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Subject: [Axiom-developer] Axiom on savannah.nongnu.org has moved to git
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There was a hard disk failure on the savannah.nongnu.org server.
As a result the Axiom CVS sources were lost.

The latest git version has been posted at 
http://savannah.nongnu.org/projects/axiom

I have been debating the wisdom of maintaining CVS and SVN versions of
Axiom. At this point, the debate is closed. I see no value in
maintaining CVS and SVN versions so they will be dropped everywhere
and moved to git.

The distributed version control model used by git means that every
copy of the repository (including your own) IS the master repository.
There is no need for a central server although these will still be 
maintained for git.

Axiom release sources are available with git using:

git clone git://github.com/daly/axiom.git  (github)
git clone git://git.sv.gnu.org/axiom.git   (savannah)




If you do need a CVS checkout you can use:

cvs -d:pserver:anonymous@pserver.git.sv.gnu.org:/autoconf.git co -d autoconf master

Detailed instructions are at:

http://savannah.gnu.org/maintenance/UsingGit

Tim





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Subject: [Axiom-developer] Re: [fricas-devel] Re: [Axiom-mail] InputForm
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Gabriel Dos Reis wrote:
> Tim Daly <daly@axiom-developer.org> writes:
>
> | I've been reading this thread. It seems to me that what people are seeking
> | is a symbolic algebra rather than a computer algebra system. The distinction
> | is that a symbolic system manipulates input as parse trees in
> | syntactic form.
> | A computer algebra system manipulates input as semantic forms. It appears
> | that you want to recover the syntax from the semantics, a very hard problem.
>
> OpenAxiom has the Syntax domain for matters that are purely syntactic,
>
> OpenAxiom's intended  of InputForm is that of expressions the semantics
> of which yield computer representation of mathematical object.  In
> particular, you can think of Syntax objects are pre-InputForm objects --
> syntactic objects that have not yet been type checked.  So a Syntax object
> is really a member of an initial algebra -- unlike InputForm or
> SExpression objects. 
>
> | This discussion came up before. At the time I wrote the beginnings of a
> | symbolic front end to Axiom based on Joel Cohen's work. Joel has given
> | me permission to use his books as part of the effort.
>
> I'm familiar with his work (and his two books).  I would think that
> there already exist a domain constructor, Expression, that is most
> suited for the work presented in the two volumes.  The fundamental
> building block is the Kernel domain constructor.  I know some people
> have expressed profound dislikes of the Expression domain constructor.
> But, I suspect that they would have a deeper appreciation of it after
> reading Cohen's work.
>
> The need for InputForm is not just for 'symbolic mathematics'.  A proper
> support for the compilation model of the Spad language requires that any
> constructor argument be coercible to InputForm.  A fact that is not --
> at the moment -- enforced, but that is deeply relied upon.  See what the
> devaluate functions do and the unspolem assumptions behind.
>
> It is on my TODO list that OpenAxiom-1.3.x and up will enforce those
> assumptions. 
>
> -- Gaby
>
>   
So you propose that there are two reasons for this discussion of InputForm,
one of which is to support a computational model of the spad language
and the other is to support symbolic manipulation?

It is unclear what to expect from InputForm.
Under the assumption of a computational model it seems that x+y^2 == y^2+x
Under the assumption of a cohen symbolic model they are not equivalent.
(assuming that plus is associative in both cases)

Given that there was a comment that the input form was not properly 
reproduced
I assumed the discussion involved symbolic issues. Perhaps I misread it.

I do not see how InputForm can be made to support both models.

Tim




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I've been reading this thread. It seems to me that what people are seeking
is a symbolic algebra rather than a computer algebra system. The distinction
is that a symbolic system manipulates input as parse trees in syntactic 
form.
A computer algebra system manipulates input as semantic forms. It appears
that you want to recover the syntax from the semantics, a very hard problem.

This discussion came up before. At the time I wrote the beginnings of a
symbolic front end to Axiom based on Joel Cohen's work. Joel has given
me permission to use his books as part of the effort.

Joel describes a symbolic, expression tree based system for doing
computational mathematics. I call this a "Cohen Algebra". Using these
expression trees allows us to carefully craft and manipulate the expressions
in ways that Axiom would not normally permit because they are not
semantically valid. As long as the forms are never coerced to Axiom
domains until they are semantically valid, it is possible to do many
"badly formed" intermediate manipulations, some of which are very
useful for teaching purposes.

We can get the Cohen algebra into Axiom using categories, domains, and
packages that support expression tree I/O and coercions to and from
Axiom domains, e.g.
   cohenPolynomial(cohenInteger) <-> Polynomial(Integer)

This enables us to address several issues that have been outstanding
in the field for a while, including those mentioned at the last conference:

  *) It would be possible to do "step-by-step" output (Watt?)
          That is, you could show the steps of solving 3*x=6
           by showing the step of dividing both sides by 3
              3       6
              -  x =  -
              3       3
         and preserve the 3 on both sides

   *) It would be possible to do "step-by-step* explanations (Watt?)
          Algorithms in the Cohen domains could easily have
          explanations attached to the operations so that it could
          automatically print:
               "divide each side by 3"

     *) It would be possible to modify the output if the result
          turned into "wallpaper" (as mentioned by Davenport).
          So you could simply print the condensed output of a
          groebner basis computation.

      *) It would be much easier to input and output forms for
          other systems (e.g. supporting OpenMath output)
          (Davenport)

I plan to do more work on Cohen domains because all of the
above features would be useful. My simple test example domains
are attached.

In my opinion, the idea of using InputForm beyond its intended
interpreter connections is not a viable effort. It would be much
easier and more profitable to construct something like the Cohen
domains to support the goal.

