# InvolutiveBases : Table of Contents

• InvolutiveBases -- Methods for Janet bases and Pommaret bases in Macaulay 2
• basisElements -- extract the matrix of generators from an involutive basis or factor module basis
• FactorModuleBasis -- the class of all factor module bases
• factorModuleBasis -- enumerate standard monomials
• invNoetherNormalization -- Noether normalization
• Involutive -- compute a (usually non-minimal) resolution using involutive bases
• InvolutiveBasis -- the class of all involutive bases
• invReduce -- compute normal form modulo involutive basis by involutive reduction
• invSyzygies -- compute involutive basis of syzygies
• isPommaretBasis -- check whether or not a given Janet basis is also a Pommaret basis
• janetBasis -- compute Janet basis for an ideal or a submodule of a free module
• janetMultVar -- return table of multiplicative variables for given module elements as determined by Janet division
• janetResolution -- construct a free resolution for a given ideal or module using Janet bases
• multVar -- extract the sets of multiplicative variables for each generator (in several contexts)
• multVars -- key in the cache table of a differential in a Janet resolution
• PermuteVariables -- ensure that the last dim(I) var's are algebraically independent modulo I
• pommaretMultVar -- return table of multiplicative variables for given module elements as determined by Pommaret division