PolynomialRing

PolynomialRing -- denotes the class of all ordered monoid rings.

If R is a ring and M is an ordered monoid, then R M denotes the ordered monoid ring constructed from them.

If r is an element of R and m is an element of M then r m denotes the corresponding element of R M, provided R M has already been constructed.

Elements of these rings are displayed with the monoid elements appearing in decreasing order from left to right.

Operations on rings:

  • modifyRing
  • numgens
  • vars
  • Operations on ring elements:

  • +
  • -
  • *
  • coefficients
  • index
  • isPrime
  • isPrimitive
  • leadComponent
  • leadCoefficient
  • leadMonomial
  • leadTerm
  • length
  • lift
  • liftable
  • promote
  • someTerms
  • standardForm
  • substitute
  • Producing ring elements:

  • random
  • Keys used:

  • ring
  • degreesRing
  • See also OrderedMonoid and RingElement.

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