modules

For more operations in homological algebra, see chain complexes. For additional common operations and a comprehensive list of all routines in Macaulay 2 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 Macaulay 2 represents modules

homomorphisms (maps) between modules

• module homomorphisms
• canonical maps between modules -- empty
• right modules or left modules?

operations on modules

• direct sums of modules -- empty
• tensor products of modules -- empty
• Hom modules and homomorphisms -- empty
• annihilators and submodule quotients -- empty

graded modules

• Hilbert functions and free resolutions -- including degree and betti numbers
• degrees of elements and free modules -- empty
• degree and multiplicity of a module -- empty
• basis -- basis of all or part of a module or ring
• Hilbert functions and polynomials -- empty
• homogenization -- empty
• truncation and homogeneous components of a graded module -- empty

multilinear algebra

• exterior power of a module
• Fitting ideals -- empty
• adjoints of maps -- empty

homological algebra

• Ext and Tor -- empty
• local cohomology -- empty
• is a module Cohen-Macaulay? -- empty