add binomial and borel transforms for acb_poly

acb_poly.h

@@ -171,6 +171,30 @@ void _acb_poly_integral(acb_ptr res, acb_srcptr poly, slong len, slong prec);
 
 void acb_poly_integral(acb_poly_t res, const acb_poly_t poly, slong prec);
 
+/* Transforms */
+
+void acb_poly_borel_transform(acb_poly_t res, const acb_poly_t poly, slong prec);
+
+void _acb_poly_borel_transform(acb_ptr res, acb_srcptr poly, slong len, slong prec);
+
+void acb_poly_inv_borel_transform(acb_poly_t res, const acb_poly_t poly, slong prec);
+
+void _acb_poly_inv_borel_transform(acb_ptr res, acb_srcptr poly, slong len, slong prec);
+
+void _acb_poly_binomial_transform_basecase(acb_ptr b, acb_srcptr a, slong alen, slong len, slong prec);
+
+void acb_poly_binomial_transform_basecase(acb_poly_t b, const acb_poly_t a, slong len, slong prec);
+
+void _acb_poly_binomial_transform_convolution(acb_ptr b, acb_srcptr a, slong alen, slong len, slong prec);
+
+void acb_poly_binomial_transform_convolution(acb_poly_t b, const acb_poly_t a, slong len, slong prec);
+
+void _acb_poly_binomial_transform(acb_ptr b, acb_srcptr a, slong alen, slong len, slong prec);
+
+void acb_poly_binomial_transform(acb_poly_t b, const acb_poly_t a, slong len, slong prec);
+
+
+
 void acb_poly_set(acb_poly_t dest, const acb_poly_t src);
 
 void acb_poly_set_round(acb_poly_t dest, const acb_poly_t src, slong prec);

acb_poly/binomial_transform.c

@@ -0,0 +1,49 @@
+/*
+    Copyright (C) 2013 Fredrik Johansson
+
+    This file is part of Arb.
+
+    Arb 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 2.1 of the License, or
+    (at your option) any later version.  See <http://www.gnu.org/licenses/>.
+*/
+
+#include "acb_poly.h"
+
+void
+_acb_poly_binomial_transform(acb_ptr b, acb_srcptr a, slong alen, slong len, slong prec)
+{
+    if (alen < 10 || len < 10)
+        _acb_poly_binomial_transform_basecase(b, a, alen, len, prec);
+    else
+        _acb_poly_binomial_transform_convolution(b, a, alen, len, prec);
+}
+
+void
+acb_poly_binomial_transform(acb_poly_t b, const acb_poly_t a, slong len, slong prec)
+{
+    if (len == 0 || a->length == 0)
+    {
+        acb_poly_zero(b);
+        return;
+    }
+
+    if (b == a)
+    {
+        acb_poly_t c;
+        acb_poly_init2(c, len);
+        _acb_poly_binomial_transform(c->coeffs, a->coeffs, a->length, len, prec);
+        acb_poly_swap(b, c);
+        acb_poly_clear(c);
+    }
+    else
+    {
+        acb_poly_fit_length(b, len);
+        _acb_poly_binomial_transform(b->coeffs, a->coeffs, a->length, len, prec);
+    }
+
+    _acb_poly_set_length(b, len);
+    _acb_poly_normalise(b);
+}
+

