[Axiom-developer] [Axiom-mail]

[Bill Page]

Changes http://page.axiom-developer.org/zope/mathaction/AxiomMail/diff
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-On Wednesday, December 29, 2004 2:28 AM you wrote:
-> 
-> seems to be a categorical error of some sort.
-> 
-> A: Complex Polynomial Integer
-> 
-> tells the system that 'A' is expected to have a value which is
-> Complex Polynomial Integer.
-> 
-> 'conjugate' works on values, not potential values.
-> 
-> Thus, conjugate(A) has no meaning as 'A' has no value.
-> This should probably be an error.
-> 
-> If axiom could work with so that conjugate worked on the type
-> then axiom could work at some sort of an 'axiomatic' level
-> rather than a symbolic computation level. Perhaps when we join
-> forces with the ACL2 crowd we could state certain theorems and
-> have them applied in the absence of a value.
-> 

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-> On Wednesday, December 29, 2004 2:28 AM you wrote:
-> > 
-> > seems to be a categorical error of some sort.
-> > 
-> > A: Complex Polynomial Integer
-> > 
-> > tells the system that 'A' is expected to have a value which is
-> > Complex Polynomial Integer.
-> > 
-> > 'conjugate' works on values, not potential values.
-> > 
-> > Thus, conjugate(A) has no meaning as 'A' has no value.
-> > This should probably be an error.
-> > 
-> > If axiom could work with so that conjugate worked on the type
-> > then axiom could work at some sort of an 'axiomatic' level
-> > rather than a symbolic computation level. Perhaps when we join
-> > forces with the ACL2 crowd we could state certain theorems and
-> > have them applied in the absence of a value.
-[29 more lines...]

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++added:


??changed:
-                                                                       Type: 
Void
                                                      Type: Void

??changed:
-                                                                       Type: 
Void
                                                      Type: Void

??changed:
-                                                 Type: Complex Polynomial 
Integer
                                    Type: Complex Polynomial Integer

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-    "It's not the people who vote that count. It's the people who count the
-    votes." -- Joseph Stalin
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-From root Fri Dec 31 03:21:28 -0600 2004
-From: root
-Date: Fri, 31 Dec 2004 03:21:28 -0600
-Subject: happy new year
-Message-ID: <address@hidden>
-
-*,
-
-Well, it's not merged yet and on linux only so far but ....
-
-axiom
-
-
-starts axiom and hypertex. from hypertex it is possible to go into
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-In-Reply-To: <address@hidden>
-       (message from bertrand roessli on Fri, 14 Jan 2005 16:14:34 +0100
-       (CET))

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-From Billinghurst,David(CALCRTS) Tue Jan 18 16:58:15 -0600 2005
-From: Billinghurst,
-       David (CALCRTS)
-Date: Tue, 18 Jan 2005 16:58:15 -0600
-Subject: Building axiom on windows
-Message-ID: <address@hidden>
-
-I would like to try and build axiom under windows/mingw. I already know how to:
- - compile gcl-2.6.5 and gcl-2.6.6pre (from CVS)
- - compile, test and package maxima
- - compile and test ACL2
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??changed:
-In ...\mnt\windows\
In ...\mnt\windows\ ::

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-On Friday, January 14, 2005 7:05 AM Billinghurst, David (CALCRTS)
-wrote:
-
-> > 
-> > So this would be the minimum list of files that are needed
-> > by GCL in order to do a compile and where to put them?
-> > 
-> > I would also prefer to include these files in the Axiom
-> > installation program so that no other software installations
-> > are required by the user to get a fully functional system.
-> > 
->
- 
-> This is the setup for maxima-5.9.1, using gcc-3.3.1.  There
-> will be slight variation for other versions of gcc.
-> 
-> First we need to put gcc.exe somewhere in the path.
-> I think that the logical place is axiom/mnt/windows/bin.  
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??changed:
-> 
-> I am trying to make Axiom evaluate sum(1/k^2, k=1..n).  It 
-> returns the sum unevaluated.  I suspect that I should be
-> using the sum functions defined in package SUMRF,
-> RationalFunctionSum, but how do I make Axiom use those
-> functions?  For example, I tried
-> 
-> (1) -> sum(1/k^2, k=1..n)$SUMRF
-> 
->   Although RationalFunctionSum is the name of a constructor,
->   a full type must be specified in the context you have used
->   it. Issue
->        )show RationalFunctionSum for more information.
-> (1) ->
-> 


??changed:
-says:
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-(2) -> )show RationalFunctionSum
says::

 (2) -> )show RationalFunctionSum

??changed:
-------------------------------- Operations --------------------------------
 --------------------------- Operations --------------------------------

??changed:
-RetractableTo Integer
RetractableTo Integer::

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??changed:
-exactly which one you mean.
-
-(2) -> )display op sum
-
-There are 6 exposed functions called sum :
exactly which one you mean.::

 (2) -> )display op sum

 There are 6 exposed functions called sum :

??changed:
-There are 5 unexposed functions called sum :
There are 5 unexposed functions called sum ::


??changed:
-                                          Type: Union(Expression
-Integer,...)
                          Type: Union(Expression Integer,...)

