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3.9.3. Commands and Functions for Polynomials
The following are commands and functions for polynomials:

  * Bin -- binomial coefficient
  * BringIn -- bring in objects from another ring
  * Coefficients -- list of coefficients of a polynomial or vector
  * CoeffOfTerm -- coefficient of a term of a polynomial or vector
  * Colon, :, HColon -- ideal or module quotient
  * Deg -- the degree of a polynomial or vector
  * DensePoly -- the sum of all power-products of a given degree
  * Der -- the derivative of a rational function
  * Discriminant -- the discriminant of a polynomial
  * DivAlg -- division algorithm
  * Eval -- substitute numbers or polynomials for indeterminates
  * Factor -- factor a polynomial
  * Fraction -- returns the quotient of its arguments
  * GCD, LCM -- greatest common divisor, least common multiple
  * GenRepr -- representation in terms of generators
  * Homogenized -- homogenize with respect to an indeterminate
  * Interpolate -- interpolating polynomial
  * Inverse -- multiplicative inverse
  * IsHomog -- test whether given polynomials are homogeneous
  * IsIn -- check if one object is contained in another
  * IsTerm -- checks if the argument is a term
  * IsZero -- test whether an object is zero
  * Jacobian -- the Jacobian of a list of polynomials
  * LC -- the leading coefficient of a polynomial or vector
  * Len -- the length of an object
  * LM -- the leading monomial of a polynomial or vector
  * Log -- the list of exponents of the leading term of a polynomial
  * LogToTerm -- returns a monomial (power-product) with given exponents
  * LPP -- the leading power-product of a polynomial or vector
  * LT -- the leading term of an object
  * MapDown -- convert a constant polynomial to a number
  * MDeg -- multi-degree of an polynomial
  * Monic -- divide polynomials by their leading coefficients
  * Monomials -- the list of monomials of a polynomial or vector
  * NF -- normal form
  * NFsAreZero -- test if normal forms are zero
  * NR -- normal reduction
  * Num, Den -- numerator, denominator
  * Poly -- convert an expression into a polynomial
  * Product, Sum -- the product or sum of the elements of a list
  * QZP, ZPQ -- change field for polynomials and ideals
  * Randomize, Randomized -- randomize the coefficients of a given polynomial
  * RealRootRefine -- refine a root of a univariate polynomial over Q
  * RealRoots -- computes a root of a univariate polynomial over Q
  * Resultant -- the resultant of two polynomials
  * RootBound -- bound on roots of a polynomial over Q
  * Size -- the amount of memory used by an object
  * StarPrint -- print polynomial with *'s for multiplications
  * Subst -- substitute values for indeterminates
  * Support -- the list of terms of a polynomial or vector
  * Sylvester -- the Sylvester matrix of two polynomials
  * WLog -- weighted list of exponents

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