acb_poly/binomial_transform_basecase.c

@@ -0,0 +1,71 @@
+/*
+    Copyright (C) 2013 Fredrik Johansson
+
+    This file is part of Arb.
+
+    Arb 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 2.1 of the License, or
+    (at your option) any later version.  See <http://www.gnu.org/licenses/>.
+*/
+
+#include "acb_poly.h"
+
+void
+_acb_poly_binomial_transform_basecase(acb_ptr b, acb_srcptr a, slong alen, slong len, slong prec)
+{
+    slong n, k;
+
+    fmpz_t t;
+    fmpz_init(t);
+
+    for (n = 0; n < len; n++)
+    {
+        acb_zero(b + n);
+
+        for (k = 0; k < FLINT_MIN(n + 1, alen); k++)
+        {
+            if (k == 0)
+            {
+                fmpz_one(t);
+            }
+            else
+            {
+                fmpz_mul_si(t, t, -(n - k + 1));
+                fmpz_divexact_ui(t, t, k);
+            }
+
+            acb_addmul_fmpz(b + n, a + k, t, prec);
+        }
+    }
+
+    fmpz_clear(t);
+}
+
+void
+acb_poly_binomial_transform_basecase(acb_poly_t b, const acb_poly_t a, slong len, slong prec)
+{
+    if (len == 0 || a->length == 0)
+    {
+        acb_poly_zero(b);
+        return;
+    }
+
+    if (b == a)
+    {
+        acb_poly_t c;
+        acb_poly_init2(c, len);
+        _acb_poly_binomial_transform_basecase(c->coeffs, a->coeffs, a->length, len, prec);
+        acb_poly_swap(b, c);
+        acb_poly_clear(c);
+    }
+    else
+    {
+        acb_poly_fit_length(b, len);
+        _acb_poly_binomial_transform_basecase(b->coeffs, a->coeffs, a->length, len, prec);
+    }
+
+    _acb_poly_set_length(b, len);
+    _acb_poly_normalise(b);
+}
+

acb_poly/binomial_transform_convolution.c

@@ -0,0 +1,68 @@
+/*
+    Copyright (C) 2013 Fredrik Johansson
+
+    This file is part of Arb.
+
+    Arb 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 2.1 of the License, or
+    (at your option) any later version.  See <http://www.gnu.org/licenses/>.
+*/
+
+#include <math.h>
+#include "acb_poly.h"
+
+void
+_acb_poly_binomial_transform_convolution(acb_ptr b, acb_srcptr a, slong alen, slong len, slong prec)
+{
+    slong i;
+    acb_ptr c, d;
+
+    alen = FLINT_MIN(alen, len);
+
+    c = _acb_vec_init(alen);
+    d = _acb_vec_init(len);
+
+    _acb_poly_borel_transform(c, a, alen, prec);
+    for (i = 1; i < alen; i += 2)
+        acb_neg(c + i, c + i);
+
+    acb_one(d);
+    for (i = 1; i < len; i++)
+        acb_div_ui(d + i, d + i - 1, i, prec);
+
+    _acb_poly_mullow(b, d, len, c, alen, len, prec);
+
+    _acb_poly_inv_borel_transform(b, b, len, prec);
+
+    _acb_vec_clear(c, alen);
+    _acb_vec_clear(d, len);
+}
+
+void
+acb_poly_binomial_transform_convolution(acb_poly_t b, const acb_poly_t a, slong len, slong prec)
+{
+    if (len == 0 || a->length == 0)
+    {
+        acb_poly_zero(b);
+        return;
+    }
+
+    if (b == a)
+    {
+        acb_poly_t c;
+        acb_poly_init2(c, len);
+        _acb_poly_binomial_transform_convolution(c->coeffs, a->coeffs, a->length, len, prec);
+        acb_poly_swap(b, c);
+        acb_poly_clear(c);
+    }
+    else
+    {
+        acb_poly_fit_length(b, len);
+        _acb_poly_binomial_transform_convolution(b->coeffs, a->coeffs, a->length, len, prec);
+    }
+
+    _acb_poly_set_length(b, len);
+    _acb_poly_normalise(b);
+}
+

acb_poly/borel_transform.c

@@ -0,0 +1,43 @@
+/*
+    Copyright (C) 2013 Fredrik Johansson
+
+    This file is part of Arb.
+
+    Arb 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 2.1 of the License, or
+    (at your option) any later version.  See <http://www.gnu.org/licenses/>.
+*/
+
+#include "acb_poly.h"
+
+void
+_acb_poly_borel_transform(acb_ptr res, acb_srcptr poly, slong len, slong prec)
+{
+    slong i;
+
+    arb_t t;
+    arb_init(t);
+
+    arb_one(t);
+
+    for (i = 0; i < len; i++)
+    {
+        if (i > 1)
+            arb_mul_ui(t, t, i, prec);
+
+        acb_div_arb(res + i, poly + i, t, prec);
+    }
+
+    arb_clear(t);
+}
+
+void
+acb_poly_borel_transform(acb_poly_t res, const acb_poly_t poly, slong prec)
+{
+    acb_poly_fit_length(res, poly->length);
+    _acb_poly_borel_transform(res->coeffs, poly->coeffs, poly->length, prec);
+    _acb_poly_set_length(res, poly->length);
+    _acb_poly_normalise(res);
+}
+

