|  |  5.1.28 eliminate 
 
See
 hilb;
 ideal;
 module;
 std.Syntax:eliminate (ideal_expression,product_of_ring_variables)
 eliminate (module_expression,product_of_ring_variables)
 eliminate (ideal_expression,intvec_expression)
 eliminate (module_expression,intvec_expression)
 eliminate (ideal_expression,product_of_ring_variables,intvec_hilb)
 eliminate (module_expression,product_of_ring_variables,intvec_hilb)Type:the same as the type of the first argument
Purpose:eliminates variables occurring as factors/entries of the second argument from an
ideal (resp. a submodule of a free module), by intersecting it
(resp. each component of the submodule) with the subring not containing these variables.
 eliminatedoes not need a special ordering nor a standard basis as input.Note:Since elimination is expensive, for homogeneous input it might be useful
first to compute the Hilbert function of the ideal (first
argument) with a fast ordering (e.g., dp). Then make use of it to speed
up the computation: a Hilbert-driven elimination uses the intvec
provided as the third argument.If the ideal (resp. module) is not homogeneous with weights 1,
this intvec will be silently ignored.
Example:|  |   ring r=32003,(x,y,z),dp;
  ideal i=x2,xy,y5;
  eliminate(i,x);
==> _[1]=y5
  ring R=0,(x,y,t,s,z),dp;
  ideal i=x-t,y-t2,z-t3,s-x+y3;
  eliminate(i,ts);
==> _[1]=y2-xz
==> _[2]=xy-z
==> _[3]=x2-y
  ideal j=x2,xy,y2;
  intvec v=hilb(std(j),1);
  eliminate(j,y,v);
==> _[1]=x2
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