Tim

============================================

)abbrev category CCAT CohenCategory

+++ Author: Timothy Daly
+++ Date Created: 7 April 2007
+++ Description: Joel Cohen's Computer Algebra and Symbolic Computation
CohenCategory(): Category == SetCategory with

  kind:(CExpr)->Boolean
    ++ kind(CExpr)
  operand:(CExpr,Integer)->CExpr
    ++ operand:(CExpr,Integer)
  numberOfOperand:(CExpr)->Integer
    ++ numberOfOperand:(CExpr)->Integer
  construct:(CExpr,CExpr)->CExpr
    ++ construct:(CExpr,CExpr)->CExpr

-------------------------------------------------------------------
)abbrev domain CTERM CohenTerm

+++ Author: Timothy Daly
+++ Date Created: 7 April 2007
+++ Description: Joel Cohen's Computer Algebra and Symbolic Computation
CohenTerm(): Exports == Implementation where
  OUT     ==> OutputForm
  ATTRIBS ==> Record(attrib: String, value: String)
  UNION   ==> Union(Symbol,String,Integer)
  TAGS    ==> Record(name:UNION, tags:List ATTRIBS)

  Exports ==> CohenCategory with
    term: () -> %
    term: Symbol -> %
    term: String -> %
    term: Integer -> %
    name: % -> String
    tags: % -> List ATTRIBS
    coerce: Symbol -> %
    coerce: String -> %
    coerce: Integer -> %
    coerce: % -> OUT
    _=: (%,%) -> Boolean

  Implementation ==> add

    Rep := TAGS

    tagPair(atype:String,thetype:String):ATTRIBS ==
      attr:ATTRIBS:=[atype,thetype]

    name(t0:%):String ==
      t1:=t0.name
      t1 case Symbol  => string t1
      t1 case String  => t1
      t1 case Integer => string t1
      "failed"

    tags(t0:%):List ATTRIBS == t0.tags

    term():% ==
      attr:List ATTRIBS:= list tagPair("type","String")
      aname:=""::UNION
      result:TAGS:=[aname,attr]
      result

    term(s:Symbol):%  == [s,[tagPair("type","Symbol")]]
    coerce(s:Symbol):%  == [s,[tagPair("type","Symbol")]]

    term(s:String):%  == [s,[tagPair("type","String")]]
    coerce(s:String):%  == [s,[tagPair("type","String")]]

    term(s:Integer):% == [s,[tagPair("type","Integer")]]
    coerce(s:Integer):% == [s,[tagPair("type","Integer")]]

    coerce(arg:%):OUT ==
      t0:=arg.name
      t1:=arg.tags
      t2:=
        t0 case Symbol  => outputForm t0
        t0 case String  => outputForm t0
        t0 case Integer => outputForm t0
        "failed"
      --bracket [ t2, t1.1 ]
      t2
 
    a = b ==
      a.name = b.name


-------------------------------------------------------------------
)abbrev domain CTREE CohenTree

+++ Author: Timothy Daly
+++ Date Created: 7 April 2007
+++ Description: Joel Cohen's Computer Algebra and Symbolic Computation
CohenTree(S: CohenCategory): Exports == Implementation where
  Exports == BinaryTreeCategory(S) with
   cohenTree: S -> %
    ++ cohenTree(v) is an non-empty cohen tree
    ++ with value v, and left and right empty.
    ++
    ++X t1:=cohenTree([1,2,3])
   
   cohenTree: (%,S,%) -> %   
    ++ cohenTree(l,v,r) creates a cohen tree with
    ++ value v with left subtree l and right subtree r.
    ++
    ++X t1:=cohenTree([1,2,3])
    ++X t2:=cohenTree([4,5,6])
    ++X cohenTree(t1,[7,8,9],t2)

   cohenTree: (%,S) -> %
    ++ cohenTree(v,r) creates a cohen tree with
    ++ value v with right subtree r.

   cohenTree: (S,%) -> %
    ++ cohenTree(l,v) creates a cohen tree with
    ++ value v with left subtree l

   empty: () -> %
    ++ empty()
   empty?: % -> Boolean
    ++ empty?(a)
   leaf?: % -> Boolean
    ++ leaf?(a)
   left: % -> %
    ++ left(a)
   node: (%,S,%) -> %
    ++ node(a,b,c)
   right: % -> %
    ++ right(a)
   setleft_!: (%,%) -> %
    ++ setleft!(a,b)
   setright_!: (%,%) -> %
    ++ setright!(a,b)
   setvalue_!: (%,S) -> S
    ++ setvalue!(a,b)
   value: % -> S
    ++ value(a)
   
  Implementation == add
   Rep := List Tree S

   cohenTree(v:S) == node(empty(),v,empty())
   cohenTree(l:%,v:S,r:%):% == node(l,v,r)
   cohenTree(l:%,v:S):% == node(l,v,empty())
   cohenTree(v:S,r:%):% == node(empty(),v,r)
   empty()== [] pretend %
   empty? t == empty?(t)$Rep
   leaf? t  == empty? t or empty? left t and empty? right t
   left t ==
     empty? t => error "cohenTree:no left"
     children first t
   node(l,v,r) == cons(tree(v,l:Rep),r:Rep)
   right t ==
     empty? t => error "cohenTree:no right"
     rest t
   setleft_!(t1,t2) ==
     empty? t1 => error "cohenTree:no left to set"
     setchildren_!(first(t1:Rep),t2:Rep)
     t1
   setright_!(t1,t2) ==
     empty? t1 => error "cohenTree:no right to set"
     setrest_!(t1:List Tree S,t2)
   setvalue_!(t,nd) ==
     empty? t => error "cohenTree:no value to set"
     setvalue_!(first(t:Rep),nd)
     nd
   value t ==
     empty? t => error "cohenTree:no value"
     value first t
   t1 = t2 == (t1::Rep) =$Rep (t2::Rep)


