_div.c"
+#include "t-sum_powers.c"
+#include "t-sum_divisors.c"
 #include "t-swap.c"
 #include "t-tdiv_q_2exp.c"
 #include "t-tdiv_q.c"
@@ -190,10 +194,6 @@
 #include "t-xgcd_canonical_bezout.c"
 #include "t-xgcd_partial.c"
 #include "t-xor.c"
-#include "t-sum_powers_horner.c"
-#include "t-sum_powers_div.c"
-#include "t-sum_powers.c"
-#include "t-sum_divisors.c"
 
 /* Array of test functions ***************************************************/
 
@@ -350,6 +350,10 @@ test_struct tests[] =
     TEST_FUNCTION(fmpz_submul),
     TEST_FUNCTION(fmpz_submul_si),
     TEST_FUNCTION(fmpz_submul_ui),
+    TEST_FUNCTION(fmpz_sum_powers_horner),
+    TEST_FUNCTION(fmpz_sum_powers_div),
+    TEST_FUNCTION(fmpz_sum_powers),
+    TEST_FUNCTION(fmpz_sum_divisors),
     TEST_FUNCTION(fmpz_swap),
     TEST_FUNCTION(fmpz_tdiv_q_2exp),
     TEST_FUNCTION(fmpz_tdiv_q),
@@ -363,11 +367,7 @@ test_struct tests[] =
     TEST_FUNCTION(fmpz_xgcd),
     TEST_FUNCTION(fmpz_xgcd_canonical_bezout),
     TEST_FUNCTION(fmpz_xgcd_partial),
-    TEST_FUNCTION(fmpz_xor),
-    TEST_FUNCTION(fmpz_sum_powers_horner),
-    TEST_FUNCTION(fmpz_sum_powers_div),
-    TEST_FUNCTION(fmpz_sum_powers),
-    TEST_FUNCTION(fmpz_sum_divisors)
+    TEST_FUNCTION(fmpz_xor)
 };
 
 /* main function *************************************************************/

From dd7748386948a99d5fea8efd93048640263226d9 Mon Sep 17 00:00:00 2001
From: Matthias Gessinger <matthias@gessinger.de>
Date: Sat, 6 Jul 2024 14:44:17 +0200
Subject: [PATCH 9/9] Fix formatting and check example

Add aliquot example in check_examples.sh
Fix indentation to use spaces instead of tabs
Fix test failure to use TEST_FUNCTION_FAIL macro
---
 dev/check_examples.sh               |  17 +++
 doc/source/fmpz.rst                 |   6 +-
 src/fmpz/sum_divisors.c             |   2 +-
 src/fmpz/test/t-sum_divisors.c      | 188 +++++++++++++---------------
 src/fmpz/test/t-sum_powers.c        |  16 +--
 src/fmpz/test/t-sum_powers_div.c    |  16 +--
 src/fmpz/test/t-sum_powers_horner.c |  16 +--
 7 files changed, 122 insertions(+), 139 deletions(-)

diff --git a/dev/check_examples.sh b/dev/check_examples.sh
index 356c348ddc..418f2d2cfc 100755
--- a/dev/check_examples.sh
+++ b/dev/check_examples.sh
@@ -298,6 +298,23 @@ then
     fi
     echo "PASS"
     exit 0
+elif test "$1" = "aliquot";
+then
+    echo -n "aliquot...."
+    res=$($2/aliquot)
+    if test "$?" != "0";
+    then
+        echo "FAIL"
+        exit 1
+    fi
+    echo "$res" | perl -0ne 'if (/\b117 : 179931895322\b/) { $found=1; last } END { exit !$found }'
+    if test "$?" != "0";
+    then
+        echo "FAIL"
+        exit 2
+    fi
+    echo "PASS"
+    exit 0
 else
     exit 3
 fi
diff --git a/doc/source/fmpz.rst b/doc/source/fmpz.rst
index 34e06f3f5f..45d8530ad8 100644
--- a/doc/source/fmpz.rst
+++ b/doc/source/fmpz.rst
@@ -960,10 +960,8 @@ Basic arithmetic
     Assumes that `m \neq 0`, raises an ``abort`` signal otherwise.
 
