Contents

• Introduction to Macaulay
  • Background
  • Summary of New Features
  • Conventions
  • Acknowledgements
• Getting Started with Macaulay
  • Using Macaulay on Unix Systems
    • Starting up Macaulay
    • Command line editing
    • Controlling scrolling of the screen
    • Using Emacs, Suntools, or Xwindows
• Input Syntax
  • How to Input a Command
  • Special Characters
  • User Defined Variables (Identifiers)
    • Indexed Identifiers
  • Naming polynomial ring variables (indeterminants)
  • Integer Expressions
  • Polynomial expressions
  • Integer lists
  • Variable lists
• User Defined Variables
  • Types of Variables
  • Commands to display and remove variables
  • Referencing variables
  • Reusing Variable Names
  • Integer Variables
• Rings
  • The ``ring'' command
  • Other ring commands
  • Quotient Rings
  • Monomial orders in Macaulay
    • Reverse lexicographic order
    • Product and elimination orders
    • Monomial orders for free modules
    • General monomial orders in Macaulay
• Matrices
  • Matrix creation
  • Displaying Matrices
  • Operations on matrices
  • Editing Commands
  • Graded Matrices and Homogeniety
• Standard (Gröbner) Basis Computations
  • Standard basis and syzygy computations
  • Other computation commands
  • Internal format of a computation
  • Fine control of standard basis computations
    • Interrupting computations
    • Feedback during computations
    • Controlling computation
• Operations on standard bases
  • Elimination of variables
  • Ideal or submodule membership
  • Treating variables as constants
  • Saturation of ideals or submodules
  • Computing numerical information
  • Displaying Information about Resolutions
• Ring maps
  • Introduction to ring maps
  • Commands for defining and using ring maps
• System commands
  • Finding help about Macaulay
  • Recording a Macaulay session
  • Macaulay parameters
  • Space Utilization
  • Interrupting Macaulay's computations
  • Redirection of input and output
• Command Files
  • Running scripts
  • Creating scripts
  • Tour mode
  • Passing parameters to scripts
  • Silence is sometimes golden
  • If statements and jumps
  • Summary
• Examples
  • The rational quartic in P3
  • An elliptic curve on the Veronese in
  • The tangent developable of a rational normal curve
  • Finding an inhomogeneous standard basis
  • The ideal of the 3 by 3 commuting matrices
  • Linkage of curves in
• Macaulay under MPW
  • Controlling Macaulay from a window
  • Customizing the MPW environment
  • Some Peculiarities of Macaulay under MPW
• Scripts of Macaulay (by D. Eisenbud, M. Stillman
  • adj_of_cat
  • adjoin_fractions
  • adjoint
  • annihilator1
  • annihilator2
  • binomial
  • block_map
  • blowup
  • blowup0
  • cohomology
  • cohomology1
  • complement
  • copyring
  • cotan
  • cotan_bihom
  • deg01
  • diagonal_submodule
  • double_dual
  • double_dual1
  • dual_variety
  • ext
  • ext(-,R)
  • extend_ring
  • from_bigraded
  • from_div_powers
  • generic_mat
  • getvars
  • hom
  • hom_and_map
  • hom_is_0
  • homology
  • ideal
  • idencoldegs
  • idenrowdegs
  • inhomog_std
  • interchange
  • interchange_permutation
  • inverse
  • j_from_lambda
  • j_invariant
  • kernel
  • kernel_and_map
  • kosz_hom1
  • kosz_hom2
  • l_dual0
  • l_from_dual
  • l_homog0
  • l_minimal
  • l_minimal0
  • l_tangentcone
  • l_to_dual
  • line_bundle_image
  • minpres
  • monomial_curve
  • nbyn_commuting
  • normal_cone
  • normal_sheaf
  • nzd
  • orbit_equations
  • permutation
  • points
  • powers
  • project_from_product
  • prune
  • prune_and_map
  • pts_linear
  • push_forward
  • push_forward1
  • random_mat
  • representatives
  • representatives1
  • ring
  • rmap
  • sat
  • sat1
  • subring
  • symmetric_algebra
  • to_div_powers
  • tor
  • x_to_last
  • zeromat