[Axiom-developer] efficiency consideration in Axiom

[Renaud . Rioboo]

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-------------------------------

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
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
----------------NAG Axiom's 2.3-------------------------------

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

                Renaud