Renaud wrote to the axiom-developer:

Dear Axiom fans,

I am wanting to produce new versions for my Real Closure package and I am willing to use Open Axiom while I was mainly using NAG's Axion version.

I am using my RealClosure package which is the same for Open Axiom than the one I use in NAG's Axiom 2.3 since Tim downloaded the RECLOS version from my website.

I am however experiencing efficiency problems. Here is an example:

   ----------------Open Axiom-------------------------------
   (6) -> a3 := sqrt(-(5739 - 9473525*a2),3)

          +------------------------------------------------------------------+
          |        +-------------------------------------------------+
          |        |         +-------------------------------+
         3|       3|        3|            3+-+
    (6)  \|9473525\|92526953\|316737007504\|2  - 399063623035  - 5539  - 5739
                                            Type: RealClosure Fraction Integer
                         Time: 48.04 (EV) + 0.01 (OT) + 15.60 (GC) = 63.65 sec
 (7) -> a4 := sqrt(-(1 - 1283*a3),3)

    (7)
    ROOT
           1283
        *
            +------------------------------------------------------------------+
            |        +-------------------------------------------------+
            |        |         +-------------------------------+
           3|       3|        3|            3+-+
           \|9473525\|92526953\|316737007504\|2  - 399063623035  - 5539  - 5739
       +
         - 1
   ,
       3
                                            Type: RealClosure Fraction Integer
                                  Time: 744.11 (EV) + 182.66 (GC) = 926.77 sec

   ----------------Open Axiom-------------------------------

Open Axiom

Let's compare this to a live test of Axiom here on the AxiomWiki.

)set message time on

Creates an algebraic number

Ran := RealClosure( Fraction(Integer) )

(1)

Time: 0.05 (OT) + 0.03 (GC) = 0.08 sec

a2 := sqrt(2)$Ran

(2)

Time: 0.04 (OT) = 0.04 sec

a3 := sqrt(-(5739 - 9473525*a2),3)

(3)

Time: 0.01 (EV) = 0.01 sec

a4 := sqrt(-(1 - 1283*a3),3)

(4)

Time: 0.04 (EV) + 0.01 (OT) + 0.04 (GC) = 0.09 sec

Compared to:

  Time: 744.11 (EV) + 182.66 (GC) = 926.77 sec

Renaud continues...

wheras

NAG Axiom's 2.3:

  G82322 (5) -> a3 := sqrt(-(5739 - 9473525*a2),3)

         +------------------------------------------------------------------+
         |        +-------------------------------------------------+
         |        |         +-------------------------------+
        3|       3|        3|            3+-+
   (5)  \|9473525\|92526953\|316737007504\|2  - 399063623035  - 5539  - 5739
                                           Type: RealClosure Fraction Integer

 Time: 0.07 (EV) = 0.07 sec

NAG Axiom's 2.3:

  G82322 (6) -> a4 := sqrt(-(1 - 1283*a3),3)

   (6)
   ROOT
          1283
       *
           +------------------------------------------------------------------+
           |        +-------------------------------------------------+
           |        |         +-------------------------------+
          3|       3|        3|            3+-+
          \|9473525\|92526953\|316737007504\|2  - 399063623035  - 5539  - 5739
      +
        - 1
  ,
      3
                                           Type: RealClosure Fraction Integer

 Time: 0.59 (EV) + 0.11 (GC) = 0.70 sec

Which makes a factor above 1000 ! Anyone has an idea ?

Renaud

http://www-calfor.lip6.fr/~rr/

It seems that this problem is solved: http://lists.nongnu.org/archive/html/axiom-developer/2004-07/msg00132.html

It was in cvs by July 19, http://lists.nongnu.org/archive/html/axiom-developer/2004-07/msg00154.html but the version of Axiom that we are using here on MathAction was built before that

)version

Value = "Friday November 9, 2007 at 19:35:06 "