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3.6.2. Commands and Functions for Vectors
The following are commands and functions for vectors:

  * BringIn -- bring in objects from another ring
  * CoeffOfTerm -- coefficient of a term of a polynomial or vector
  * Colon, :, HColon -- ideal or module quotient
  * ColumnVectors -- the list of column vectors of a matrix
  * Comp -- the N-th component of a list
  * Comps -- list of components of a vector
  * Deg -- the degree of a polynomial or vector
  * DivAlg -- division algorithm
  * E_ -- canonical vector
  * FirstNonZero, FirstNonZeroPos -- the first non-zero entry in a vector
  * GenRepr -- representation in terms of generators
  * IsIn -- check if one object is contained in another
  * IsTerm -- checks if the argument is a term
  * IsZero -- test whether an object is zero
  * LC -- the leading coefficient of a polynomial or vector
  * Len -- the length of an object
  * List -- convert an expression into a list
  * LM -- the leading monomial of a polynomial or vector
  * LPos -- the position of the leading power-product in a vector
  * LPP -- the leading power-product of a polynomial or vector
  * LT -- the leading term of an object
  * Mat -- convert an expression into a matrix
  * Monomials -- the list of monomials of a polynomial or vector
  * NewVector -- create a new vector
  * NF -- normal form
  * NFsAreZero -- test if normal forms are zero
  * NonZero -- remove zeroes from a list
  * NR -- normal remainder
  * NumComps -- the number of components of a vector
  * Product, Sum -- the product or sum of the elements of a list
  * ScalarProduct -- scalar product
  * Size -- the amount of memory used by an object
  * Support -- the list of terms of a polynomial or vector
  * Vector -- create a vector

Details can be found by looking up each item by name.  Online, try
'?ItemName' or 'H.Syntax("ItemName")'.