-------------------------------------------------------------------
--  a:=a::CTERM
--  b:=b::CTERM
--  c:=a+b
--  left(c)
--  right(c)
--  d:=3::CTERM
--  e:=d*c
--  left(e)
--  right(e)
-- 
--  -- Figure 3.4 p88
--  )clear all
-- 
--  c:=c::CTERM
--  d:=d::CTERM
--  x:=x::CTERM
--  two:=2::CTERM
--  e:=c+d*x^2
-- 
--  -- Figure 3.5a p89
--  )clear all
--  a:=a::CTERM
--  b:=b::CTERM
--  c:=c::CTERM
--  d:=a*b+c
--  e:=-d

-------------------------------------------------------------------
)abbrev package CMATH CohenMath

+++ Author: Timothy Daly
+++ Date Created: 7 April 2007
+++ Description: Joel Cohen's Computer Algebra and Symbolic Computation
CohenMath: Exports == Implementation where
  TERM ==> CohenTerm
  TREE ==> CohenTree(TERM)
 
  Exports ==> with
   _-: (TERM) -> TREE
    ++ -a
   _-: (TREE) -> TREE
    ++ -a

--   "!": (TERM) -> TREE
--    ++ a!
--   "!": (TREE) -> TREE
--    ++ a!

   _-: (TERM,TERM) -> TREE
    ++ a-b
   _-: (TERM,TREE) -> TREE
    ++ a-b
   _-: (TREE,TERM) -> TREE
    ++ a-b
   _-: (TREE,TREE) -> TREE
    ++ a-b

   _+: (TERM,TERM) -> TREE
    ++ a+b
   _+: (TERM,TREE) -> TREE
    ++ a+b
   _+: (TREE,TERM) -> TREE
    ++ a+b
   _+: (TREE,TREE) -> TREE
    ++ a+b

   _*: (TERM,TERM) -> TREE
    ++ a*b
   _*: (TERM,TREE) -> TREE
    ++ a*b
   _*: (TREE,TERM) -> TREE
    ++ a*b
   _*: (TREE,TREE) -> TREE
    ++ a*b

   _^: (TERM,TERM) -> TREE
    ++ a*b
   _^: (TERM,TREE) -> TREE
    ++ a*b
   _^: (TREE,TERM) -> TREE
    ++ a*b
   _^: (TREE,TREE) -> TREE
    ++ a*b

  Implementation ==> add

   --- handle unary prefix terms

   prefixTerm(op:TERM,b:TERM):TREE  == cohenTree(op,cohenTree(b))
   prefixTree(op:TERM,b:TREE):TREE  == cohenTree(op,b)

   --- handle unary postfix terms

   postfixTerm(a:TERM,op:TERM):TREE == cohenTree(cohenTree(a),op)
   postfixTree(a:TREE,op:TERM):TREE == cohenTree(a,op)

   --- handle binary terms

   termOpTerm(a:TERM,op:TERM,b:TERM):TREE ==
      cohenTree(cohenTree(a),op,cohenTree(b))

   termOpTree(a:TERM,op:TERM,b:TREE):TREE ==
      cohenTree(cohenTree(a),op,b)

   treeOpTerm(a:TREE,op:TERM,b:TERM):TREE ==
      cohenTree(a,op,cohenTree(b))

   treeOpTree(a:TREE,op:TERM,b:TREE):TREE ==
      cohenTree(a,op,b)

   _-(b:TERM):TREE         == prefixTerm(term("-")$TERM,b)
   _-(c:TREE):TREE         == prefixTree(term("-")$TERM,c)

--   "!"(a:TERM):TREE         == postfixTerm(a,term("!")$TERM)
--   "!"(a:TREE):TREE         == postfixTree(a,term("!")$TERM)

   _-(a:TERM, b:TERM):TREE == termOpTerm(a,term("-")$TERM,b)
   _-(a:TERM, b:TREE):TREE == termOpTree(a,term("-")$TERM,b)
   _-(a:TREE, b:TERM):TREE == treeOpTerm(a,term("-")$TERM,b)
   _-(a:TREE, b:TREE):TREE == treeOpTree(a,term("-")$TERM,b)

   _+(a:TERM, b:TERM):TREE == termOpTerm(a,term("+")$TERM,b)
   _+(a:TERM, b:TREE):TREE == termOpTree(a,term("+")$TERM,b)
   _+(a:TREE, b:TERM):TREE == treeOpTerm(a,term("+")$TERM,b)
   _+(a:TREE, b:TREE):TREE == treeOpTree(a,term("+")$TERM,b)

   _*(a:TERM, b:TERM):TREE == termOpTerm(a,term("*")$TERM,b)
   _*(a:TERM, b:TREE):TREE == termOpTree(a,term("*")$TERM,b)
   _*(a:TREE, b:TERM):TREE == treeOpTerm(a,term("*")$TERM,b)
   _*(a:TREE, b:TREE):TREE == treeOpTree(a,term("*")$TERM,b)

   _^(a:TERM, b:TERM):TREE == termOpTerm(a,term("^")$TERM,b)
   _^(a:TERM, b:TREE):TREE == termOpTree(a,term("^")$TERM,b)
   _^(a:TREE, b:TERM):TREE == treeOpTerm(a,term("^")$TERM,b)
   _^(a:TREE, b:TREE):TREE == treeOpTree(a,term("^")$TERM,b)


-------------------------------------------------------------------
)abbrev domain COHEN CohenAlgebra

+++ Author: Timothy Daly (based on Joel Cohen's books)
+++ Date Created: 7 April 2007
+++ Description:
+++ This type represents symbolic algebra as detailed in Joel Cohen's
+++ books "Computer Algebra and Symbolic Computation"
+++ A.K. Peters, Ltd. ISBN 1-56881-159-4
+++
+++ Elements of this domain are purely symbolic expressions represented
+++ in a tree structure.

