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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