diff -r 237190475d79 -r 7957d26c3334 src/HOL/Algebra/README.html --- a/src/HOL/Algebra/README.html Mon Mar 25 19:53:44 2013 +0100 +++ b/src/HOL/Algebra/README.html Mon Mar 25 20:00:27 2013 +0100 @@ -68,42 +68,10 @@ Degree function. Universal Property. -

Legacy Development of Rings using Axiomatic Type Classes

- -

This development of univariate polynomials is separated into an -abstract development of rings and the development of polynomials -itself. The formalisation is based on [Jacobson1985], and polynomials -have a sparse, mathematical representation. These theories were -developed as a base for the integration of a computer algebra system -to Isabelle [Ballarin1999], and was designed to match implementations -of these domains in some typed computer algebra systems. Summary: - -

Rings: - Classes of rings are represented by axiomatic type classes. The - following are available: +

Development of Polynomials using Type Classes

-
-  ring:		Commutative rings with one (including a summation
-		operator, which is needed for the polynomials)
-  domain:	Integral domains
-  factorial:	Factorial domains (divisor chain condition is missing)
-  pid:		Principal ideal domains
-  field:	Fields
-
- - Also, some facts about ring homomorphisms and ideals are mechanised. - -

Polynomials: - Polynomials have a natural, mathematical representation. Facts about - the following topics are provided: - -

-
  • Degree function -
  • Universal Property, evaluation homomorphism -
  • Long division (existence and uniqueness) -
  • Polynomials over a ring form a ring -
  • Polynomials over an integral domain form an integral domain -
  • +

    A development of univariate polynomials for HOL's ring classes +is available at HOL/Library/Polynomial.

    [Jacobson1985] Nathan Jacobson, Basic Algebra I, Freeman, 1985.