CohenAlgebra(X : CohenCategory) : CohenCategory with

  _+: (X,X) -> %
   ++ x + y is the formal sum of the input arguments

  _/: (X,X) -> %
   ++ x / y is the formal fraction of the input arguments

  numer : % -> X
   ++ numer(x) is the numerator of the formal fraction

  denom : % -> X
   ++ denom(x) is the denominator of the formal fraction

  if X has IntegralDomain then
 
    coerce : % -> Fraction(X)
     ++ coerce(x) from here to Fraction(there)

    coerce : Fraction(X) -> %
     ++ coerce(x) from Fraction(there) to here

  if X has Field then
   
    coerce : % -> X
     ++ coerce from here to Field(there)

 == add

  import Record(num : X, den : X)
 
  Rep := Record(num : X, den : X)  -- representation

-- (a::CTERM + b::CTERM)$COHEN(CTERM)
-- c:CTERM:=d
-- e:CTERM:=f
-- (c+e)$COHEN(CTERM)

  (n:X + d:X):% == [n,d]
 
-- (a::CTERM / b::CTERM)$COHEN(CTERM)
-- c:CTERM:=d
-- e:CTERM:=f
-- (c/e)$COHEN(CTERM)

  (n:X / d:X):% == [n,d]
 
-- g:=(c/e)$COHEN(CTERM)
-- h:=(c/e)$COHEN(CTERM)
-- (g=h)
-- (g=h)::Boolean
-- i:=(a::CTERM / b::CTERM)$COHEN(CTERM)
-- j:=(a::CTERM / b::CTERM)$COHEN(CTERM)
-- (i=j)::Boolean
-- (g=i)
-- (g=i)::Boolean

  _=(x:%, y:%):Boolean == (x.num = y.num) and (x.den = y.den)

-- numer g
-- numer i

  numer(r:%):X == r.num

--denom g
--denom i

  denom(r:%):X == r.den

  coerce(r:%):OutputForm == (r.num :: OutputForm) / (r.den :: OutputForm)



-- COMPLEX(INT) has FIELD
-- COMPLEX(INT) has IntegralDomain
-- p:COMPLEX(INT):=2
-- p::FRAC(COMPLEX(INT))::COHEN(COMPLEX(INT))

  if X has IntegralDomain then
 
    coerce(r : %) : Fraction(X)
      ==  (r.num / r.den) @ Fraction(X)

    coerce(x : Fraction(X)) : % == x pretend % 

-- FRAC(POLY(INT)) has FIELD
-- m:=(x^2)@FRAC(POLY(INT))
-- m::COHEN(POLY(INT))

  if X has Field then
    coerce(r : %) : X
      == (r.num / r.den) @ X








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Tim Daly <daly@axiom-developer.org> writes:

| Gabriel Dos Reis wrote:
| > Tim Daly <daly@axiom-developer.org> writes:
| >
| > | I've been reading this thread. It seems to me that what people are seeking
| > | is a symbolic algebra rather than a computer algebra system. The distinction
| > | is that a symbolic system manipulates input as parse trees in
| > | syntactic form.
| > | A computer algebra system manipulates input as semantic forms. It appears
| > | that you want to recover the syntax from the semantics, a very hard problem.
| >
| > OpenAxiom has the Syntax domain for matters that are purely syntactic,
| >
| > OpenAxiom's intended  of InputForm is that of expressions the semantics
| > of which yield computer representation of mathematical object.  In
| > particular, you can think of Syntax objects are pre-InputForm objects --
| > syntactic objects that have not yet been type checked.  So a Syntax object
| > is really a member of an initial algebra -- unlike InputForm or
| > SExpression objects. 
| >
| > | This discussion came up before. At the time I wrote the beginnings of a
| > | symbolic front end to Axiom based on Joel Cohen's work. Joel has given
| > | me permission to use his books as part of the effort.
| >
| > I'm familiar with his work (and his two books).  I would think that
| > there already exist a domain constructor, Expression, that is most
| > suited for the work presented in the two volumes.  The fundamental
| > building block is the Kernel domain constructor.  I know some people
| > have expressed profound dislikes of the Expression domain constructor.
| > But, I suspect that they would have a deeper appreciation of it after
| > reading Cohen's work.
| >
| > The need for InputForm is not just for 'symbolic mathematics'.  A proper
| > support for the compilation model of the Spad language requires that any
| > constructor argument be coercible to InputForm.  A fact that is not --
| > at the moment -- enforced, but that is deeply relied upon.  See what the
| > devaluate functions do and the unspolem assumptions behind.
| >
| > It is on my TODO list that OpenAxiom-1.3.x and up will enforce those
| > assumptions. 
| >
| > -- Gaby
| >
| >   
| So you propose that there are two reasons for this discussion of InputForm,
| one of which is to support a computational model of the spad language
| and the other is to support symbolic manipulation?

No -- I did not mean to give an exhaustive list of reasons to have
InputForm or not.   However, I do recognize instances of situations
where the notion of InputForm os relevant and that is what I was trying
to say.  Futhermore, I do not think the world has to be divided in terms
of algebraic computation versus symbolic computation.  Rather, my belief
is that symbolic mathematics (cross of algebraic computation and
symbolic computation) are going to be more and more prevalent.

| It is unclear what to expect from InputForm.

