Steenbrink/Singmult3Ejem1.ipynb at 6d409aacdd4e4dbf63b6d8625dab62b937ae5ef1

Enrique Artal a042341e7b deformaciones

2024-04-18 17:09:03 +02:00

24 KiB

Raw Blame History

In [2]:

load('../Descargas/ZetaFunctionsNewtonND.py')
R.<x,y,z> = QQ[]
F = z^3+(y^2+x^3)*z+x^2*y^2
Z = ZetaFunctions(F)
Zmon=Z.monodromy_zeta()
Ztop=Z.topological_zeta(local = True)
g=(y^2+x^3)*x^2*y^2
Zmon, Ztop, g

Out[2]:

((-1) * (t - 1) * (t + 1) * (t^4 - t^3 + t^2 - t + 1) * (t^4 + t^3 + t^2 + t + 1) * (t^6 + t^3 + 1),
 (-11/90) * (s + 8/9)^-1 * (s + 9/10)^-1 * (s + 1)^-1 * (s^2 - 69/11*s - 72/11),
 x^5*y^2 + x^2*y^4)

Primera explosión ---> divisor E_1 (6,2)

In [3]:

g1=g(x=x*y)/y^6
F1=F(x=x*y)
g1b=g(y=x*y)/x^6
F1b=F(y=x*y)
g1,F1, g1b, F1b

Out[3]:

(x^5*y + x^2,
 x^3*y^3*z + x^2*y^4 + y^2*z + z^3,
 y^4 + x*y^2,
 x^4*y^2 + x^2*y^2*z + x^3*z + z^3)

Aportación de estrato de intersección E_1 (6,2) y g_2=x2

In [26]:

Z1 = ZetaFunctions(F1)
A1=Z1.topological_zeta(local=True, weights=[1,2,1])
M1=Z1.monodromy_zeta()
A1, M1

Out[26]:

((-1/2) * (s + 1)^-2 * (s - 1), (-1) * (t - 1)^-1 * (t^2 + t + 1)^-1)

Aportación de estrato abierto de E_1 (6,2)

In [27]:

F1t=F1(x=x+2)
Z1t = ZetaFunctions(F1t)
A1t=Z1t.topological_zeta(local=True, weights=[1,2,1])
M1t=Z1t.monodromy_zeta()
A1t, M1t

Out[27]:

((-1/2) * (s + 1)^-2 * (s - 1), (-1) * (t - 1)^-1 * (t^2 + t + 1)^-1)

Segunda explosión E_2 (9,3)

In [28]:

g2=g1b(x=x*y)/y^3
F2=F1b(x=x*y)
g2b=g1b(y=x*y)/x^3
F2b=F1b(y=x*y)
g2, F2, g2b, F2b

Out[28]:

(x + y,
 x^4*y^6 + x^3*y^3*z + x^2*y^4*z + z^3,
 x*y^4 + y^2,
 x^6*y^2 + x^4*y^2*z + x^3*z + z^3)

Aportación de estrato de intersección E_2 (9,3) y g_3=y2

In [29]:

Z2b = ZetaFunctions(F2b)
A2b=Z2b.topological_zeta(local=True, weights=[3,1,1])
M2b=Z2b.monodromy_zeta()
A2b, M2b

Out[29]:

((1/3) * (s + 1)^-2, (t^6 + t^3 + 1)^-1)

Aportación de estrato abierto de E_1 (6,2)

In [30]:

F2t=F2(x=x+3)
Z2t = ZetaFunctions(F2t)
A2t=Z2t.topological_zeta(local=True, weights=[1,3,1])
M2t=Z2t.monodromy_zeta()
A2t, M2t

Out[30]:

((1/3) * (s + 1)^-2, (t^6 + t^3 + 1)^-1)

Tercera explosión E_3 (16,5)

In [31]:

g3=g2(x=x*y)/y
F3=F2(x=x*y)
g3b=g2(y=x*y)/x
F3b=F2(y=x*y)
g3, F3, g3b, F3b

Out[31]:

