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5.1.65 intersect

Syntax:
intersect ( expression_list of ideal_expression )
intersect ( expression_list of module_expression )
Type:
ideal, resp. module
Purpose:
computes the intersection of ideals, resp. modules.
Note:
If the option prot is enabled then the result the used method (elimination/syzygies) is displayed.
An optional last argument specifies the Groebner base algorithm to use. Possible values are "std" and "slimgb".
Example:
 
  ring R=0,(x,y),dp;
  ideal i=x;
  ideal j=y;
  intersect(i,j);
==> _[1]=xy
  ring r=181,(x,y,z),(c,ls);
  ideal id1=maxideal(3);
  ideal id2=x2+xyz,y2-z3y,z3+y5xz;
  ideal id3=intersect(id1,id2,ideal(x,y));
  ideal id4=intersect(id1,id2,"slimgb");
  id3;
==> id3[1]=yz3+xy6z
==> id3[2]=yz4-y2z
==> id3[3]=y2z3-y3
==> id3[4]=xz3+x2y5z
==> id3[5]=xyz2+x2z
==> id3[6]=xy2+x2z2
==> id3[7]=xy2z+x2y
==> id3[8]=x2yz+x3
  id4;
==> id4[1]=xyz2+x2z
==> id4[2]=xy2z+x2y
==> id4[3]=x2yz+x3
==> id4[4]=-yz4+y2z
==> id4[5]=-y2z3+y3
==> id4[6]=-xyz3+xy2
==> id4[7]=z3+xy5z
See ideal; module; option.