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Macaulay2Doc :: intersect

intersect -- compute an intersection

Synopsis

Description

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 |

                             2
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 :