acb_poly/inv_borel_transform.c

@@ -0,0 +1,43 @@
+/*
+    Copyright (C) 2013 Fredrik Johansson
+
+    This file is part of Arb.
+
+    Arb 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 2.1 of the License, or
+    (at your option) any later version.  See <http://www.gnu.org/licenses/>.
+*/
+
+#include "acb_poly.h"
+
+void
+_acb_poly_inv_borel_transform(acb_ptr res, acb_srcptr poly, slong len, slong prec)
+{
+    slong i;
+
+    arb_t t;
+    arb_init(t);
+
+    arb_one(t);
+
+    for (i = 0; i < len; i++)
+    {
+        if (i > 1)
+            arb_mul_ui(t, t, i, prec);
+
+        acb_mul_arb(res + i, poly + i, t, prec);
+    }
+
+    arb_clear(t);
+}
+
+void
+acb_poly_inv_borel_transform(acb_poly_t res, const acb_poly_t poly, slong prec)
+{
+    acb_poly_fit_length(res, poly->length);
+    _acb_poly_inv_borel_transform(res->coeffs, poly->coeffs, poly->length, prec);
+    _acb_poly_set_length(res, poly->length);
+    _acb_poly_normalise(res);
+}
+

acb_poly/test/t-binomial_transform.c

@@ -0,0 +1,105 @@
+/*
+    Copyright (C) 2013 Fredrik Johansson
+
+    This file is part of Arb.
+
+    Arb 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 2.1 of the License, or
+    (at your option) any later version.  See <http://www.gnu.org/licenses/>.
+*/
+
+#include "acb_poly.h"
+
+int main()
+{
+    slong iter;
+    flint_rand_t state;
+
+    flint_printf("binomial_transform....");
+    fflush(stdout);
+
+    flint_randinit(state);
+
+    for (iter = 0; iter < 500 * arb_test_multiplier(); iter++)
+    {
+        acb_poly_t a, b, c, d;
+        slong j, n, prec;
+
+        acb_poly_init(a);
+        acb_poly_init(b);
+        acb_poly_init(c);
+        acb_poly_init(d);
+
+        n = n_randint(state, 20);
+        prec = 2 + n_randint(state, 200);
+
+        acb_poly_randtest(a, state, n, prec, 10);
+        acb_poly_randtest(b, state, n, prec, 10);
+        acb_poly_randtest(c, state, n, prec, 10);
+
+        /* check self-inversion property */
+        acb_poly_binomial_transform(b, a, n, prec);
+        acb_poly_binomial_transform(c, b, n, prec);
+
+        acb_poly_set(d, a);
+        acb_poly_truncate(d, n);
+
+        if (!acb_poly_contains(c, d))
+        {
+            flint_printf("FAIL (containment)\n\n");
+            flint_printf("n = %wd, prec = %wd\n\n", n, prec);
+
+            flint_printf("a: "); acb_poly_printd(a, 15); flint_printf("\n\n");
+            flint_printf("b: "); acb_poly_printd(b, 15); flint_printf("\n\n");
+            flint_printf("c: "); acb_poly_printd(c, 15); flint_printf("\n\n");
+            flint_printf("d: "); acb_poly_printd(d, 15); flint_printf("\n\n");
+
+            abort();
+        }
+
+        acb_poly_set(d, a);
+        acb_poly_binomial_transform(d, d, n, prec);
+        if (!acb_poly_equal(d, b))
+        {
+            flint_printf("FAIL (aliasing)\n\n");
+
+            flint_printf("a: "); acb_poly_printd(a, 15); flint_printf("\n\n");
+            flint_printf("b: "); acb_poly_printd(b, 15); flint_printf("\n\n");
+            flint_printf("d: "); acb_poly_printd(d, 15); flint_printf("\n\n");
+
+            abort();
+        }
+
+        /* compare with power series operations */
+        acb_poly_zero(d);
+        for (j = 1; j < n; j++)
+            acb_poly_set_coeff_si(d, j, -1);
+        acb_poly_compose_series(c, a, d, n, prec);
+        for (j = 0; j < n; j++)
+            acb_poly_set_coeff_si(d, j, 1);
+        acb_poly_mullow(c, c, d, n, prec);
+
+        if (!acb_poly_overlaps(b, c))
+        {
+            flint_printf("FAIL (power series)\n\n");
+
+            flint_printf("a: "); acb_poly_printd(a, 15); flint_printf("\n\n");
+            flint_printf("b: "); acb_poly_printd(b, 15); flint_printf("\n\n");
+            flint_printf("c: "); acb_poly_printd(c, 15); flint_printf("\n\n");
+
+            abort();
+        }
+
+        acb_poly_clear(a);
+        acb_poly_clear(b);
+        acb_poly_clear(c);
+        acb_poly_clear(d);
+    }
+
+    flint_randclear(state);
+    flint_cleanup();
+    flint_printf("PASS\n");
+    return EXIT_SUCCESS;
+}
+

