intersect -- compute an intersection

Synopsis

Usage:
intersect (M,N,...,P)
Inputs:
- (M,N,...,P), a list or a sequence of modules or ideals that are submodules of the same module or ideals in the same ring
Outputs:
- a module or an ideal that is the intersection of the elements in the list or in the sequence.

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` :

intersect(List)
intersect(Sequence)

intersect -- compute an intersection

Synopsis

Description

Ways to use intersect :

Ways to use `intersect` :