def time_12_384(self):
r"""
TESTS::
sage: import henselization
sage: from henselization.benchmarks.splitting_fields import SplittingField
sage: SplittingField().time_12_384() # long time
Factoring T^12 - 4*T^11 + 2*T^10 + 13*T^8 - 16*T^7 - 36*T^6 + 168*T^5 - 209*T^4 + 52*T^3 + 26*T^2 + 8*T - 13 over a field of degree 1 * 1…
…factors with degrees [12]
Found totally ramified part of degree 12
Factoring T^12 - 4*T^11 + 2*T^10 + 13*T^8 - 16*T^7 - 36*T^6 + 168*T^5 - 209*T^4 + 52*T^3 + 26*T^2 + 8*T - 13 over a field of degree 1 * 12…
…factors with degrees [8, 2, 1, 1]
Found unramified part of degree 2
Factoring T^12 - 4*T^11 + 2*T^10 + 13*T^8 - 16*T^7 - 36*T^6 + 168*T^5 - 209*T^4 + 52*T^3 + 26*T^2 + 8*T - 13 over a field of degree 2 * 1…
…factors with degrees [12]
Found totally ramified part of degree 12
Factoring T^12 - 4*T^11 + 2*T^10 + 13*T^8 - 16*T^7 - 36*T^6 + 168*T^5 - 209*T^4 + 52*T^3 + 26*T^2 + 8*T - 13 over a field of degree 2 * 12…
…factors with degrees [4, 4, 1, 1, 1, 1]
Found totally ramified part of degree 4
Factoring T^12 - 4*T^11 + 2*T^10 + 13*T^8 - 16*T^7 - 36*T^6 + 168*T^5 - 209*T^4 + 52*T^3 + 26*T^2 + 8*T - 13 over a field of degree 2 * 48…
…factors with degrees [4, 1, 1, 1, 1, 1, 1, 1, 1]
Found totally ramified part of degree 4
Factoring T^12 - 4*T^11 + 2*T^10 + 13*T^8 - 16*T^7 - 36*T^6 + 168*T^5 - 209*T^4 + 52*T^3 + 26*T^2 + 8*T - 13 over a field of degree 2 * 192…
…factors with degrees [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]
"""
K = QQ.henselization(2)
R = PolynomialRing(K, 'T')
T = R.gen()
f = T**12 - 4 * T**11 + 2 * T**10 + 13 * T**8 - 16 * T**7 - 36 * T**6 + 168 * T**5 - 209 * T**4 + 52 * T**3 + 26 * T**2 + 8 * T - 13
splitting_field(f)
def time_6_8(self):
r"""
TESTS::
sage: import henselization
sage: from henselization.benchmarks.splitting_fields import SplittingField
sage: SplittingField().time_6_8()
Factoring T^6 + 168*T^5 - 209*T^4 + 52*T^3 + 26*T^2 + 8*T - 14 over a field of degree 1 * 1…
…factors with degrees [4, 1, 1]
Found totally ramified part of degree 4
Factoring T^6 + 168*T^5 - 209*T^4 + 52*T^3 + 26*T^2 + 8*T - 14 over a field of degree 1 * 4…
…factors with degrees [2, 1, 1, 1, 1]
Found totally ramified part of degree 2
Factoring T^6 + 168*T^5 - 209*T^4 + 52*T^3 + 26*T^2 + 8*T - 14 over a field of degree 1 * 8…
…factors with degrees [1, 1, 1, 1, 1, 1]
"""
K = QQ.henselization(2)
R = PolynomialRing(K, 'T')
T = R.gen()
f = T**6 + 168 * T**5 - 209 * T**4 + 52 * T**3 + 26 * T**2 + 8 * T - 14
splitting_field(f)
