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BernsteinSato -- algorithms for b-functions, local cohomology, and intersection cohomology



  • bFunction -- b-function
  • generalB -- global generalized Bernstein-Sato polynomial
  • globalB -- compute global b-function and b-operator for a D-module and a polynomial
  • globalBFunction -- global b-function (else known as the Bernstein-Sato polynomial)
  • globalBoperator -- compute a b-operator of a polynomial
  • localBFunction -- local b-function (a.k.a. the local Bernstein-Sato polynomial)
  • factorBFunction -- factorization of a b-function
  • bFunctionRoots -- get roots of a b-function
  • getIntRoots -- get integer roots of a b-function
  • paramBpoly -- compute the list of all possible Bernstein-Sato polynomials for a polynomial with parametric coefficients
  • AnnFs -- differential annihilator of a polynomial in a Weyl algebra
  • AnnIFs -- the annihilating ideal of f^s for an arbitrary D-module

Resolutions and Functors

  • Dresolution -- resolution of a D-module
  • Dlocalize -- localization of a D-module
  • WeylClosure -- Weyl closure of an ideal
  • Ddual -- holonomic dual of a D-module
  • Drestriction -- restriction modules of a D-module
  • Dintegration -- integration modules of a D-module
  • DHom -- D-homomorphisms between holonomic D-modules
  • DExt -- Ext groups between holonomic modules
  • polynomialExt -- Ext groups between a holonomic module and a polynomial ring
  • rationalFunctionExt -- Ext(holonomic D-module, polynomial ring localized at the singular locus)




This documentation describes version 1.0 of BernsteinSato.

Source code

The source code from which this documentation is derived is in the file BernsteinSato.m2. The auxiliary files accompanying it are in the directory BernsteinSato/.


For the programmer

The object BernsteinSato is a package.