move from sage.arith.misc to sage.combinat.q_analogues

Author: yyyyx4

src/sage/arith/all.py

@@ -81,7 +81,6 @@
     prime_factors,
     prime_range,
     valuation,
-    number_of_irreducible_polynomials,
 )
 
 lazy_import("sage.arith.misc", ("Sigma", "Moebius", "Euler_Phi"), deprecation=30322)

src/sage/arith/misc.py

@@ -6383,40 +6383,3 @@ def dedekind_psi(N):
     """
     N = Integer(N)
     return Integer(N * prod(1 + 1 / p for p in N.prime_divisors()))
-
-
-def number_of_irreducible_polynomials(q, n):
-    r"""
-    Return the number of irreducible polynomials of degree ``n``
-    over the finite field with ``q`` elements.
-
-    INPUT:
-
-    - ``q`` -- prime power
-    - ``n`` -- positive integer
-
-    OUTPUT: integer
-
-    EXAMPLES::
-
-        sage: number_of_irreducible_polynomials(2, 8)
-        30
-        sage: number_of_irreducible_polynomials(9, 9)
-        43046640
-
-    This function is *much* faster than enumerating the polynomials::
-
-        sage: num = number_of_irreducible_polynomials(101, 99)
-        sage: num.bit_length()
-        653
-
-    ALGORITHM:
-
-    Classical formula `\frac1n \sum_{d\mid n} \mu(n/d) q^d` using the
-    Möbius function `\mu`; see :func:`moebius`.
-    """
-    q, n = ZZ(q), ZZ(n)
-    r = ZZ.zero()
-    for d in n.divisors():
-        r += moebius(n//d) * q**d
-    return r // n

src/sage/combinat/all.py

@@ -247,7 +247,7 @@
 from .integer_vector_weighted import WeightedIntegerVectors
 from .integer_vectors_mod_permgroup import IntegerVectorsModPermutationGroup
 
-lazy_import('sage.combinat.q_analogues', ['gaussian_binomial', 'q_binomial'])
+lazy_import('sage.combinat.q_analogues', ['gaussian_binomial', 'q_binomial', 'number_of_irreducible_polynomials'])
 
 from .species.all import *
 

src/sage/combinat/q_analogues.py

@@ -974,3 +974,41 @@ def q_stirling_number2(n, k, q=None):
         return parent(q)(0)
     return (q**(k-1)*q_stirling_number2(n - 1, k - 1, q=q) +
             q_int(k, q=q) * q_stirling_number2(n - 1, k, q=q))
+
+
+def number_of_irreducible_polynomials(q, n):
+    r"""
+    Return the number of irreducible polynomials of degree ``n``
+    over the finite field with ``q`` elements.
+
+    INPUT:
+
+    - ``q`` -- prime power
+    - ``n`` -- positive integer
+
+    OUTPUT: integer
+
+    EXAMPLES::
+
+        sage: number_of_irreducible_polynomials(2, 8)
+        30
+        sage: number_of_irreducible_polynomials(9, 9)
+        43046640
+
+    This function is *much* faster than enumerating the polynomials::
+
+        sage: num = number_of_irreducible_polynomials(101, 99)
+        sage: num.bit_length()
+        653
+
+    ALGORITHM:
+
+    Classical formula `\frac1n \sum_{d\mid n} \mu(n/d) q^d` using the
+    Möbius function `\mu`; see :func:`moebius`.
+    """
+    from sage.arith.misc import moebius
+    q, n = ZZ(q), ZZ(n)
+    r = ZZ.zero()
+    for d in n.divisors():
+        r += moebius(n//d) * q**d
+    return r // n