COMPUTATIONS IN ALGEBRAIC GEOMETRY WITH MACAULAY2
IDEALS, VARIETIES AND MACAULAY 2 A CURVE IN A?NE THREE-SPACE INTERSECTING OUR CURVE WITH A SURFACE CHANGING THE AMBIENT POLYNOMIAL RING MONOMIALS UNDER THE STAIRCASE PENNIES, NICKELS, DIMES AND QUARTERS REFERENCES PROJECTIVE GEOMETRY AND HOMOLOGICAL ALGEBRA THE TWISTED CUBIC THE COTANGENT BUNDLE OF P3 THE COTANGENT BUNDLE OF A PROJECTIVE VARIETY INTERSECTIONS BY SERRE’S METHOD A MYSTERY VARIETY IN P3 APPENDIX A HOW THE “MYSTERY VARIETY” WAS MADE DATA TYPES, FUNCTIONS, AND PROGRAMMING BASIC DATA TYPES CONTROL STRUCTURES INPUT AND OUTPUT HASH TABLES METHODS POINTERS TO THE SOURCE CODE TEACHING THE GEOMETRY OF SCHEMES DISTINGUISHED OPEN SETS IRREDUCIBILITY SINGULAR POINTS FIELDS OF DE?NITION MULTIPLICITY FLAT FAMILIES B´EZOUT’S THEOREM CONSTRUCTING BLOW-UPS A CLASSIC BLOW-UP FANO SCHEMES PART II MATHEMATICAL COMPUTATIONS MONOMIAL IDEALS THE BASICS OF MONOMIAL IDEALS PRIMARY DECOMPOSITION STANDARD PAIRS GENERIC INITIAL IDEALS THE CHAIN PROPERTY FROM ENUMERATIVE GEOMETRY TO SOLVING SYSTEMS OF POLYNOMIAL EQUATIONS INTRODUCTION SOLVING SYSTEMS OF POLYNOMIALS SOME ENUMERATIVE GEOMETRY SCHUBERT CALCULUS THE 12 LINES: REPRISE RESOLUTIONS AND COHOMOLOGY OVER COMPLETE INTERSECTIONS MATRIX FACTORIZATIONS GRADED ALGEBRAS UNIVERSAL HOMOTOPIES COHOMOLOGY OPERATORS COMPUTATION OF EXT MODULES INVARIANTS OF MODULES INVARIANTS OF PAIRS OF MODULES APPENDIX A GRADINGS ALGORITHMS FOR THE TORIC HILBERT SCHEME GENERATING MONOMIAL IDEALS POLYHEDRAL GEOMETRY LOCAL EQUATIONS THE COHERENT COMPONENT OF THE TORIC HILBERT SCHEME APPENDIX A FOURIER-MOTZKIN ELIMINATION APPENDIX B MINIMAL PRESENTATION OF RINGS SHEAF ALGORITHMS USING THE EXTERIOR ALGEBRA BASICS OF THE BERNSTEIN-GEL’FAND-GEL’FAND CORRESPONDENCE THE COHOMOLOGY AND THE TATE RESOLUTION OF A SHEAF COHOMOLOGY AND VECTOR BUNDLES COHOMOLOGY AND MONADS THE BEILINSON MONAD EXAMPLES NEEDLES IN A HAYSTACK: SPECIAL VARIETIES VIA SMALL FIELDS HOW TO MAKE RANDOM CURVES UP TO GENUS 14 COMPARING GREEN’S CONJECTURE FOR CURVES AND POINTS PFA?AN CALABI-YAU THREEFOLDS IN P6 D-MODULES AND COHOMOLOGY OF VARIETIES ULI WALTHER THE WEYL ALGEBRA AND GR¨OBNER BASES BERNSTEIN-SATO POLYNOMIALS AND LOCALIZATION LOCAL COHOMOLOGY COMPUTATIONS IMPLEMENTATION, EXAMPLES, QUESTIONS