next | previous | forward | backward | up | top | index | toc | Macaulay2 web site
Macaulay2Doc :: intersect

intersect -- compute an intersection



This function calculates the intersection of submodules of the same free module, or of ideals in the same ring.

The following example computes the intersection of a sequence of ideals.

i1 : R=ZZ/101[a..d];
i2 : I=intersect(ideal(a,b),ideal(b,c),ideal(c,d),ideal(d,a))

o2 = ideal (b*d, a*c)

o2 : Ideal of R

The following example computes the intersection of a list of modules.

i3 : R=ZZ[x,y,z];
i4 : M=image matrix{{3*x},{3*x}};
i5 : N=image matrix{{5*y},{5*y}};
i6 : P=image matrix{{7*z},{7*z}};
i7 : intersect{M,N,P}

o7 = image | 105xyz |
           | 105xyz |

o7 : R-module, submodule of R

The command intersect will only work with proper ideals. To intersect an ideal with a ring, use selectInSubring along with the elimination ordering, see Eliminate.

Ways to use intersect :