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D.5.2.5 Nonhyp
Procedure from library resbinomial.lib (see resbinomial_lib).
- Compute:
- The "ideal" generated by the non hyperbolic generators of J
- Return:
- lists with the following information
newcoef,newJ: coefficients and exponents of the non hyperbolic generators
totalhyp,totalgen: coefficients and exponents of the hyperbolic generators
flaglist: new list saying status of variables
- Note:
- the basering r is supposed to be a polynomial ring K[x,y],
in fact, we work in a localization of K[x,y], of type K[x,y]_y with y invertible variables.
Example:
| | LIB "resbinomial.lib";
ring r = 0,(x(1),y(2),x(3),y(4),x(5..7)),dp;
list flag=identifyvar(); // List giving flag=1 to invertible variables: y(2),y(4)
ideal J=x(1)^3-x(3)^2*y(4)^2,x(1)*x(7)*y(2)-x(6)^3*x(5)*y(4)^3,1-x(5)^2*y(2)^2;
list L=data(J,3,7);
list L2=maxEord(L[1],L[2],3,7,flag);
L2[1]; // Maximum E-order
==> 0
list New=Nonhyp(L[1],L[2],3,7,flag,L2[2]);
New[1]; // Coefficients of the non hyperbolic part
==> [1]:
==> [1]:
==> -1
==> [2]:
==> 1
==> [2]:
==> [1]:
==> -1
==> [2]:
==> 1
New[2]; // Exponents of the non hyperbolic part
==> [1]:
==> [1]:
==> [1]:
==> 0
==> [2]:
==> 0
==> [3]:
==> 2
==> [4]:
==> 2
==> [5]:
==> 0
==> [6]:
==> 0
==> [7]:
==> 0
==> [2]:
==> [1]:
==> 3
==> [2]:
==> 0
==> [3]:
==> 0
==> [4]:
==> 0
==> [5]:
==> 0
==> [6]:
==> 0
==> [7]:
==> 0
==> [2]:
==> [1]:
==> [1]:
==> 0
==> [2]:
==> 0
==> [3]:
==> 0
==> [4]:
==> 3
==> [5]:
==> 1
==> [6]:
==> 3
==> [7]:
==> 0
==> [2]:
==> [1]:
==> 1
==> [2]:
==> 1
==> [3]:
==> 0
==> [4]:
==> 0
==> [5]:
==> 0
==> [6]:
==> 0
==> [7]:
==> 1
New[3]; // Coefficients of the hyperbolic part
==> [1]:
==> [1]:
==> -1
==> [2]:
==> 1
New[4]; // New hyperbolic equations
==> [1]:
==> [1]:
==> [1]:
==> 0
==> [2]:
==> 2
==> [3]:
==> 0
==> [4]:
==> 0
==> [5]:
==> 2
==> [6]:
==> 0
==> [7]:
==> 0
==> [2]:
==> [1]:
==> 0
==> [2]:
==> 0
==> [3]:
==> 0
==> [4]:
==> 0
==> [5]:
==> 0
==> [6]:
==> 0
==> [7]:
==> 0
New[5]; // New list giving flag=1 to invertible variables: y(2),y(4),y(5)
==> [1]:
==> 0
==> [2]:
==> 1
==> [3]:
==> 0
==> [4]:
==> 1
==> [5]:
==> 1
==> [6]:
==> 0
==> [7]:
==> 0
ring r = 0,(x(1..4)),dp;
==> // ** redefining r **
list flag=identifyvar();
==> // ** redefining flag **
ideal J=1-x(1)^5*x(2)^2*x(3)^5, x(1)^2*x(3)^3+x(1)^4*x(4)^6;
list L=data(J,2,4);
list L2=maxEord(L[1],L[2],2,4,flag);
L2[1]; // Maximum E-order
==> 0
list New=Nonhyp(L[1],L[2],2,4,flag,L2[2]);
New;
==> [1]:
==> empty list
==> [2]:
==> empty list
==> [3]:
==> [1]:
==> [1]:
==> -1
==> [2]:
==> 1
==> [2]:
==> [1]:
==> 1
==> [2]:
==> 1
==> [4]:
==> [1]:
==> [1]:
==> [1]:
==> 5
==> [2]:
==> 2
==> [3]:
==> 5
==> [4]:
==> 0
==> [2]:
==> [1]:
==> 0
==> [2]:
==> 0
==> [3]:
==> 0
==> [4]:
==> 0
==> [2]:
==> [1]:
==> [1]:
==> 4
==> [2]:
==> 0
==> [3]:
==> 0
==> [4]:
==> 6
==> [2]:
==> [1]:
==> 2
==> [2]:
==> 0
==> [3]:
==> 3
==> [4]:
==> 0
==> [5]:
==> [1]:
==> 1
==> [2]:
==> 1
==> [3]:
==> 1
==> [4]:
==> 1
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