I think an operational definition of InputForm may be that of syntactic
normal forms of mathematical objects.  This is required for handling
categories and domains properly (or any form of dependent types).

| Under the assumption of a computational model it seems that x+y^2 == y^2+x

Note that the linear display of the InputForm x + y^2 as y^2 + x
reflects the semantics of the polynomial object denoted by that form.
As such, I do not think this is a mater of algebraic versus symbolic
computation. 

| Under the assumption of a cohen symbolic model they are not equivalent.
| (assuming that plus is associative in both cases)

Cohen assumes that + is associative -- because he primarily works with
polynomials over commutative rings.

| Given that there was a comment that the input form was not properly
| reproduced
| I assumed the discussion involved symbolic issues. Perhaps I misread it.
| 
| I do not see how InputForm can be made to support both models.

Indeed.  I would reserve the use of InputForm for syntatic canonical
forms of mathematical objects.

-- Gaby



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Tim Daly <daly@axiom-developer.org> writes:

| I've been reading this thread. It seems to me that what people are seeking
| is a symbolic algebra rather than a computer algebra system. The distinction
| is that a symbolic system manipulates input as parse trees in
| syntactic form.
| A computer algebra system manipulates input as semantic forms. It appears
| that you want to recover the syntax from the semantics, a very hard problem.

OpenAxiom has the Syntax domain for matters that are purely syntactic,

OpenAxiom's intended  of InputForm is that of expressions the semantics
of which yield computer representation of mathematical object.  In
particular, you can think of Syntax objects are pre-InputForm objects --
syntactic objects that have not yet been type checked.  So a Syntax object
is really a member of an initial algebra -- unlike InputForm or
SExpression objects. 

| This discussion came up before. At the time I wrote the beginnings of a
| symbolic front end to Axiom based on Joel Cohen's work. Joel has given
| me permission to use his books as part of the effort.

I'm familiar with his work (and his two books).  I would think that
there already exist a domain constructor, Expression, that is most
suited for the work presented in the two volumes.  The fundamental
building block is the Kernel domain constructor.  I know some people
have expressed profound dislikes of the Expression domain constructor.
But, I suspect that they would have a deeper appreciation of it after
reading Cohen's work.

The need for InputForm is not just for 'symbolic mathematics'.  A proper
support for the compilation model of the Spad language requires that any
constructor argument be coercible to InputForm.  A fact that is not --
at the moment -- enforced, but that is deeply relied upon.  See what the
devaluate functions do and the unspolem assumptions behind.

It is on my TODO list that OpenAxiom-1.3.x and up will enforce those
assumptions. 

-- Gaby



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On Thu, Jun 4, 2009 at 4:43 PM, Gabriel Dos Reis wrote:
> ...
> I would reserve the use of InputForm for syntatic canonical
> forms of mathematical objects.
>

Currently InputForm values can arise both from parsing of input
strings and from coercion of values from other domains. Only the
latter are in some sense "cononical". But even these are only
cononical to the degree that the domain from which they are derived
has such properties.  So it is not clear to me how one can hope to
reserve InputForm for only this use.

Regards,
Bill Page.



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Subject: [Axiom-developer] Re: [fricas-devel] Re: [Axiom-mail] InputForm
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Bill Page <bill.page@newsynthesis.org> writes:

| On Thu, Jun 4, 2009 at 4:43 PM, Gabriel Dos Reis wrote:
| > ...
| > I would reserve the use of InputForm for syntatic canonical
| > forms of mathematical objects.
| >
| 
| Currently InputForm values can arise both from parsing of input
| strings and 

That is the job of Syntax domain in OpenAxiom.

| from coercion of values from other domains. Only the
| latter are in some sense "cononical". But even these are only
| cononical to the degree that the domain from which they are derived
| has such properties.

Obviously.  For OpenAxiom, a domain that can see its values used as
constructor arguments should satisfy both SetCategory and 
CoercibleTo InputForm.  If a domain cannot satisfy those too
constraints, there is little point in trying to use its value as
constructor arguments.

| So it is not clear to me how one can hope to reserve InputForm for
| only this use. 

It is a design choice.  However, I fully appreciate there are many
choices to make and people are likely to make different choices.

-- Gaby



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> | On Thu, Jun 4, 2009 at 4:43 PM, Gabriel Dos Reis wrote:
> | > ...
> | > I would reserve the use of InputForm for syntatic canonical
> | > forms of mathematical objects.
> | >
> | Bill Page wrote:
> | Currently InputForm values can arise both from parsing of input
> | strings and
>

On Thu, Jun 4, 2009 at 9:48 PM, Gabriel Dos Reis wrote:
>
> That is the job of Syntax domain in OpenAxiom.
>

Although it sounds logical and desirable, I suppose that direct
conversion of values in the Syntax domain to "canonical" values in
InputForm is a rather hard problem. No?

I am tempted to argue in fact that the primary purpose of most of the
rest of panAxiom is to do just this sort of conversion - through the
algebraic "back door" so-to-speak ...

Regards,
Bill Page.



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Bill Page <bill.page@newsynthesis.org> writes:

| > | On Thu, Jun 4, 2009 at 4:43 PM, Gabriel Dos Reis wrote:
| > | > ...
| > | > I would reserve the use of InputForm for syntatic canonical
| > | > forms of mathematical objects.
| > | >
| > | Bill Page wrote:
| > | Currently InputForm values can arise both from parsing of input
| > | strings and
| >
| 
| On Thu, Jun 4, 2009 at 9:48 PM, Gabriel Dos Reis wrote:
| >
| > That is the job of Syntax domain in OpenAxiom.
| >
| 
| Although it sounds logical and desirable, I suppose that direct
| conversion of values in the Syntax domain to "canonical" values in
| InputForm is a rather hard problem. No?

