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InvolutiveBasis -- the class of all involutive bases

Functions and methods returning an object of class InvolutiveBasis:

  • invSyzygies -- compute involutive basis of syzygies
  • janetBasis -- compute Janet basis for an ideal or a submodule of a free module

Methods that use an object of class InvolutiveBasis:

  • basisElements(InvolutiveBasis) -- see basisElements -- extract the matrix of generators from an involutive basis or factor module basis
  • factorModuleBasis(InvolutiveBasis) -- see factorModuleBasis -- enumerate standard monomials
  • invNoetherNormalization(InvolutiveBasis) -- see invNoetherNormalization -- Noether normalization
  • invReduce(Matrix,InvolutiveBasis) -- see invReduce -- compute normal form modulo involutive basis by involutive reduction
  • invReduce(RingElement,InvolutiveBasis) -- see invReduce -- compute normal form modulo involutive basis by involutive reduction
  • invSyzygies(InvolutiveBasis) -- see invSyzygies -- compute involutive basis of syzygies
  • isPommaretBasis(InvolutiveBasis) -- see isPommaretBasis -- check whether or not a given Janet basis is also a Pommaret basis
  • janetResolution(InvolutiveBasis) -- see janetResolution -- construct a free resolution for a given ideal or module using Janet bases
  • multVar(InvolutiveBasis) -- see multVar -- extract the sets of multiplicative variables for each generator (in several contexts)

For the programmer

The object InvolutiveBasis is a type, with ancestor classes HashTable < Thing.


The source of this document is in InvolutiveBases.m2:1154:0.