 .. function:: void fmpz_sum_powers_horner(fmpz_t f, const fmpz_t g, ulong e)
-
-.. function:: void fmpz_sum_powers_div(fmpz_t f, const fmpz_t g, ulong e)
-
-.. function:: void fmpz_sum_powers(fmpz_t f, const fmpz_t g, ulong e)
+              void fmpz_sum_powers_div(fmpz_t f, const fmpz_t g, ulong e)
+	      void fmpz_sum_powers(fmpz_t f, const fmpz_t g, ulong e)
 
    Sets `f` to the sum of powers of `g`, starting at `g^0 = 1` up to and
    including `p^e`.
diff --git a/src/fmpz/sum_divisors.c b/src/fmpz/sum_divisors.c
index de286e302d..defe88e3be 100644
--- a/src/fmpz/sum_divisors.c
+++ b/src/fmpz/sum_divisors.c
@@ -18,7 +18,7 @@ fmpz_sum_divisors(fmpz_t f, const fmpz_t g)
     fmpz_factor_t factors;
     fmpz * temp;
     ulong exp;
-    ulong i;
+    slong i;
 
     fmpz * p;
 
diff --git a/src/fmpz/test/t-sum_divisors.c b/src/fmpz/test/t-sum_divisors.c
index 536d2f613a..073406c32a 100644
--- a/src/fmpz/test/t-sum_divisors.c
+++ b/src/fmpz/test/t-sum_divisors.c
@@ -15,106 +15,98 @@
 
 void _fmpz_sum_divisors_naive(fmpz_t f, fmpz_t g)
 {
-	fmpz_t sqrt, temp1, temp2, temp3, out;
-
-	fmpz_init(sqrt);
-	fmpz_init(temp1);
-	fmpz_init(temp2);
-	fmpz_init(temp3);
-	fmpz_init(out);
-
-	int is_neg = fmpz_cmp_ui(g, 0) < 1;
-
-	fmpz_abs(f, g);
-	fmpz_sqrt(sqrt, f);
-
-	fmpz_set_si(temp1, 1);
-	while (fmpz_cmp(temp1, sqrt) != 1)
-	{
-		fmpz_tdiv_qr(temp3, temp2, f, temp1);
-
-		if (fmpz_is_zero(temp2))
-		{
-			fmpz_add(out, out, temp3);
-
-			if (fmpz_cmp(temp1, temp3) != 0)
-			{
-				fmpz_add(out, out, temp1);
-			}
-		}
-
-		fmpz_add_si(temp1, temp1, 1);
-	}
-
-	if (is_neg)
-	{
-		fmpz_neg(f, out);
-	}
-	else
-	{
-		fmpz_set(f, out);
-	}
-
-	fmpz_clear(out);
-	fmpz_clear(temp1);
-	fmpz_clear(temp2);
-	fmpz_clear(temp3);
-	fmpz_clear(sqrt);
+    fmpz_t sqrt, temp1, temp2, temp3, out;
+
+    fmpz_init(sqrt);
+    fmpz_init(temp1);
+    fmpz_init(temp2);
+    fmpz_init(temp3);
+    fmpz_init(out);
+
+    int is_neg = fmpz_cmp_ui(g, 0) < 1;
+
+    fmpz_abs(f, g);
+    fmpz_sqrt(sqrt, f);
+
+    fmpz_set_si(temp1, 1);
+    while (fmpz_cmp(temp1, sqrt) != 1)
+    {
+        fmpz_tdiv_qr(temp3, temp2, f, temp1);
+
+        if (fmpz_is_zero(temp2))
+        {
+            fmpz_add(out, out, temp3);
+
+            if (fmpz_cmp(temp1, temp3) != 0)
+            {
+                fmpz_add(out, out, temp1);
+            }
+        }
+
+        fmpz_add_si(temp1, temp1, 1);
+    }
+
+    if (is_neg)
+    {
+        fmpz_neg(f, out);
+    }
+    else
+    {
+        fmpz_set(f, out);
+    }
+
+    fmpz_clear(out);
+    fmpz_clear(temp1);
+    fmpz_clear(temp2);
+    fmpz_clear(temp3);
+    fmpz_clear(sqrt);
 }
 
