Ring

Ring -- the class of all rings.

A ring is a set together with operations +, -, * and elements 0, 1 satisfying the usual rules. In this system, it is also understood to be a ZZ-algebra, which means that the operations where one argument is an integer are also provided.

Here are some classes of rings.

  • Field
  • FractionField
  • GaloisField
  • PolynomialRing
  • ProductRing
  • QuotientRing
  • SchurRing

    • Here are some particular rings:

  • ZZ
  • QQ

    • Tests:

  • isAffineRing
  • isCommutative
  • isField
  • isPolynomialRing
  • isQuotientOf
  • isQuotientRing
  • isRing

    • Here are some functions:

  • ZZ _ Ring -- get integer elements of a ring.
  • Ring _ ZZ -- get a generator of a ring.
  • Ring _ String -- getting generators by name
  • Ring _ List -- getting monomials with given exponents
  • char
  • coefficientRing
  • lift
  • map
  • promote
  • ring

    • Ways to create new rings:

  • Ring ** Ring -- tensor product of rings
  • Ring OrderedMonoid -- monoid ring
  • symmetricAlgebra -- symmetric algebra

    • Here are some keys used in rings:

  • baseRings
  • Engine
  • modulus

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