Singular Manual: intersect

  | ### 5.1.63 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 algorith 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.

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