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--- status: Draft
--- author(s):Giulio
--- notes:
doc ///
Node
Key
intersect
Headline
compute an intersection
Node
Key
(intersect, List)
(intersect, Sequence)
(intersect, Ideal)
(intersect, Module)
[intersect, Strategy]
[intersect, MinimalGenerators]
Headline
compute an intersection of ideals or modules
Usage
intersect(M, N, ..., P)
Inputs
:{List,Sequence}
containing modules that are submodules of the same module or ideals in the same ring
Strategy=>Thing
specifies the algorithm
MinimalGenerators=>Boolean
indicates whether the output should be @TO2 {trim, "trimmed"}@
Outputs
:{Ideal,Module}
the intersection of the objects given
Description
Text
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.
Example
R = ZZ/101[a..d];
I = intersect(ideal(a, b), ideal(b, c), ideal(c, d), ideal(d, a))
Text
The following example computes the intersection of a list of modules.
Example
R=ZZ[x, y, z];
M=image matrix{{3*x}, {3*x}};
N=image matrix{{5*y}, {5*y}};
P=image matrix{{7*z}, {7*z}};
intersect{M, N, P}
Text
The command @TO "intersect"@ does not accept subrings. To intersect an ideal with a subring,
use @TO "selectInSubring"@ along with the elimination ordering, see @TO "Eliminate"@.
Multiple strategies are implemented via @TO2 {"Macaulay2Doc :: using hooks", "hooks"}@ and
can be listed using the function @TO hooks@. More strategies may be added using @TO addHook@.
Example
hooks(intersect, Ideal, Ideal)
hooks(intersect, Module, Module)
Text
By default, the strategies are attempted in the reverse order in which the were added, until one is successful.
To run a specific strategy instead, use the optional argument @TT "Strategy"@.
Example
intersect(ideal(x, y), (ideal(x, y, z))^2, Strategy => Monomial)
SeeAlso
selectInSubring
///
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