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5.1.53 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 returnSB is enabled then the result is a standard basis.

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));
  id3;
→ id3[1]=yz3+xy6z
→ id3[2]=yz4-y2z
→ id3[3]=y2z3-y3
→ id3[4]=xz3+x2y5z
→ id3[5]=xyz2+x2z
→ id3[6]=xyz3-xy2
→ id3[7]=xy2z+x2y
→ id3[8]=x2yz+x3

See ideal; module; option.


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