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Re: [Axiomdeveloper] about Expression Integer
From: 
Gabriel Dos Reis 
Subject: 
Re: [Axiomdeveloper] about Expression Integer 
Date: 
21 Feb 2006 12:57:12 +0100 
Ralf Hemmecke <address@hidden> writes:
 On 02/20/2006 10:02 PM, Gabriel Dos Reis wrote:
 > Ralf Hemmecke <address@hidden> writes:
 >  Hmm, do you call the following objectoriented?
 > Yes.
 >  (That code appears in libalgebra distributed with Aldor and it
 >  basically provides a generic function that given a function "f: R >
 >  S" returns a function "map(f)" of type "RX > SX" that applies "f" on
 >  the coefficients of a univariate polynomial.)
 >   UnivariateFreeRing2(
 >  R : Join(ArithmeticType, ExpressionType),
 >  RX: UnivariateFreeRing R,
 >  S : Join(ArithmeticType, ExpressionType),
 >  SX: UnivariateFreeRing S
 >  ): with {
 >  map: (R > S) > RX > SX;
 >  } == add {
 >  map(f:R > S)(p:RX):SX == {
 >  q:SX := 0;
 >  for term in p repeat {
 >  (c, n) := term;
 >  q := add!(q, f c, n);
 >  }
 >  q;
 >  }
 >  }
 >   What is the class and what are the methods?
 > The class is the collection of "things" that you can "pretend" to be
 > univariate polynomials.

 Oh, I think that is wrong.
I don't think so.
 The "univariate polynomials" come as a
 parameter and have nothing to do with UnivariateFreeRing2.
Not quite. "Univariate polynomial" is a bundle of methods, whether it
is a parameter database or a global database is largely irrelevant.
What is relevant is the structure it exposes both interface and
overridable functions.
 Gaby
 [Axiomdeveloper] Re: 1: %, (continued)
 [Axiomdeveloper] Re: 1: %, Gabriel Dos Reis, 2006/02/21
 [Axiomdeveloper] Re: 1: %, Gabriel Dos Reis, 2006/02/21
 [Axiomdeveloper] Re: 1: %, Ralf Hemmecke, 2006/02/22
 [Axiomdeveloper] Re: 1: %, Gabriel Dos Reis, 2006/02/23
 [Axiomdeveloper] Re: 1: %, Ralf Hemmecke, 2006/02/22
 [Axiomdeveloper] Re: 1: %, Gabriel Dos Reis, 2006/02/23
 [Axiomdeveloper] Re: 1: %, Ralf Hemmecke, 2006/02/22
 Re: [Axiomdeveloper] about Expression Integer, Ralf Hemmecke, 2006/02/21
 Re: [Axiomdeveloper] about Expression Integer, Gabriel Dos Reis, 2006/02/20
 Re: [Axiomdeveloper] about Expression Integer, Ralf Hemmecke, 2006/02/21
 Re: [Axiomdeveloper] about Expression Integer,
Gabriel Dos Reis <=
 RE: [Axiomdeveloper] about Expression Integer, Bill Page, 2006/02/20
 Re: [Axiomdeveloper] about Expression Integer, Ralf Hemmecke, 2006/02/21
 Re: [Axiomdeveloper] about Expression Integer, Ralf Hemmecke, 2006/02/21
 RE: [Axiomdeveloper] about Expression Integer, Bill Page, 2006/02/21
 Re: [Axiomdeveloper] about Expression Integer, Ralf Hemmecke, 2006/02/21
 RE: [Axiomdeveloper] about Expression Integer, Bill Page, 2006/02/21
 Re: [Axiomdeveloper] about Expression Integer, Doug Stewart, 2006/02/20
 RE: [Axiomdeveloper] about Expression Integer, Bill Page, 2006/02/21
 Re: [Axiomdeveloper] about Expression Integer, Francois Maltey, 2006/02/19
 RE: [Axiomdeveloper] about Expression Integer, Bill Page, 2006/02/19