acb_poly/test/t-binomial_transform_basecase.c

@@ -0,0 +1,105 @@
+/*
+    Copyright (C) 2013 Fredrik Johansson
+
+    This file is part of Arb.
+
+    Arb 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 2.1 of the License, or
+    (at your option) any later version.  See <http://www.gnu.org/licenses/>.
+*/
+
+#include "acb_poly.h"
+
+int main()
+{
+    slong iter;
+    flint_rand_t state;
+
+    flint_printf("binomial_transform_basecase....");
+    fflush(stdout);
+
+    flint_randinit(state);
+
+    for (iter = 0; iter < 500 * arb_test_multiplier(); iter++)
+    {
+        acb_poly_t a, b, c, d;
+        slong j, n, prec;
+
+        acb_poly_init(a);
+        acb_poly_init(b);
+        acb_poly_init(c);
+        acb_poly_init(d);
+
+        n = n_randint(state, 20);
+        prec = 2 + n_randint(state, 200);
+
+        acb_poly_randtest(a, state, n, prec, 10);
+        acb_poly_randtest(b, state, n, prec, 10);
+        acb_poly_randtest(c, state, n, prec, 10);
+
+        /* check self-inversion property */
+        acb_poly_binomial_transform_basecase(b, a, n, prec);
+        acb_poly_binomial_transform_basecase(c, b, n, prec);
+
+        acb_poly_set(d, a);
+        acb_poly_truncate(d, n);
+
+        if (!acb_poly_contains(c, d))
+        {
+            flint_printf("FAIL (containment)\n\n");
+            flint_printf("n = %wd, prec = %wd\n\n", n, prec);
+
+            flint_printf("a: "); acb_poly_printd(a, 15); flint_printf("\n\n");
+            flint_printf("b: "); acb_poly_printd(b, 15); flint_printf("\n\n");
+            flint_printf("c: "); acb_poly_printd(c, 15); flint_printf("\n\n");
+            flint_printf("d: "); acb_poly_printd(d, 15); flint_printf("\n\n");
+
+            abort();
+        }
+
+        acb_poly_set(d, a);
+        acb_poly_binomial_transform_basecase(d, d, n, prec);
+        if (!acb_poly_equal(d, b))
+        {
+            flint_printf("FAIL (aliasing)\n\n");
+
+            flint_printf("a: "); acb_poly_printd(a, 15); flint_printf("\n\n");
+            flint_printf("b: "); acb_poly_printd(b, 15); flint_printf("\n\n");
+            flint_printf("d: "); acb_poly_printd(d, 15); flint_printf("\n\n");
+
+            abort();
+        }
+
+        /* compare with power series operations */
+        acb_poly_zero(d);
+        for (j = 1; j < n; j++)
+            acb_poly_set_coeff_si(d, j, -1);
+        acb_poly_compose_series(c, a, d, n, prec);
+        for (j = 0; j < n; j++)
+            acb_poly_set_coeff_si(d, j, 1);
+        acb_poly_mullow(c, c, d, n, prec);
+
+        if (!acb_poly_overlaps(b, c))
+        {
+            flint_printf("FAIL (power series)\n\n");
+
+            flint_printf("a: "); acb_poly_printd(a, 15); flint_printf("\n\n");
+            flint_printf("b: "); acb_poly_printd(b, 15); flint_printf("\n\n");
+            flint_printf("c: "); acb_poly_printd(c, 15); flint_printf("\n\n");
+
+            abort();
+        }
+
+        acb_poly_clear(a);
+        acb_poly_clear(b);
+        acb_poly_clear(c);
+        acb_poly_clear(d);
+    }
+
+    flint_randclear(state);
+    flint_cleanup();
+    flint_printf("PASS\n");
+    return EXIT_SUCCESS;
+}
+

