V = [v1, v2]
print "Computing stable reduction Yb:"
for v in V:
print "over ", v
reduction_component(v, vL, f)
for i in range(len(filt)):
m = filt[i][0]+1
vLm = filt[i][2]
print "Computing Y_m for m=%s:"%m
for v in V:
print "over ", v
reduction_component(v, vLm, f)
Computing stable reduction Yb:
over [ Gauss valuation induced by 2-adic valuation, v(x + 1) = 1/4, v(x^4 + 14*x^2 + 72*x - 41) = 3 ]
Reduction component:
Function field in u2 defined by u2^3 + z^4 + z^2
Valuation on rational function field induced by [ Gauss valuation induced by Valuation on rational function field induced by [ Gauss valuation induced by pi-adic valuation, v(z + pi^9 + pi^6 + 1) = 18 ], v(y) = 24, v(y^3 - z^4 - 14*z^2 - 72*z + 41) = +Infinity ]
ground field: Number Field in pi with defining polynomial x^24 + 20*x^21 + 8*x^18 + 72*x^15 + 70*x^12 + 48*x^9 + 76*x^6 + 16*x^3 + 82
------------
over [ Gauss valuation induced by 2-adic valuation, v(x + 1) = 1/4, v(x^4 + 14*x^2 + 72*x - 41) = 7/2 ]
Reduction component:
Function field in u2 defined by u2^3 + z^2 + z
Valuation on rational function field induced by [ Gauss valuation induced by Valuation on rational function field induced by [ Gauss valuation induced by pi-adic valuation, v(z + pi^21 + pi^18 + pi^9 + pi^6 + 1) = 24 ], v(y) = 28, v(y^3 - z^4 - 14*z^2 - 72*z + 41) = +Infinity ]
ground field: Number Field in pi with defining polynomial x^24 + 20*x^21 + 8*x^18 + 72*x^15 + 70*x^12 + 48*x^9 + 76*x^6 + 16*x^3 + 82
------------
Reduction component:
Function field in u2 defined by u2^3 + z^2 + z
Valuation on rational function field induced by [ Gauss valuation induced by Valuation on rational function field induced by [ Gauss valuation induced by pi-adic valuation, v(z + pi^21 + pi^9 + pi^6 + 1) = 24 ], v(y) = 28, v(y^3 - z^4 - 14*z^2 - 72*z + 41) = +Infinity ]
ground field: Number Field in pi with defining polynomial x^24 + 20*x^21 + 8*x^18 + 72*x^15 + 70*x^12 + 48*x^9 + 76*x^6 + 16*x^3 + 82
------------
Computing Y_m for m=16:
over [ Gauss valuation induced by 2-adic valuation, v(x + 1) = 1/4, v(x^4 + 14*x^2 + 72*x - 41) = 3 ]
Reduction component:
Function field in u2 defined by u2^3 + z^2 + z
Valuation on rational function field induced by [ Gauss valuation induced by Valuation on rational function field induced by [ Gauss valuation induced by pi12-adic valuation, v(z + pi12^3 + 1) = 9/2, v(z^2 + (-4*pi12^9 - 6*pi12^6 - 2*pi12^3)*z + 7*pi12^9 + 15*pi12^6 + 12*pi12^3 + 7) = 18 ], v(y) = 12, v(y^3 - z^4 - 14*z^2 - 72*z + 41) = +Infinity ]
ground field: Number Field in pi12 with defining polynomial x^12 + 4*x^9 + 6*x^6 + 4*x^3 + 2
------------
over [ Gauss valuation induced by 2-adic valuation, v(x + 1) = 1/4, v(x^4 + 14*x^2 + 72*x - 41) = 7/2 ]
Reduction component:
Function field in u2 defined by u2^3 + z + 1
Valuation on rational function field induced by [ Gauss valuation induced by Valuation on rational function field induced by [ Gauss valuation induced by pi12-adic valuation, v(z + pi12^3 + 1) = 9/2, v(z^2 + (6*pi12^9 + 14*pi12^6 + 12*pi12^3 + 8)*z - 23*pi12^9 - 57*pi12^6 - 38*pi12^3 - 25) = 24 ], v(y) = 14, v(y^3 - z^4 - 14*z^2 - 72*z + 41) = +Infinity ]
ground field: Number Field in pi12 with defining polynomial x^12 + 4*x^9 + 6*x^6 + 4*x^3 + 2
------------
Reduction component:
Function field in u2 defined by u2^3 + z
Valuation on rational function field induced by [ Gauss valuation induced by Valuation on rational function field induced by [ Gauss valuation induced by pi12-adic valuation, v(z + pi12^3 + 1) = 9/2, v(z^2 + (6*pi12^9 + 14*pi12^6 + 12*pi12^3 + 8)*z + 31*pi12^9 + 77*pi12^6 + 54*pi12^3 + 35) = 24 ], v(y) = 14, v(y^3 - z^4 - 14*z^2 - 72*z + 41) = +Infinity ]