The Syntax domain's primary purpose is as vehicle for terms.  Terms are
semanticalled analyzed (e.g. type checked, resolved), and evaluated.
The evaluation produces a computer representation of a mathematical
object, specified by a domain.  That domain provides -a- canonical
internal repsentation (e.g. dense vs. sparse, factored vs. fully expanded).
To get from internal to external representation, OpenAxiom uses
InputForm, which in displayed form is a linear notation for the
canonical internal representation.  So, I do not know you understand by
'direct conversion'.  A Syntax domain object does not necessarily makes
sense (e.g. may NOT type check), whereas an InputForm is supposed to
have a meaning.

| I am tempted to argue in fact that the primary purpose of most of the
| rest of panAxiom is to do just this sort of conversion - through the
| algebraic "back door" so-to-speak ...

I see OpenAxiom as aiming at computational mathematics as opposed to
just being specialized for algebraic computations only.

-- Gaby



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On Thu, Jun 4, 2009 at 10:47 PM, Gabriel Dos Reis  wrote:
> ...
> I see OpenAxiom as aiming at computational mathematics as opposed
> to just being specialized for algebraic computations only.
>

+1 I am in full agreement with your general goals and methods.

Regards,
Bill Page.



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Subject: [Axiom-developer] Axiom on Sourceforge moved to git
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The Axiom repository on Sourceforge has been moved to git.
The CVS and SVN repositories are no longer maintained and
have been withdrawn.

You can get the latest sources by doing:

git clone git://axiom.git.sourceforge.net/gitroot/axiom (sourceforge)
git clone git://git.sv.gnu.org/axiom.git (savannah)
git clone git://github.com/daly/axiom.git (github)

These will all be maintained at the latest levels as soon as the
update process completes.

Tim




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Martin,

The "lot of bogus expressions" in mapleok seem only to occur in the
fricas version. They have long since been fixed in Axiom. If you know
of more errors please let me know.

There are two integral test suites, one based on Bondarenko's
published Maple failures and the other based on Schaums outline.

The Bondarenko test suite was a measure of how well Axiom
handles known Maple failures. More "comparative test suites"
are "in process" against Mathematica, Maple and Maxima.

Tim Lahey is using the Schaums test suite.
The Schaums test suite is part of the CATS (Computer
Algebra Test Suite) which is intended to validate Axiom's results
against known-good, published results. Note that Axiom found
2 errors in the published Schaums results and one error caused by
a bad patch to the integration routines. More "published results"
test suites are "in process" for series.

Tim




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Subject: [Axiom-developer] 20090607.03.tpd.patch (tpiezas.input CATS
	algebraic identities)
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T. Piezas has published a book of algebraic identities.
This is the first in a set of CATS tests to exercise Axiom with
those identities.