acb_poly/test/t-binomial_transform_convolution.c

@@ -0,0 +1,105 @@
+/*
+    Copyright (C) 2013 Fredrik Johansson
+
+    This file is part of Arb.
+
+    Arb 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 2.1 of the License, or
+    (at your option) any later version.  See <http://www.gnu.org/licenses/>.
+*/
+
+#include "acb_poly.h"
+
+int main()
+{
+    slong iter;
+    flint_rand_t state;
+
+    flint_printf("binomial_transform_convolution....");
+    fflush(stdout);
+
+    flint_randinit(state);
+
+    for (iter = 0; iter < 500 * arb_test_multiplier(); iter++)
+    {
+        acb_poly_t a, b, c, d;
+        slong j, n, prec;
+
+        acb_poly_init(a);
+        acb_poly_init(b);
+        acb_poly_init(c);
+        acb_poly_init(d);
+
+        n = n_randint(state, 20);
+        prec = 2 + n_randint(state, 200);
+
+        acb_poly_randtest(a, state, n, prec, 10);
+        acb_poly_randtest(b, state, n, prec, 10);
+        acb_poly_randtest(c, state, n, prec, 10);
+
+        /* check self-inversion property */
+        acb_poly_binomial_transform_convolution(b, a, n, prec);
+        acb_poly_binomial_transform_convolution(c, b, n, prec);
+
+        acb_poly_set(d, a);
+        acb_poly_truncate(d, n);
+
+        if (!acb_poly_contains(c, d))
+        {
+            flint_printf("FAIL (containment)\n\n");
+            flint_printf("n = %wd, prec = %wd\n\n", n, prec);
+
+            flint_printf("a: "); acb_poly_printd(a, 15); flint_printf("\n\n");
+            flint_printf("b: "); acb_poly_printd(b, 15); flint_printf("\n\n");
+            flint_printf("c: "); acb_poly_printd(c, 15); flint_printf("\n\n");
+            flint_printf("d: "); acb_poly_printd(d, 15); flint_printf("\n\n");
+
+            abort();
+        }
+
+        acb_poly_set(d, a);
+        acb_poly_binomial_transform_convolution(d, d, n, prec);
+        if (!acb_poly_equal(d, b))
+        {
+            flint_printf("FAIL (aliasing)\n\n");
+
+            flint_printf("a: "); acb_poly_printd(a, 15); flint_printf("\n\n");
+            flint_printf("b: "); acb_poly_printd(b, 15); flint_printf("\n\n");
+            flint_printf("d: "); acb_poly_printd(d, 15); flint_printf("\n\n");
+
+            abort();
+        }
+
+        /* compare with power series operations */
+        acb_poly_zero(d);
+        for (j = 1; j < n; j++)
+            acb_poly_set_coeff_si(d, j, -1);
+        acb_poly_compose_series(c, a, d, n, prec);
+        for (j = 0; j < n; j++)
+            acb_poly_set_coeff_si(d, j, 1);
+        acb_poly_mullow(c, c, d, n, prec);
+
+        if (!acb_poly_overlaps(b, c))
+        {
+            flint_printf("FAIL (power series)\n\n");
+
+            flint_printf("a: "); acb_poly_printd(a, 15); flint_printf("\n\n");
+            flint_printf("b: "); acb_poly_printd(b, 15); flint_printf("\n\n");
+            flint_printf("c: "); acb_poly_printd(c, 15); flint_printf("\n\n");
+
+            abort();
+        }
+
+        acb_poly_clear(a);
+        acb_poly_clear(b);
+        acb_poly_clear(c);
+        acb_poly_clear(d);
+    }
+
+    flint_randclear(state);
+    flint_cleanup();
+    flint_printf("PASS\n");
+    return EXIT_SUCCESS;
+}
+

