Memoize slow polynomial search functions

Fixes #295

galois/_fields/_factory.py

@@ -3,6 +3,7 @@
 irreducible, primitive, and Conway polynomials. They are included here due to a circular dependence with the
 Galois field class factory.
 """
+import functools
 import random
 import types
 from typing import Sequence, List, Optional, Union, Type
@@ -550,15 +551,27 @@ def irreducible_poly(
  if is_irreducible(poly):
  break
  else:
- elements = range(min_, max_) if method == "min" else range(max_ - 1, min_ - 1, -1)
- for element in elements:
- poly = Poly.Integer(element, field=field)
- if is_irreducible(poly):
- break
+ # The search produces a deterministic result, so we can memoize the output
+ poly = _irreducible_poly_search(min_, max_, method, field)
 
  return poly
 
 
+@functools.lru_cache(maxsize=128)
+def _irreducible_poly_search(min_, max_, method, field):
+ """
+ Searches for an irreducible polynomial in the range using the specified deterministic method.
+ """
+ elements = range(min_, max_) if method == "min" else range(max_ - 1, min_ - 1, -1)
+
+ for element in elements:
+ poly = Poly.Integer(element, field=field)
+ if is_irreducible(poly):
+ return poly
+
+ raise RuntimeError(f"No irreducible polynomials exist in {field.name} between {Poly.Integer(min_, field=field)} and {Poly.Integer(max_ - 1, field=field)}.")
+
+
 @set_module("galois")
 def irreducible_polys(order: int, degree: int) -> List[Poly]:
  r"""
@@ -794,15 +807,27 @@ def primitive_poly(order: int, degree: int, method: Literal["min", "max", "rando
  if is_primitive(poly):
  break
  else:
- elements = range(min_, max_) if method == "min" else range(max_ - 1, min_ - 1, -1)
- for element in elements:
- poly = Poly.Integer(element, field=field)
- if is_primitive(poly):
- break
+ # The search produces a deterministic result, so we can memoize the output
+ poly = _primitive_poly_search(min_, max_, method, field)
 
  return poly
 
 
+@functools.lru_cache(maxsize=128)
+def _primitive_poly_search(min_, max_, method, field):
+ """
+ Searches for an primitive polynomial in the range using the specified deterministic method.
+ """
+ elements = range(min_, max_) if method == "min" else range(max_ - 1, min_ - 1, -1)
+
+ for element in elements:
+ poly = Poly.Integer(element, field=field)
+ if is_primitive(poly):
+ return poly
+
+ raise RuntimeError(f"No primitive polynomials exist in {field.name} between {Poly.Integer(min_, field=field)} and {Poly.Integer(max_ - 1, field=field)}.")
+
+
 @set_module("galois")
 def primitive_polys(order: int, degree: int) -> Poly:
  r"""