(x + 1,
 x^4*y^10 + x^3*y^6*z + x^2*y^6*z + z^3,
 y + 1,
 x^10*y^6 + x^6*y^4*z + x^6*y^3*z + z^3)

In [32]:

Aportación de intersección de E_1 (6,2) y E_3 (16,5)

  Cell In [32], line 1
    Aportación de intersección de E_1 (Integer(6),Integer(2)) y E_3 (Integer(16),Integer(5))
               ^
SyntaxError: invalid syntax

In [33]:

Z13 = ZetaFunctions(F3)
A13=Z13.topological_zeta(local=True, weights=[2,5,1])
M13=Z13.monodromy_zeta()
A13, M13

Out[33]:

((1/30) * (s + 1)^-2 * (s + 8/9)^-1 * (s^2 + 1/3*s + 8/3),
 (-1) * (t - 1) * (t^2 + t + 1))

Aportación de intersección de E_2 (9,3) y E_3 (16,5)

In [34]:

Z23 = ZetaFunctions(F3b)
A23=Z23.topological_zeta(local=True, weights=[5,3,1])
M23=Z23.monodromy_zeta()
A13, M23

Out[34]:

((1/30) * (s + 1)^-2 * (s + 8/9)^-1 * (s^2 + 1/3*s + 8/3),
 (-1) * (t - 1) * (t^2 + t + 1))

Aportación de estrato abierto de E_3 (16,5)

In [35]:

F3t=F3(x=x+3)
Z3t = ZetaFunctions(F3t)
A3t=Z3t.topological_zeta(local=True, weights=[1,5,1])
M3t=Z3t.monodromy_zeta()
A3t, M3t

Out[35]:

((-7/45) * (s + 8/9)^-1 * (s + 1)^-1 * (s - 8/7),
 (-1) * (t - 1)^-1 * (t^2 + t + 1)^-1 * (t^6 + t^3 + 1)^-2)

In [36]:

F3bt=F3b(y=y+3)
Z3bt = ZetaFunctions(F3bt)
A3bt=Z3bt.topological_zeta(local=True, weights=[5,1,1])
M3bt=Z3bt.monodromy_zeta()
A3bt, M3bt

Out[36]:

((-7/45) * (s + 8/9)^-1 * (s + 1)^-1 * (s - 8/7),
 (-1) * (t - 1)^-1 * (t^2 + t + 1)^-1 * (t^6 + t^3 + 1)^-2)

Aportación de intersección de E_3 (16,5) y g_1

In [37]:

F30=F3(x=x-1)
Z30 = ZetaFunctions(F30)
A30=Z30.topological_zeta(local=True, weights=[1,5,1])
M30=Z30.monodromy_zeta()
A30, M30

Out[37]:

((1/6) * (s + 8/9)^-1 * (s + 9/10)^-1 * (s + 1)^-1 * (s^2 + 142/75*s + 24/25),
 (t + 1) * (t - 1)^2 * (t^2 + t + 1) * (t^4 - t^3 + t^2 - t + 1) * (t^4 + t^3 + t^2 + t + 1))

In [38]:

F3b0=F3b(y=y-1)
Z3b0 = ZetaFunctions(F3b0)
A3b0=Z3b0.topological_zeta(local=True, weights=[5,1,1])
M3b0=Z3b0.monodromy_zeta()
A3b0, M3b0

Out[38]:

((1/6) * (s + 8/9)^-1 * (s + 9/10)^-1 * (s + 1)^-1 * (s^2 + 142/75*s + 24/25),
 (t + 1) * (t - 1)^2 * (t^2 + t + 1) * (t^4 - t^3 + t^2 - t + 1) * (t^4 + t^3 + t^2 + t + 1))

In [ ]:

In [49]:

T.<s> = QQ[]
A=A1+A2b+A13+A23-A3t+A30
B=(-11/90) * (s + 8/9)^-1 * (s + 9/10)^-1 * (s + 1)^-1 * (s^2 - 69/11*s - 72/11)
A-B