acb_poly/test/t-borel_transform.c

@@ -0,0 +1,77 @@
+/*
+    Copyright (C) 2013 Fredrik Johansson
+
+    This file is part of Arb.
+
+    Arb 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 2.1 of the License, or
+    (at your option) any later version.  See <http://www.gnu.org/licenses/>.
+*/
+
+#include "acb_poly.h"
+
+int main()
+{
+    slong iter;
+    flint_rand_t state;
+
+    flint_printf("borel_transform....");
+    fflush(stdout);
+
+    flint_randinit(state);
+
+    for (iter = 0; iter < 500 * arb_test_multiplier(); iter++)
+    {
+        acb_poly_t a, b, c, d;
+        slong n, prec;
+
+        acb_poly_init(a);
+        acb_poly_init(b);
+        acb_poly_init(c);
+        acb_poly_init(d);
+
+        n = n_randint(state, 30);
+        prec = n_randint(state, 200);
+
+        acb_poly_randtest(a, state, n, prec, 10);
+        acb_poly_randtest(b, state, n, prec, 10);
+        acb_poly_randtest(c, state, n, prec, 10);
+
+        acb_poly_borel_transform(b, a, prec);
+        acb_poly_inv_borel_transform(c, b, prec);
+
+        if (!acb_poly_contains(c, a))
+        {
+            flint_printf("FAIL (containment)\n\n");
+            abort();
+        }
+
+        acb_poly_set(d, a);
+        acb_poly_borel_transform(d, d, prec);
+        if (!acb_poly_equal(d, b))
+        {
+            flint_printf("FAIL (aliasing 1)\n\n");
+            abort();
+        }
+
+        acb_poly_set(d, b);
+        acb_poly_inv_borel_transform(d, d, prec);
+        if (!acb_poly_equal(d, c))
+        {
+            flint_printf("FAIL (aliasing 2)\n\n");
+            abort();
+        }
+
+        acb_poly_clear(a);
+        acb_poly_clear(b);
+        acb_poly_clear(c);
+        acb_poly_clear(d);
+    }
+
+    flint_randclear(state);
+    flint_cleanup();
+    flint_printf("PASS\n");
+    return EXIT_SUCCESS;
+}
+

doc/source/acb_poly.rst

@@ -614,6 +614,43 @@ Differentiation
     Sets *res* to the integral of *poly*.
 
 
+Transforms
+-------------------------------------------------------------------------------
+
+.. function:: void _acb_poly_borel_transform(acb_ptr res, acb_srcptr poly, slong len, slong prec)
+
+.. function:: void acb_poly_borel_transform(acb_poly_t res, const acb_poly_t poly, slong prec)
+
+    Computes the Borel transform of the input polynomial, mapping `\sum_k a_k x^k`
+    to `\sum_k (a_k / k!) x^k`. The underscore method allows aliasing.
+
+.. function:: void _acb_poly_inv_borel_transform(acb_ptr res, acb_srcptr poly, slong len, slong prec)
+
+.. function:: void acb_poly_inv_borel_transform(acb_poly_t res, const acb_poly_t poly, slong prec)
+
+    Computes the inverse Borel transform of the input polynomial, mapping `\sum_k a_k x^k`
+    to `\sum_k a_k k! x^k`. The underscore method allows aliasing.
+
+.. function:: void _acb_poly_binomial_transform_basecase(acb_ptr b, acb_srcptr a, slong alen, slong len, slong prec)
+
+.. function:: void acb_poly_binomial_transform_basecase(acb_poly_t b, const acb_poly_t a, slong len, slong prec)
+
+.. function:: void _acb_poly_binomial_transform_convolution(acb_ptr b, acb_srcptr a, slong alen, slong len, slong prec)
+
+.. function:: void acb_poly_binomial_transform_convolution(acb_poly_t b, const acb_poly_t a, slong len, slong prec)
+
+.. function:: void _acb_poly_binomial_transform(acb_ptr b, acb_srcptr a, slong alen, slong len, slong prec)
+
+.. function:: void acb_poly_binomial_transform(acb_poly_t b, const acb_poly_t a, slong len, slong prec)
+
+    Computes the binomial transform of the input polynomial, truncating
+    the output to length *len*. See :func:`arb_poly_binomial_transform` for
+    details.
+
+    The underscore methods do not support aliasing, and assume that
+    the lengths are nonzero.
+
+
 Elementary functions
 -------------------------------------------------------------------------------