ground field: Number Field in pi12 with defining polynomial x^12 + 4*x^9 + 6*x^6 + 4*x^3 + 2
------------
Computing Y_m for m=10:
over [ Gauss valuation induced by 2-adic valuation, v(x + 1) = 1/4, v(x^4 + 14*x^2 + 72*x - 41) = 3 ]
Reduction component:
Function field in u2 defined by u2^3 + z
Valuation on rational function field induced by [ Gauss valuation induced by Valuation on rational function field induced by [ Gauss valuation induced by pi6-adic valuation, v(z + 1) = 3/2, v(z^2 + (pi6^3 + 2)*z + 2*pi6^3 + 1) = 21/4, v(z^4 + 14*z^2 + 72*z - 41) = 18 ], v(y) = 6, v(y^3 - z^4 - 14*z^2 - 72*z + 41) = +Infinity ]
ground field: Number Field in pi6 with defining polynomial x^6 + 2*x^3 + 2
------------
over [ Gauss valuation induced by 2-adic valuation, v(x + 1) = 1/4, v(x^4 + 14*x^2 + 72*x - 41) = 7/2 ]
Reduction component:
Function field in u2 defined by u2^3 + z
Valuation on rational function field induced by [ Gauss valuation induced by Valuation on rational function field induced by [ Gauss valuation induced by pi6-adic valuation, v(z + 1) = 3/2, v(z^2 + (pi6^3 + 2)*z + 2*pi6^3 + 1) = 21/4, v(z^4 + 14*z^2 + 72*z - 41) = 21 ], v(y) = 7, v(y^3 - z^4 - 14*z^2 - 72*z + 41) = +Infinity ]
ground field: Number Field in pi6 with defining polynomial x^6 + 2*x^3 + 2
------------
Computing Y_m for m=4:
over [ Gauss valuation induced by 2-adic valuation, v(x + 1) = 1/4, v(x^4 + 14*x^2 + 72*x - 41) = 3 ]
Reduction component:
Function field in u2 defined by u2^3 + z
Valuation on rational function field induced by [ Gauss valuation induced by Valuation on rational function field induced by [ Gauss valuation induced by pi3-adic valuation, v(z + 1) = 3/4, v(z^4 + 14*z^2 + 72*z - 41) = 9 ], v(y) = 3, v(y^3 - z^4 - 14*z^2 - 72*z + 41) = +Infinity ]
ground field: Number Field in pi3 with defining polynomial x^3 + 2
------------
over [ Gauss valuation induced by 2-adic valuation, v(x + 1) = 1/4, v(x^4 + 14*x^2 + 72*x - 41) = 7/2 ]
Reduction component:
Function field in u2 defined by u2^3 + z
Valuation on rational function field induced by [ Gauss valuation induced by Valuation on rational function field induced by [ Gauss valuation induced by pi3-adic valuation, v(z + 1) = 3/4, v(z^4 + 14*z^2 + 72*z - 41) = 21/2 ], v(y) = 7/2, v(y^3 - z^4 - 14*z^2 - 72*z + 41) = +Infinity ]
ground field: Number Field in pi3 with defining polynomial x^3 + 2
------------
Computing Y_m for m=1:
over [ Gauss valuation induced by 2-adic valuation, v(x + 1) = 1/4, v(x^4 + 14*x^2 + 72*x - 41) = 3 ]
Reduction component:
Function field in u2 defined by u2^3 + z
Valuation on rational function field induced by [ Gauss valuation induced by Valuation on rational function field induced by [ Gauss valuation induced by 2-adic valuation, v(z + 1) = 1/4, v(z^4 + 14*z^2 + 72*z - 41) = 3 ], v(y) = 1, v(y^3 - z^4 - 14*z^2 - 72*z + 41) = +Infinity ]
ground field: Rational Field
------------
over [ Gauss valuation induced by 2-adic valuation, v(x + 1) = 1/4, v(x^4 + 14*x^2 + 72*x - 41) = 7/2 ]
Reduction component:
Rational function field in z over Finite Field of size 2
Valuation on rational function field induced by [ Gauss valuation induced by Valuation on rational function field induced by [ Gauss valuation induced by 2-adic valuation, v(z + 1) = 1/4, v(z^4 + 14*z^2 + 72*z - 41) = 7/2 ], v(y) = 7/6, v(y^3 - z^4 - 14*z^2 - 72*z + 41) = +Infinity ]
ground field: Rational Field
------------