========================================================================
diff --git a/changelog b/changelog
index 5c96725..0826802 100644
--- a/changelog
+++ b/changelog
@@ -1,7 +1,10 @@
-20090606 tpd src/axiom-website/patches.html 20090607.02.tpd.patch
-20090606 tpd books/bookvol10.4 MAPPKG2 +-> conversion
-20090606 tpd src/axiom-website/patches.html 20090607.01.tpd.patch
-20090606 tpd books/bookvol10.4 MAPPGK1 +-> conversion
+20090607 tpd src/axiom-website/patches.html 20090607.03.tpd.patch
+20090607 tpd src/input/Makefile add tpiezas.input algebraic identities
+20090607 tpd src/input/tpiezas.input CATS tests of algebraic identities
+20090607 tpd src/axiom-website/patches.html 20090607.02.tpd.patch
+20090607 tpd books/bookvol10.4 MAPPKG2 +-> conversion
+20090607 tpd src/axiom-website/patches.html 20090607.01.tpd.patch
+20090607 tpd books/bookvol10.4 MAPPGK1 +-> conversion
 20090606 tpd src/axiom-website/patches.html 20090606.07.tpd.patch
 20090606 tpd books/bookvol10.4 MKUCFUNC +-> conversion
 20090606 tpd src/axiom-website/patches.html 20090606.06.tpd.patch
diff --git a/src/axiom-website/patches.html b/src/axiom-website/patches.html
index 9c71f66..8ec5f5d 100644
--- a/src/axiom-website/patches.html
+++ b/src/axiom-website/patches.html
@@ -1481,5 +1481,7 @@ bookvol10.4 MKUCFUNC +-> conversion<br/>
 bookvol10.4 MAPPGK1 +-> conversion<br/>
 <a href="patches/20090607.02.tpd.patch">20090607.02.tpd.patch</a>
 bookvol10.4 MAPPGK2 +-> conversion<br/>
+<a href="patches/20090607.03.tpd.patch">20090607.03.tpd.patch</a>
+tpieazas.input CATS tests of algebraic identites<br/>
  </body>
 </html>
diff --git a/src/input/Makefile.pamphlet b/src/input/Makefile.pamphlet
index 536385f..f92241d 100644
--- a/src/input/Makefile.pamphlet
+++ b/src/input/Makefile.pamphlet
@@ -384,6 +384,7 @@ REGRES= algaggr.regress algbrbf.regress  algfacob.regress alist.regress  \
     symbol.regress    t111293.regress  table.regress    tancot.regress \
     tanhcoth.regress  tanatan.regress  tbagg.regress    test.regress \
     textfile.regress  torus.regress \
+    tpiezas.regress \
     triglim.regress   tsetcatvermeer.regress            tutchap1.regress \
     typetower.regress void.regress      uniseg.regress \
     unittest1.regress unittest2.regress unittest3.regress unittest4.regress
@@ -692,6 +693,7 @@ FILES= ${OUT}/algaggr.input  ${OUT}/algbrbf.input    ${OUT}/algfacob.input \
        ${OUT}/table.input    ${OUT}/tancot.input     ${OUT}/tanhcoth.input \
        ${OUT}/tanatan.input  ${OUT}/tbagg.input      ${OUT}/test.input \
        ${OUT}/tetra.input    ${OUT}/textfile.input   ${OUT}/tknot.input \
+       ${OUT}/tpiezas.input \
        ${OUT}/tree.input \
        ${OUT}/triglim.input  ${OUT}/tschirn.input ${OUT}/tsetcatbutcher.input \
        ${OUT}/tsetcatchemical.input ${OUT}/tsetcatvermeer.input \
@@ -1049,7 +1051,9 @@ DOCFILES= \
   ${DOC}/tbagg.input.dvi       \
   ${DOC}/test.input.dvi        ${DOC}/tetra.input.dvi      \
   ${DOC}/textfile.input.dvi    ${DOC}/tknot.input.dvi      \
-  ${DOC}/torus.input.dvi       ${DOC}/tree.input.dvi       \
+  ${DOC}/torus.input.dvi \
+  ${DOC}/tpiezas.input.dvi \
+  ${DOC}/tree.input.dvi       \
   ${DOC}/triglim.input.dvi     ${DOC}/tschirn.input.dvi    \
   ${DOC}/tsetcatbutcher.input.dvi    \
   ${DOC}/tsetcatchemical.input.dvi   \
diff --git a/src/input/tpiezas.input.pamphlet b/src/input/tpiezas.input.pamphlet
new file mode 100644
index 0000000..f60ad7e
--- /dev/null
+++ b/src/input/tpiezas.input.pamphlet
@@ -0,0 +1,829 @@
+\documentclass{article}
+\usepackage{axiom}
+\begin{document}
+\title{\$SPAD/src/input tpiezas.input}
+\author{Timothy Daly}
+\maketitle
+\begin{abstract}
+This is from ``A Collection of Algebraic Identities'' by T. Piezas III\cite{1}
+\end{abstract}
+\eject
+\tableofcontents
+\eject
+\section{Part 1. Assorted Identities}
+\begin{chunk}{*}
+)set break resume
+)spool tpiezas.output
+)set message test on
+)set message auto off
+)clear all
+\end{chunk}
+
+\subsection{E. Maillet}
+\[(a+b)^3+(a+c)^3+(a+d)^3+(a-b)^3+(a-c)^3+(a-d)^3 = 6a(a^2+b^2+c^2+d^2)\]
+\begin{chunk}{*} 
+--S 1 of 63
+t1a:=(a+b)^3 + (a+c)^3 + (a+d)^3 + (a-b)^3 + (a-c)^3 + (a-d)^3
+--R 
+--R
+--R            2       2       2     3
+--R   (1)  6a d  + 6a c  + 6a b  + 6a
+--R                                                     Type: Polynomial Integer
+--E 1
+
+--S 2 of 63
+t1b:=6*a*(a^2+b^2+c^2+d^2)
+--R 
+--R
+--R            2       2       2     3
+--R   (2)  6a d  + 6a c  + 6a b  + 6a
+--R                                                     Type: Polynomial Integer
+--E 2
+
+--S 3 of 63
+t1a-t1b
+--R 
+--R
+--R   (3)  0
+--R                                                     Type: Polynomial Integer
+--E 3
+\end{chunk}
+
+\subsection{E. Lucas-Liouville}
+\[\begin{array}{ll}
+(a+b)^k+(a+c)^k+(a+d)^k+(b+c)^k+(b+d)^k+(c+d)^k+\\
+(a-b)^k+(a-c)^k+(a-d)^k+(b-c)^k+(b-d)^k+(c-d)^k
+\end{array}\]
+\[=6(a^2+b^2+c^2+d^2)^{k/2}\quad {\rm\ for\ }k=2,4\]
+\begin{chunk}{*} 
+--S 4 of 63
+t2a(k)==(a+b)^k + (a+c)^k + (a+d)^k + (b+c)^k + (b+d)^k + (c+d)^k +_
+        (a-b)^k + (a-c)^k + (a-d)^k + (b-c)^k + (b-d)^k + (c-d)^k 
+--R 
+--R                                                                   Type: Void
+--E 4
+
+--S 5 of 63
+t2b(k)==6*(a^2+b^2+c^2+d^2)^(k/2)
+--R 
+--R                                                                   Type: Void
+--E 5
+
+--S 6 of 63
+t2a(k)
+--R 
+--R   Compiling function t2a with type Variable k -> Expression Integer 
+--R
+--R   (6)
+--R            k          k          k          k          k          k
+--R     (d + c)  + (d + b)  + (d + a)  + (c + b)  + (c + a)  + (b + a)
+--R   + 
+--R            k            k            k            k            k            k
+--R   (- b + a)  + (- c + b)  + (- c + a)  + (- d + c)  + (- d + b)  + (- d + a)
+--R                                                     Type: Expression Integer
+--E 6
+
+--S 7 of 63
+t2b(k)
+--R 
