def test_eisenstein(self):
criterion = EisensteinCriterion()
result, context = criterion.check(create_polynomial("x^2+2x+2"))
self.assertEqual(IRREDUCIBLE, result)
self.assertEqual({"p": 2}, context)
result, _ = criterion.check(create_polynomial("x^2+2x+1"))
self.assertNotEqual(IRREDUCIBLE, result)
def test_perron(self):
criterion = PerronCriterion()
result, context = criterion.check(create_polynomial("x^2+3x+1"))
self.assertEqual(IRREDUCIBLE, result)
self.assertEqual(None, context)
result, _ = criterion.check(create_polynomial("x^2+2x+1"))
self.assertNotEqual(IRREDUCIBLE, result)
from irreduc_types import IRREDUCIBLE, UNKNOWN
class MurtyCriterion:
def __init__(self, max_p=None):
self.name = "Murty's irreducibility criterion"
self.max_p = max_p
def name(self):
return self.name
def check(self, f):
# http://cms.dm.uba.ar/academico/materias/2docuat2011/teoria_de_numeros/Irreducible.pdf
# Theorem 1
h = 0
for exp, coeff in poly_non_zero_exps(f):
if exp != f.degree():
h = max(h, abs(coeff / f.LC()))
nmin = int(math.ceil(h + 2))
for n in range(nmin, nmin + 5):
val = f.eval(n)
if sympy.isprime(val) and (not self.max_p or val < self.max_p):
return IRREDUCIBLE, {'n': n, 'p': val}
return UNKNOWN, None
if __name__ == '__main__':
poly = create_polynomial(sys.argv[1])
check_common(poly, sys.argv[1], MurtyCriterion())
from criteria.galois_fields import GaloisFieldsCriterion
from criteria.complex_roots import ComplexRootsCriterion, ComplexRootsCriterion2, ComplexRootsCriterion3
from criteria.levit import LevitCriterion
from irreduc_utils import check_common
# TODO: find On the irreducibility of polynomials taking small values by Tverberg H., 1973, should have nice criteria
# TODO: checking if polynomial is attain just enough of (small) primes
if __name__ == '__main__':
import sys
from irreduc_utils import create_polynomial
input = sys.argv[1]
poly = create_polynomial(input)
polys = list()
subs = True
polys.append((poly, 1, 0, False))
if subs:
# generate list of polynomials (including substitutions) to check on
poly_reverted = sympy.Poly(reversed(poly.all_coeffs()), VAR_X)
polys.append((poly_reverted, 1, 0, True))
#for a in (1,):
for a in (-1, 1,): # we need to substitute only units... which in Z are just -1, +1
#for b in range(0,):
for b in range(-5, 5 + 1):
if a == 0 or (a == 1 and b == 0):
continue