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-> Kostas,
->
-> My previous reply did not address the issue of the reason why
-> Axiom returns the sum unevaluated. Here is what I could find out:
->
-> On Sunday, January 23, 2005 11:08 AM you wrote:
->>
->> I am trying to make Axiom evaluate sum(1/k^2, k=1..n).  It
->> returns the sum unevaluated.
->
-> I expect the reason that it returns unevaluated is because Axiom
-> is simply incomplete. For example Maple gives:
->
->> sum(1/k^2, k=1..n);
->                                       1   2
->                      -Psi(1, n + 1) + - Pi
->                                       6
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-On Sun, 30 Jan 2005 08:23:33 -0500
-  root <address@hidden> wrote:
->The February 2005 release of Axiom has been posted to:
->
->  savannah.nongnu.org/projects/axiom
->  sourceforge.net/projects/axiom
->  arch.axiom-developer.org as axiom--main--1--patch-29
->
->This is the first "feature complete" release of Axiom. It 
->includes
->all of the algebra we have available, working graphics, 
->and a working
->hyperdoc browser. Once you build the system you can test 
->it by typing:
->
->axiom
->
->when the hyperdoc browser starts choose
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-On Sunday, January 30, 2005 1:23 PM Gilbert Baumslag wrote:
-> 
-> I looked in all three sites for the February release, but 
-> it appears nowhere to my relatively unpracticed eye. Is 
-> this release really where advertized below?
-> 
-> Gilbert
-> 
-> On Sun, 30 Jan 2005 08:23:33 -0500
->   root <address@hidden> wrote:
-> >The February 2005 release of Axiom has been posted to:
-> >
-> >  savannah.nongnu.org/projects/axiom
-> >  sourceforge.net/projects/axiom
-> >  arch.axiom-developer.org as axiom--main--1--patch-29
-> >
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-Kostas Oikonomou writes:
- > 
- > But I was disappointed by the sum(1/k^2, k=1..n) example.  I saw that
- > Gosper's method is implemented in sum.spad.pamphlet, but this (rather
- > simple) sum needs symbolic manipulation of gamma and psi functions, which is
- > not there.  More generally, special functions seem to be handled only
- > numerically.  At least for my prospective use of Axiom, this points to a
- > rather big "hole". And I wonder how many others of this sort there are.
- > 
- > I also tried sum(1/(k*(k+a)), k=1..n).  That was also returned unevaluated,
- > although Gosper's method should handle it.

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-Page, Bill wrote:
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->Changes http://page.axiom-developer.org/zope/mathaction/AxiomMail/diff
->--
->On Thursday, February 17, 2005 3:29 PM Ning Wang wrote:
->  
->
->>Can I define an infinite set by the axiom of comprehension
->>or the axiom of replacement?
->>
->>    
->>
->
->The short (but incomplete) answer is "no". At least not in an
->entirely abstract manner. But Axiom does provide tools
->specifically for dealing with "infinite", i.e. indefinitely
->large, lists called streams.
->
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-On Thursday, March 17, 2005 12:29 AM Zoran Spasojevic wrote:
-> I previously compiled axiom without problems but this time
-> on Fedora Core 3 I get the  error below after a few minutes
-> of compiling. I would appreciate any suggestions that anyone
-> may have to resolve this problem.
-> Thanks,
-> Zoran
-> 
-> gcc -c -Wall -DVOL=volatile -fsigned-char -pipe -O3 
-> -fomit-frame-pointer  -I/home/zoran/axiom/lsp/gcl-2.6.5/o -I../h 
-> -I../gcl-tk sfasl.c
-> In file included from sfasl.c:40:
-> sfaslbfd.c: In function `fasload':
-> sfaslbfd.c:266: error: structure has no member named `_raw_size'
-> ...
-
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??changed:
-Examples:
-
-base of 4     base of 5 
-n  FF BFF     n  FF BFF 
-----------    ----------
-0  0   0      0  0   0  
-1  1   1      1  1   1  
-2  2   2      2  2   2  
-3  3  -1      3  3  -2  
-4  0   0      4  0  -1  
-5  1   1      5  1   0  
-              6  0   0  
Examples::

  base of 4     base of 5 
  n  FF BFF     n  FF BFF 
  ----------    ----------
  0  0   0      0  0   0  
  1  1   1      1  1   1  
  2  2   2      2  2   2  
  3  3  -1      3  3  -2  
  4  0   0      4  0  -1  
  5  1   1      5  1   0  
                6  0   0  

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??changed:
-It will roughly work as follows:
-
-
-)abbrev domain BAL Balanced
-Balanced(n:PositiveInteger):Exports == Implementation where
- 
-  Exports == with
-    coerce: PrimeField n -> $
-    coerce: $ -> OutputForm
-
---    coerce: $ -> PrimeField n
-
-  Implementation == add
-    Rep := Integer
-
-    coerce(a: PrimeField n):$ == convert(a)@Integer - n
-    coerce(x:%):OutputForm == coerce(x)$Rep
-
--------------------------------------------------------------------------------
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It will roughly work as follows::

  )abbrev domain BAL Balanced
  Balanced(n:PositiveInteger):Exports == Implementation where
 
    Exports == with
      coerce: PrimeField n -> $
      coerce: $ -> OutputForm

  --  coerce: $ -> PrimeField n

    Implementation == add
      Rep := Integer

      coerce(a: PrimeField n):$ == convert(a)@Integer - n
      coerce(x:%):OutputForm == coerce(x)$Rep

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

  If you need explanation, ask for it. (No time right now)

  Martin

  See also: BalancedFiniteField

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