Out[49]:

In [ ]:

In [24]:

load('ZetaFunctionsNewtonND.py')
R.<x,y,z> = QQ[]
F = z^3+(y^2+x^3)*z+x^2*y^2
Z = ZetaFunctions(F)
Zmon=Z.monodromy_zeta()
Ztop=Z.topological_zeta(local = True)
g=(y^2+x^3)*x^2*y^2
Zmon, Ztop, g

Out[24]:

((-1) * (t - 1) * (t + 1) * (t^4 - t^3 + t^2 - t + 1) * (t^4 + t^3 + t^2 + t + 1) * (t^6 + t^3 + 1),
 (-11/90) * (s + 8/9)^-1 * (s + 9/10)^-1 * (s + 1)^-1 * (s^2 - 69/11*s - 72/11),
 x^5*y^2 + x^2*y^4)

Primera explosión ---> divisor E_1 (6,2)

In [25]:

g1=g(x=x*y)/y^6
F1=F(x=x*y)
g1b=g(y=x*y)/x^6
F1b=F(y=x*y)
g1,F1, g1b, F1b

Out[25]:

(x^5*y + x^2,
 x^3*y^3*z + x^2*y^4 + y^2*z + z^3,
 y^4 + x*y^2,
 x^4*y^2 + x^2*y^2*z + x^3*z + z^3)

Aportación de estrato de intersección E_1 (6,2) y g_2=x2

In [26]:

Z1 = ZetaFunctions(F1)
A1=Z1.topological_zeta(local=True, weights=[1,2,1])
M1=Z1.monodromy_zeta()
A1, M1

Out[26]:

((-1/2) * (s + 1)^-2 * (s - 1), (-1) * (t - 1)^-1 * (t^2 + t + 1)^-1)

Aportación de estrato abierto de E_1 (6,2)

In [27]:

F1t=F1(x=x+2)
Z1t = ZetaFunctions(F1t)
A1t=Z1t.topological_zeta(local=True, weights=[1,2,1])
M1t=Z1t.monodromy_zeta()
A1t, M1t

Out[27]:

((-1/2) * (s + 1)^-2 * (s - 1), (-1) * (t - 1)^-1 * (t^2 + t + 1)^-1)

Segunda explosión E_2 (9,3)

In [28]:

g2=g1b(x=x*y)/y^3
F2=F1b(x=x*y)
g2b=g1b(y=x*y)/x^3
F2b=F1b(y=x*y)
g2, F2, g2b, F2b

Out[28]:

(x + y,
 x^4*y^6 + x^3*y^3*z + x^2*y^4*z + z^3,
 x*y^4 + y^2,
 x^6*y^2 + x^4*y^2*z + x^3*z + z^3)

Aportación de estrato de intersección E_2 (9,3) y g_3=y2

In [29]:

Z2b = ZetaFunctions(F2b)
A2b=Z2b.topological_zeta(local=True, weights=[3,1,1])
M2b=Z2b.monodromy_zeta()
A2b, M2b

Out[29]:

((1/3) * (s + 1)^-2, (t^6 + t^3 + 1)^-1)

Aportación de estrato abierto de E_1 (6,2)

In [30]:

F2t=F2(x=x+3)
Z2t = ZetaFunctions(F2t)
A2t=Z2t.topological_zeta(local=True, weights=[1,3,1])
M2t=Z2t.monodromy_zeta()
A2t, M2t

Out[30]:

((1/3) * (s + 1)^-2, (t^6 + t^3 + 1)^-1)

Tercera explosión E_3 (16,5)

In [31]:

g3=g2(x=x*y)/y
F3=F2(x=x*y)
g3b=g2(y=x*y)/x
F3b=F2(y=x*y)
g3, F3, g3b, F3b

Out[31]:

(x + 1,
 x^4*y^10 + x^3*y^6*z + x^2*y^6*z + z^3,
 y + 1,
 x^10*y^6 + x^6*y^4*z + x^6*y^3*z + z^3)

