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D.5.5.12 Emaxcont
Procedure from library resbinomial.lib (see resbinomial_lib).
- Usage:
- Emaxcont(Coef,Exp,k,n,flag);
Coef,Exp,flag lists, k,n, integers
Exp is a list of lists of exponents, k=size(Exp)
- Compute:
- Identify ALL the variables of E-maximal contact
- Return:
- a list with the indexes of the variables of E-maximal contact
Example:
| | LIB "resbinomial.lib";
ring r = 0,(x(1),y(2),x(3),y(4),x(5..7),y(8)),dp;
list flag=identifyvar();
ideal J=x(1)^3*x(3)-y(2)*y(4)^2,x(5)*y(2)-x(7)*y(4)^2,x(6)^2*(1-y(4)*y(8)^5),x(7)^4*y(8)^2;
list L=data(J,4,8);
list hyp=Emaxcont(L[1],L[2],4,8,flag);
hyp[1]; // max E-order=0
==> 0
hyp[2]; // There are no hypersurfaces of E-maximal contact
==> empty list
ring r = 0,(x(1),y(2),x(3),y(4),x(5..7),y(8)),dp;
==> // ** redefining r **
list flag=identifyvar();
==> // ** redefining flag **
ideal J=x(1)^3*x(3)-y(2)*y(4)^2*x(3),x(5)*y(2)-x(7)*y(4)^2,x(6)^2*(1-y(4)*y(8)^5),x(7)^4*y(8)^2;
list L=data(J,4,8);
list hyp=Emaxcont(L[1],L[2],4,8,flag);
hyp[1]; // the E-order is 1
==> 1
hyp[2]; // {x(3)=0},{x(5)=0},{x(7)=0} are hypersurfaces of E-maximal contact
==> [1]:
==> 3
==> [2]:
==> 7
==> [3]:
==> 5
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