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D.5.12.3 determinecenter
Procedure from library resbinomial.lib (see resbinomial_lib).
- Usage:
- determinecenter(Coef,expJ,c,n,Y,a,listmb,flag,control3,Hhist);
Coef, expJ, listmb, flag lists, c number, n, Y, control3 integers, a, Hhist intvec
- Compute:
- next center of blowing up and related information, see example
- Return:
- several lists defining the center and related information
Example:
| | LIB "resbinomial.lib";
ring r = 0,(x(1..4)),dp;
list flag=identifyvar();
ideal J=x(1)^2-x(2)^2*x(3)^5, x(1)*x(3)^3+x(4)^6;
list Lmb=1,list(0,0,0,0),list(0,0,0,0),list(0,0,0,0),iniD(4),iniD(4),list(0,0,0,0),-1;
list L=data(J,2,4);
list LL=determinecenter(L[1],L[2],2,4,0,0,Lmb,flag,0,-1); // Compute the first center
LL[1]; // index of variables in the center
==> [1]:
==> 1
==> [2]:
==> 4
==> [3]:
==> 3
==> [4]:
==> 2
LL[2]; // exponents of ideals J_4,J_3,J_2,J_1
==> [1]:
==> [1]:
==> [1]:
==> [1]:
==> 0
==> [2]:
==> 2
==> [3]:
==> 5
==> [4]:
==> 0
==> [2]:
==> [1]:
==> 2
==> [2]:
==> 0
==> [3]:
==> 0
==> [4]:
==> 0
==> [2]:
==> [1]:
==> [1]:
==> 0
==> [2]:
==> 0
==> [3]:
==> 0
==> [4]:
==> 6
==> [2]:
==> [1]:
==> 1
==> [2]:
==> 0
==> [3]:
==> 3
==> [4]:
==> 0
==> [2]:
==> [1]:
==> [1]:
==> [1]:
==> 0
==> [2]:
==> 2
==> [3]:
==> 5
==> [4]:
==> 0
==> [2]:
==> [1]:
==> [1]:
==> 0
==> [2]:
==> 0
==> [3]:
==> 0
==> [4]:
==> 6
==> [3]:
==> [1]:
==> [1]:
==> 0
==> [2]:
==> 0
==> [3]:
==> 6
==> [4]:
==> 0
==> [3]:
==> [1]:
==> [1]:
==> [1]:
==> 0
==> [2]:
==> 2
==> [3]:
==> 5
==> [4]:
==> 0
==> [2]:
==> [1]:
==> [1]:
==> 0
==> [2]:
==> 0
==> [3]:
==> 6
==> [4]:
==> 0
==> [4]:
==> [1]:
==> [1]:
==> [1]:
==> 0
==> [2]:
==> 12
==> [3]:
==> 0
==> [4]:
==> 0
LL[3]; // list of orders of J_4,J_3,J_2,J_1
==> [1]:
==> 2
==> [2]:
==> 6
==> [3]:
==> 6
==> [4]:
==> 12
LL[4]; // list of critical values
==> [1]:
==> 2
==> [2]:
==> 2
==> [3]:
==> 6
==> [4]:
==> 6
LL[5]; // components of the resolution function t
==> [1]:
==> 1
==> [2]:
==> 3
==> [3]:
==> 1
==> [4]:
==> 2
LL[6]; // list of D_4,D_3,D_2,D_1
==> [1]:
==> [1]:
==> 0
==> [2]:
==> 0
==> [3]:
==> 0
==> [4]:
==> 0
==> [2]:
==> [1]:
==> 0
==> [2]:
==> 0
==> [3]:
==> 0
==> [4]:
==> 0
==> [3]:
==> [1]:
==> 0
==> [2]:
==> 0
==> [3]:
==> 0
==> [4]:
==> 0
==> [4]:
==> [1]:
==> 0
==> [2]:
==> 0
==> [3]:
==> 0
==> [4]:
==> 0
LL[7]; // list of H_4,H_3,H_2,H_1 (exceptional divisors)