In [32]:

Aportación de intersección de E_1 (6,2) y E_3 (16,5)

  Cell In [32], line 1
    Aportación de intersección de E_1 (Integer(6),Integer(2)) y E_3 (Integer(16),Integer(5))
               ^
SyntaxError: invalid syntax

In [33]:

Z13 = ZetaFunctions(F3)
A13=Z13.topological_zeta(local=True, weights=[2,5,1])
M13=Z13.monodromy_zeta()
A13, M13

Out[33]:

((1/30) * (s + 1)^-2 * (s + 8/9)^-1 * (s^2 + 1/3*s + 8/3),
 (-1) * (t - 1) * (t^2 + t + 1))

Aportación de intersección de E_2 (9,3) y E_3 (16,5)

In [34]:

Z23 = ZetaFunctions(F3b)
A23=Z23.topological_zeta(local=True, weights=[5,3,1])
M23=Z23.monodromy_zeta()
A13, M23

Out[34]:

((1/30) * (s + 1)^-2 * (s + 8/9)^-1 * (s^2 + 1/3*s + 8/3),
 (-1) * (t - 1) * (t^2 + t + 1))

Aportación de estrato abierto de E_3 (16,5)

In [35]:

F3t=F3(x=x+3)
Z3t = ZetaFunctions(F3t)
A3t=Z3t.topological_zeta(local=True, weights=[1,5,1])
M3t=Z3t.monodromy_zeta()
A3t, M3t

Out[35]:

((-7/45) * (s + 8/9)^-1 * (s + 1)^-1 * (s - 8/7),
 (-1) * (t - 1)^-1 * (t^2 + t + 1)^-1 * (t^6 + t^3 + 1)^-2)

In [36]:

F3bt=F3b(y=y+3)
Z3bt = ZetaFunctions(F3bt)
A3bt=Z3bt.topological_zeta(local=True, weights=[5,1,1])
M3bt=Z3bt.monodromy_zeta()
A3bt, M3bt

Out[36]:

((-7/45) * (s + 8/9)^-1 * (s + 1)^-1 * (s - 8/7),
 (-1) * (t - 1)^-1 * (t^2 + t + 1)^-1 * (t^6 + t^3 + 1)^-2)

Aportación de intersección de E_3 (16,5) y g_1

In [37]:

F30=F3(x=x-1)
Z30 = ZetaFunctions(F30)
A30=Z30.topological_zeta(local=True, weights=[1,5,1])
M30=Z30.monodromy_zeta()
A30, M30

Out[37]:

((1/6) * (s + 8/9)^-1 * (s + 9/10)^-1 * (s + 1)^-1 * (s^2 + 142/75*s + 24/25),
 (t + 1) * (t - 1)^2 * (t^2 + t + 1) * (t^4 - t^3 + t^2 - t + 1) * (t^4 + t^3 + t^2 + t + 1))

In [38]:

F3b0=F3b(y=y-1)
Z3b0 = ZetaFunctions(F3b0)
A3b0=Z3b0.topological_zeta(local=True, weights=[5,1,1])
M3b0=Z3b0.monodromy_zeta()
A3b0, M3b0

Out[38]:

((1/6) * (s + 8/9)^-1 * (s + 9/10)^-1 * (s + 1)^-1 * (s^2 + 142/75*s + 24/25),
 (t + 1) * (t - 1)^2 * (t^2 + t + 1) * (t^4 - t^3 + t^2 - t + 1) * (t^4 + t^3 + t^2 + t + 1))

In [ ]:

In [49]:

T.<s> = QQ[]
A=A1+A2b+A13+A23-A3t+A30
B=(-11/90) * (s + 8/9)^-1 * (s + 9/10)^-1 * (s + 1)^-1 * (s^2 - 69/11*s - 72/11)
A-B

Out[49]:

In [ ]:

24 KiB Raw Blame History

24 KiB

Raw Blame History