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isDirectSummand -- test whether one module is a direct summand of another

Description

This function tries to detect whether $L$ is a direct summand of $M$ by searching for maps $L \to M$ and $M \to L$ whose composition is an isomorphism of $L$.

The computation is randomized, so a return value of true certifies that a summand was found, while a return value of false only means that no splitting was found within the allotted number of attempts. The alias isSummand is provided for convenience.

When $L$ is free, the method instead searches for a surjection $M \to L$, which is enough to split off a free summand.

See also

Ways to use isDirectSummand:

  • isDirectSummand(Module,Module)

For the programmer

The object isDirectSummand is a method function with options.


The source of this document is in /build/reproducible-path/macaulay2-1.26.06+ds/M2/Macaulay2/packages/DirectSummands/docs.m2:680:0.