==> [1]:
==> [1]:
==> 0
==> [2]:
==> 0
==> [3]:
==> 0
==> [4]:
==> 0
==> [2]:
==> [1]:
==> 0
==> [2]:
==> 0
==> [3]:
==> 0
==> [4]:
==> 0
==> [3]:
==> [1]:
==> 0
==> [2]:
==> 0
==> [3]:
==> 0
==> [4]:
==> 0
==> [4]:
==> [1]:
==> 0
==> [2]:
==> 0
==> [3]:
==> 0
==> [4]:
==> 0
LL[8]; // list of all exceptional divisors accumulated
==> [1]:
==> 0
==> [2]:
==> 0
==> [3]:
==> 0
==> [4]:
==> 0
LL[9]; // auxiliary invariant
==> [1]:
==> 0
LL[10]; // intvec pointing out the last step where the function t has dropped
==> -1,-1,-1,-1
ring r= 0,(x(1..4)),dp;
==> // ** redefining r (ring r= 0,(x(1..4)),dp;) ./examples/determinecenter.s\
ing:18
list flag=identifyvar();
==> // ** redefining flag (list flag=identifyvar();) ./examples/determinecent\
er.sing:19
ideal J=x(1)^3-x(2)^2*x(3)^5, x(1)*x(3)^3+x(4)^5;
list Lmb=2,list(0,0,0,0),list(0,0,0,0),list(0,0,0,0),iniD(4),iniD(4),list(0,0,0,0),-1;
==> // ** redefining Lmb (=2,list(0,0,0,0),list(0,0,0,0),list(0,0,0,0),iniD(4\
),iniD(4),list(0,0,0,0),-1;) ./examples/determinecenter.sing:21
list L2=data(J,2,4);
list L3=determinecenter(L2[1],L2[2],2,4,0,0,Lmb,flag,0,-1); // Example with rational exponents in E-Coeff
L3[1]; // index of variables in the center
==> [1]:
==> 1
==> [2]:
==> 3
==> [3]:
==> 4
L3[2]; // exponents of ideals J_4,J_3,J_2,J_1
==> [1]:
==> [1]:
==> [1]:
==> [1]:
==> 0
==> [2]:
==> 2
==> [3]:
==> 5
==> [4]:
==> 0
==> [2]:
==> [1]:
==> 3
==> [2]:
==> 0
==> [3]:
==> 0
==> [4]:
==> 0
==> [2]:
==> [1]:
==> [1]:
==> 0
==> [2]:
==> 0
==> [3]:
==> 0
==> [4]:
==> 5
==> [2]:
==> [1]:
==> 1
==> [2]:
==> 0
==> [3]:
==> 3
==> [4]:
==> 0
==> [2]:
==> [1]:
==> [1]:
==> [1]:
==> 0
==> [2]:
==> 2
==> [3]:
==> 5
==> [4]:
==> 0
==> [2]:
==> [1]:
==> [1]:
==> 0
==> [2]:
==> 0
==> [3]:
==> 0
==> [4]:
==> 5
==> [3]:
==> [1]:
==> [1]:
==> 0
==> [2]:
==> 0
==> [3]:
==> 9/2
==> [4]:
==> 0
==> [3]:
==> [1]:
==> [1]:
==> [1]:
==> 0
==> [2]:
==> 0
==> [3]:
==> 0
==> [4]:
==> 5
==> [4]:
==> [1]:
==> [1]:
==> [1]:
==> 0
==> [2]:
==> 0
==> [3]:
==> 0
==> [4]:
==> 0
L3[3]; // list of orders of J_4,J_3,J_2,J_1
==> [1]:
==> 3
==> [2]:
==> 9/2
==> [3]:
==> 5
L3[4]; // list of critical values
==> [1]:
==> 2
==> [2]:
==> 3
==> [3]:
==> 9/2
L3[5]; // components of the resolution function
==> [1]:
==> 3/2
==> [2]:
==> 3/2
==> [3]:
==> 10/9
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