Use IrreduciblePolyDatabase with terms="min"

Similar to the changes in primitive_poly(), try to fetch nonzero degrees
and coefficients from the database when irreducible_poly() is called
with terms="min". If poly is not in the database, fallback to compute
it.

src/galois/_polys/_irreducible.py

@@ -8,6 +8,7 @@
 
 from typing_extensions import Literal
 
+from .._databases import IrreduciblePolyDatabase
 from .._domains import _factory
 from .._helper import export, method_of, verify_isinstance
 from .._prime import factors, is_prime_power
@@ -128,6 +129,7 @@ def irreducible_poly(
  degree: int,
  terms: int | str | None = None,
  method: Literal["min", "max", "random"] = "min",
+ use_database: bool = True,
 ) -> Poly:
  r"""
  Returns a monic irreducible polynomial :math:`f(x)` over :math:`\mathrm{GF}(q)` with degree :math:`m`.
@@ -215,6 +217,16 @@ def irreducible_poly(
  if not method in ["min", "max", "random"]:
  raise ValueError(f"Argument 'method' must be in ['min', 'max', 'random'], not {method!r}.")
 
+ if terms == "min" and method == "min" and use_database:
+ try:
+ db = IrreduciblePolyDatabase()
+ degrees, coeffs = db.fetch(order, degree)
+ field = _factory.FIELD_FACTORY(order)
+ poly = Poly.Degrees(degrees, coeffs, field=field)
+ return poly
+ except LookupError:
+ pass
+
  try:
  if method == "min":
  return next(irreducible_polys(order, degree, terms))