modules

For more operations in homological algebra, see chain complexes. For additional common operations and a comprehensive list of all routines in Macaulay2 which return or use modules, see Module.

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construction of modules

• free modules
• matrices to and from modules -- including kernel, cokernel and image
• submodules and quotients
• subquotient modules -- the way Macaulay2 represents modules

homomorphisms (maps) between modules

• module homomorphisms
• right modules or left modules?
• module quotients, saturation, and annihilator

graded modules

• Hilbert functions and free resolutions -- including degree and betti numbers
• basis -- basis or generating set of all or part of a ring, ideal or module

multilinear algebra

• exterior power of a module