Singular

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