add polynomial valuation functions

acb_poly.h

@@ -69,6 +69,8 @@ ACB_POLY_INLINE slong acb_poly_degree(const acb_poly_t poly)
     return poly->length - 1;
 }
 
+slong acb_poly_valuation(const acb_poly_t poly);
+
 ACB_POLY_INLINE int
 acb_poly_is_zero(const acb_poly_t z)
 {

acb_poly/valuation.c

@@ -0,0 +1,25 @@
+/*
+    Copyright (C) 2016 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"
+
+slong
+acb_poly_valuation(const acb_poly_t poly)
+{
+    slong i, len = poly->length;
+
+    for (i = 0; i < len; i++)
+        if (!acb_is_zero(poly->coeffs + i))
+            return i;
+
+    return -1;
+}
+

arb_poly.h

@@ -81,6 +81,8 @@ ARB_POLY_INLINE slong arb_poly_degree(const arb_poly_t poly)
     return poly->length - 1;
 }
 
+slong arb_poly_valuation(const arb_poly_t poly);
+
 ARB_POLY_INLINE int
 arb_poly_is_zero(const arb_poly_t z)
 {

arb_poly/valuation.c

@@ -0,0 +1,25 @@
+/*
+    Copyright (C) 2016 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 "arb_poly.h"
+
+slong
+arb_poly_valuation(const arb_poly_t poly)
+{
+    slong i, len = poly->length;
+
+    for (i = 0; i < len; i++)
+        if (!arb_is_zero(poly->coeffs + i))
+            return i;
+
+    return -1;
+}
+

doc/source/acb_poly.rst

@@ -143,6 +143,11 @@ Basic properties and manipulation
     Truncates *poly* to have length at most *n*, i.e. degree
     strictly smaller than *n*.
 
+.. function:: slong acb_poly_valuation(const acb_poly_t poly)
+
+    Returns the degree of the lowest term that is not exactly zero in *poly*.
+    Returns -1 if *poly* is the zero polynomial.
+
 Input and output
 -------------------------------------------------------------------------------
 

doc/source/arb_poly.rst

@@ -137,6 +137,11 @@ Basic manipulation
     Truncates *poly* to have length at most *n*, i.e. degree
     strictly smaller than *n*.
 
+.. function:: slong arb_poly_valuation(const arb_poly_t poly)
+
+    Returns the degree of the lowest term that is not exactly zero in *poly*.
+    Returns -1 if *poly* is the zero polynomial.
+
 Conversions
 -------------------------------------------------------------------------------