 TEST_FUNCTION_START(fmpz_sum_divisors, state)
 {
-	int i, result;
-
-	for (i = 0; i < 1000 * flint_test_multiplier(); i++)
-	{
-		fmpz_t a, b, c;
-		int aliasing;
-
-		fmpz_init(a);
-		fmpz_init(b);
-		fmpz_init(c);
-
-		fmpz_randtest(a, state, 32);
-
-		aliasing = n_randint(state, 2);
-
-		/* The reference result */
-		_fmpz_sum_divisors_naive(c, a);
-
-		/* general function */
-		if (aliasing == 1)
-		{
-			fmpz_sum_divisors(a, a);
-			fmpz_set(b, a);
-		}
-		else
-		{
-			fmpz_sum_divisors(b, a);
-		}
-
-		result = (fmpz_cmp(c, b) == 0);
-
-		if (!result)
-		{
-			flint_printf("FAIL:\n");
-
-			flint_printf("Expected: ");
-			fmpz_print(c);
-			flint_printf("\n");
-
-			flint_printf("Actual: ");
-			fmpz_print(b);
-			flint_printf("\n");
-
-			fflush(stdout);
-			flint_abort();
-		}
-
-		fmpz_clear(a);
-		fmpz_clear(b);
-		fmpz_clear(c);
-	}
-
-	TEST_FUNCTION_END(state);
+    int i, result;
+
+    for (i = 0; i < 1000 * flint_test_multiplier(); i++)
+    {
+        fmpz_t a, b, c;
+        int aliasing;
+
+        fmpz_init(a);
+        fmpz_init(b);
+        fmpz_init(c);
+
+        fmpz_randtest(a, state, 32);
+
+        aliasing = n_randint(state, 2);
+
+        /* The reference result */
+        _fmpz_sum_divisors_naive(c, a);
+
+        /* general function */
+        if (aliasing == 1)
+        {
+            fmpz_sum_divisors(a, a);
+            fmpz_set(b, a);
+        }
+        else
+        {
+            fmpz_sum_divisors(b, a);
+        }
+
+        result = (fmpz_cmp(c, b) == 0);
+
+        if (!result)
+        {
+            TEST_FUNCTION_FAIL(
+                "Expected: %{fmpz}\n"
+                "Got: %{fmpz}\n",
+                c, b);
+        }
+
+        fmpz_clear(a);
+        fmpz_clear(b);
+        fmpz_clear(c);
+    }
+
+    TEST_FUNCTION_END(state);
 }
diff --git a/src/fmpz/test/t-sum_powers.c b/src/fmpz/test/t-sum_powers.c
index fcb3accde6..30d651ca93 100644
--- a/src/fmpz/test/t-sum_powers.c
+++ b/src/fmpz/test/t-sum_powers.c
@@ -67,18 +67,10 @@ TEST_FUNCTION_START(fmpz_sum_powers, state)
 
         if (!result)
         {
-            flint_printf("FAIL:\n");
-
-            flint_printf("Expected: ");
-            fmpz_print(c);
-            flint_printf("\n");
-
-            flint_printf("Actual: ");
-            fmpz_print(b);
-            flint_printf("\n");
-
-            fflush(stdout);
-            flint_abort();
+            TEST_FUNCTION_FAIL(
+                "Expected: %{fmpz}\n"
+                "Got: %{fmpz}\n",
+                c, b);
         }
 
         fmpz_clear(a);
diff --git a/src/fmpz/test/t-sum_powers_div.c b/src/fmpz/test/t-sum_powers_div.c
index 38e1728888..b4cee271f8 100644
--- a/src/fmpz/test/t-sum_powers_div.c
+++ b/src/fmpz/test/t-sum_powers_div.c
@@ -67,18 +67,10 @@ TEST_FUNCTION_START(fmpz_sum_powers_div, state)
 
         if (!result)
         {
-            flint_printf("FAIL:\n");
-
-            flint_printf("Expected: ");
-            fmpz_print(c);
-            flint_printf("\n");
-
-            flint_printf("Actual: ");
-            fmpz_print(b);
-            flint_printf("\n");
-
-            fflush(stdout);
-            flint_abort();
+            TEST_FUNCTION_FAIL(
+                "Expected: %{fmpz}\n"
+                "Got: %{fmpz}\n",
+                c, b);
         }
 
         fmpz_clear(a);
diff --git a/src/fmpz/test/t-sum_powers_horner.c b/src/fmpz/test/t-sum_powers_horner.c
index 8a61de4d77..53fda5cc33 100644
--- a/src/fmpz/test/t-sum_powers_horner.c
+++ b/src/fmpz/test/t-sum_powers_horner.c
@@ -67,18 +67,10 @@ TEST_FUNCTION_START(fmpz_sum_powers_horner, state)
 
         if (!result)
         {
-            flint_printf("FAIL:\n");
-
-            flint_printf("Expected: ");
-            fmpz_print(c);
-            flint_printf("\n");
-
-            flint_printf("Actual: ");
-            fmpz_print(b);
-            flint_printf("\n");
-
-            fflush(stdout);
-            flint_abort();
+            TEST_FUNCTION_FAIL(
+                "Expected: %{fmpz}\n"
+                "Got: %{fmpz}\n",
+                c, b);
         }
 
         fmpz_clear(a);