DirectSummands : Table of Contents

• DirectSummands -- decompositions of modules and coherent sheaves
  • Example: summands of the Frobenius pushforward
    • frobeniusMap -- the iterated Frobenius map of a ring in positive characteristic
    • frobeniusRing -- construct the source ring for an iterated Frobenius map
    • frobeniusPullback -- compute Frobenius pullbacks
    • frobeniusPushforward -- compute Frobenius pushforwards
    • frobeniusTwist -- apply the Frobenius twist to rings, modules, and matrices
  • Example: syzygies over Artinian rings
  • Example: symbolic diagonalization
  • directSummands -- compute the direct summands of a module or coherent sheaf
  • isDirectSummand -- test whether one module is a direct summand of another
  • isIndecomposable -- tests whether a module or coherent sheaf is indecomposable
  • findProjectors -- construct projectors on a homogeneous module
  • findIdempotents -- construct idempotent endomorphisms
  • findSplitInclusion -- construct a split inclusion of one module into another
  • generalEndomorphism -- construct a generic degree-zero endomorphism
  • isomorphismTally -- group isomorphic modules or sheaves in a list
  • tallySummands -- tally a list of modules up to isomorphism
  • potentialExtension -- suggest a field extension where splitting may become visible
  • changeBaseField -- extend scalars for modules, matrices, and coherent sheaves