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Mathematical Overview

In this section we give a comprehensive overview of the main mathematical features of Macaulay 2.

  • rings
  • basic rings
  • polynomial rings
  • manipulating polynomials
  • polynomial rings with other monomial orderings
  • multi-graded polynomial rings
  • maps between rings
  • ideals
  • quotient rings
  • finite fields
  • fraction fields
  • tensor products of rings
  • exterior algebras
  • symmetric algebras
  • Weyl algebras
  • associative algebras
  • algebraic varieties

  • matrices
  • making matrices
  • making random matrices
  • making generic matrices
  • displaying matrices
  • manipulating matrices
  • diff and contract

  • modules
  • free modules
  • making modules from matrices
  • manipulating modules
  • maps between modules
  • bases of parts of modules
  • coherent sheaves

  • chain complexes
  • free resolutions of modules
  • making chain complexes by hand
  • extracting information from chain complexes
  • manipulating chain complexes
  • maps between chain complexes

  • computations
  • Groebner bases
  • computing Groebner bases
  • computing syzygies
  • computing resolutions

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