add poly is_zero, is_one, is_x methods

acb_poly.h

@@ -69,6 +69,25 @@ ACB_POLY_INLINE slong acb_poly_degree(const acb_poly_t poly)
     return poly->length - 1;
 }
 
+ACB_POLY_INLINE int
+acb_poly_is_zero(const acb_poly_t z)
+{
+    return acb_poly_length(z) == 0;
+}
+
+ACB_POLY_INLINE int
+acb_poly_is_one(const acb_poly_t z)
+{
+    return (acb_poly_length(z) == 1) && acb_is_one(z->coeffs);
+}
+
+ACB_POLY_INLINE int
+acb_poly_is_x(const acb_poly_t z)
+{
+    return (acb_poly_length(z) == 2) && acb_is_zero(z->coeffs)
+        && acb_is_one(z->coeffs + 1);
+}
+
 ACB_POLY_INLINE void acb_poly_zero(acb_poly_t poly)
 {
     poly->length = 0;

arb_poly.h

@@ -77,6 +77,25 @@ ARB_POLY_INLINE slong arb_poly_degree(const arb_poly_t poly)
     return poly->length - 1;
 }
 
+ARB_POLY_INLINE int
+arb_poly_is_zero(const arb_poly_t z)
+{
+    return arb_poly_length(z) == 0;
+}
+
+ARB_POLY_INLINE int
+arb_poly_is_one(const arb_poly_t z)
+{
+    return (arb_poly_length(z) == 1) && arb_is_one(z->coeffs);
+}
+
+ARB_POLY_INLINE int
+arb_poly_is_x(const arb_poly_t z)
+{
+    return (arb_poly_length(z) == 2) && arb_is_zero(z->coeffs)
+        && arb_is_one(z->coeffs + 1);
+}
+
 ARB_POLY_INLINE void arb_poly_zero(arb_poly_t poly)
 {
     poly->length = 0;

doc/source/acb_poly.rst

@@ -76,6 +76,15 @@ Basic properties and manipulation
     so the return value of this function is effectively
     an upper bound.
 
+.. function:: int acb_poly_is_zero(const acb_poly_t poly)
+
+.. function:: int acb_poly_is_one(const acb_poly_t poly)
+
+.. function:: int acb_poly_is_x(const acb_poly_t poly)
+
+    Returns 1 if *poly* is exactly the polynomial 0, 1 or *x*
+    respectively. Returns 0 otherwise.
+
 .. function:: void acb_poly_zero(acb_poly_t poly)
 
     Sets *poly* to the zero polynomial.

doc/source/arb_poly.rst

@@ -57,6 +57,30 @@ Memory management
 Basic manipulation
 -------------------------------------------------------------------------------
 
+.. function:: slong arb_poly_length(const arb_poly_t poly)
+
+    Returns the length of *poly*, i.e. zero if *poly* is
+    identically zero, and otherwise one more than the index
+    of the highest term that is not identically zero.
+
+.. function:: slong arb_poly_degree(const arb_poly_t poly)
+
+    Returns the degree of *poly*, defined as one less than its length.
+    Note that if one or several leading coefficients are balls
+    containing zero, this value can be larger than the true
+    degree of the exact polynomial represented by *poly*,
+    so the return value of this function is effectively
+    an upper bound.
+
+.. function:: int arb_poly_is_zero(const arb_poly_t poly)
+
+.. function:: int arb_poly_is_one(const arb_poly_t poly)
+
+.. function:: int arb_poly_is_x(const arb_poly_t poly)
+
+    Returns 1 if *poly* is exactly the polynomial 0, 1 or *x*
+    respectively. Returns 0 otherwise.
+
 .. function:: void arb_poly_zero(arb_poly_t poly)
 
 .. function:: void arb_poly_one(arb_poly_t poly)
@@ -107,21 +131,6 @@ Basic manipulation
     Truncates *poly* to have length at most *n*, i.e. degree
     strictly smaller than *n*.
 
-.. function:: slong arb_poly_length(const arb_poly_t poly)
-
-    Returns the length of *poly*, i.e. zero if *poly* is
-    identically zero, and otherwise one more than the index
-    of the highest term that is not identically zero.
-
-.. function:: slong arb_poly_degree(const arb_poly_t poly)
-
-    Returns the degree of *poly*, defined as one less than its length.
-    Note that if one or several leading coefficients are balls
-    containing zero, this value can be larger than the true
-    degree of the exact polynomial represented by *poly*,
-    so the return value of this function is effectively
-    an upper bound.
-
 Conversions
 -------------------------------------------------------------------------------