+--R   Compiling function t2b with type Variable k -> Expression Integer 
+--R
+--R                            k
+--R                            -
+--R           2    2    2    2 2
+--R   (7)  6(d  + c  + b  + a )
+--R                                                     Type: Expression Integer
+--E 7
+
+--S 8 of 63
+t2a(2)
+--R 
+--R   Compiling function t2a with type PositiveInteger -> Polynomial 
+--R      Integer 
+--R
+--R          2     2     2     2
+--R   (8)  6d  + 6c  + 6b  + 6a
+--R                                                     Type: Polynomial Integer
+--E 8
+
+--S 9 of 63
+t2b(2)
+--R 
+--R   Compiling function t2b with type PositiveInteger -> Expression 
+--R      Integer 
+--R
+--R          2     2     2     2
+--R   (9)  6d  + 6c  + 6b  + 6a
+--R                                                     Type: Expression Integer
+--E 9
+
+--S 10 of 63
+t2a(2)-t2b(2)
+--R 
+--R
+--R   (10)  0
+--R                                                     Type: Expression Integer
+--E 10
+
+--S 11 of 63
+t2a(4)
+--R 
+--R
+--R   (11)
+--R     4       2      2      2  2     4       2      2  2     4      2 2     4
+--R   6d  + (12c  + 12b  + 12a )d  + 6c  + (12b  + 12a )c  + 6b  + 12a b  + 6a
+--R                                                     Type: Polynomial Integer
+--E 11
+
+--S 12 of 63
+t2b(4)
+--R 
+--R
+--R   (12)
+--R     4       2      2      2  2     4       2      2  2     4      2 2     4
+--R   6d  + (12c  + 12b  + 12a )d  + 6c  + (12b  + 12a )c  + 6b  + 12a b  + 6a
+--R                                                     Type: Expression Integer
+--E 12
+
+--S 13 of 63
+t2a(4)-t2b(4)
+--R 
+--R
+--R   (13)  0
+--R                                                     Type: Expression Integer
+--E 13
+\end{chunk}
+
+\subsection{Boutin's Identity}
+\[S\pm(x_1\pm x_2\pm \ldots \pm x_k)^k = k!\: 2^{k-1} x_1 x_2 \ldots x_k\]
+where the exterior sign is the product of the interior signs so
+the term is negative if there is an odd number of negative interior signs,
+otherwise positive
+\begin{chunk}{*} 
+
+--S 14 of 63
+t3a1 := (a+b)^2 - (a-b)^2
+--R 
+--R
+--R   (14)  4a b
+--R                                                     Type: Polynomial Integer
+--E 14
+
+--S 15 of 63
+t3b1 := 4*a*b
+--R 
+--R
+--R   (15)  4a b
+--R                                                     Type: Polynomial Integer
+--E 15
+
+--S 16 of 63
+t3a1-t3b1
+--R 
+--R
+--R   (16)  0
+--R                                                     Type: Polynomial Integer
+--E 16
+
+--S 17 of 63
+t3a2 := (a+b+c)^3 - (a-b+c)^3 - (a+b-c)^3 + (a-b-c)^3
+--R 
+--R
+--R   (17)  24a b c
+--R                                                     Type: Polynomial Integer
+--E 17
+
+--S 18 of 63
+t3b2 := 24*a*b*c
+--R 
+--R
+--R   (18)  24a b c
+--R                                                     Type: Polynomial Integer
+--E 18
+
+--S 19 of 63
+t3a2-t3b2
+--R 
+--R
+--R   (19)  0
+--R                                                     Type: Polynomial Integer
+--E 19
+
+--S 20 of 63
+t3a3 := (a+b+c+d)^4 - (a-b+c+d)^4 - (a+b-c+d)^4 - (a+b+c-d)^4 
+      + (a-b-c+d)^4 + (a-b+c-d)^4 + (a+b-c-d)^4 - (a-b-c-d)^4
+--R 
+--R
+--R   (20)  192a b c d
+--R                                                     Type: Polynomial Integer
+--E 20
+
+--S 21 of 63
+t3b3 := 192*a*b*c*d
+--R 
+--R
+--R   (21)  192a b c d
+--R                                                     Type: Polynomial Integer
+--E 21
+
+--S 22 of 63
+t3a3-t3b3
+--R 
+--R
+--R   (22)  0
+--R                                                     Type: Polynomial Integer
+--E 22
+
+\end{chunk}
+We can create the general case using some functions.
+
+The ``bitlist'' function creates a list of the sign changes needed
+to form each term. If a term is 4 variables long we need all possible
+combinations of 3 signs. In order to generate this we create a list
+of all possible bit combinations of the numbers from 0 to $2^{n-1}-1$,
+which for the case of 4 would be from 0 to 7:
+\begin{verbatim}
+   [[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1]]
+\end{verbatim}
+We do this using an outer loop to generate the correct number of lists
+and an inner loop to create each list.
+\begin{chunk}{*}
+--S 23 of 63
+bitlist(size:Integer):List List INT ==
+  result:List List INT:=[]
+  size <= 1 => result
+  bound:PI:=size-1
+  bitlength:INT:=2^bound
+  for i in (bitlength-1)::PI..0 by -1 repeat
+    t1:=[1::INT for k in 1..bound]
+    for j in 0..(#t1-1) repeat 
+      if not bit?(i,j) then t1(bound-j):=0
+    result:=cons(t1,result)
+  result
+--R 
+--R   Function declaration bitlist : Integer -> List List Integer has been
+--R      added to workspace.
+--R                                                                   Type: Void
+--E 23
+
+\end{chunk}
+These are the test cases.
+\begin{chunk}{*}
+--S 24 of 63
+bitlist(1)
+--R 
+--R   Compiling function bitlist with type Integer -> List List Integer 
+--R
+--R   (24)  []
+--R                                                      Type: List List Integer
+--E 24
+
+--S 25 of 63
+bitlist(2)
+--R 
+--I   Compiling function G7153 with type Integer -> Boolean 
+--I   Compiling function G7332 with type NonNegativeInteger -> Boolean 
+--R
+--R   (25)  [[0],[1]]
+--R                                                      Type: List List Integer
+--E 25
+
+--S 26 of 63
+bitlist(3)
+--R 
+--R
+--R   (26)  [[0,0],[0,1],[1,0],[1,1]]
+--R                                                      Type: List List Integer
+--E 26
+
+--S 27 of 63
+bitlist(4)
+--R 
+--R
+--R   (27)  [[0,0,0],[0,0,1],[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,1,0],[1,1,1]]
+--R                                                      Type: List List Integer
+--E 27
+
+\end{chunk}
+
+Now we need a function to generate a list of subscripted symbols
+\begin{chunk}{*}
+--S 28 of 63
+symgen(var:Symbol,size:PI):List Symbol == [var.[i] for i in size..1 by -1]
+--R 
+--R   Function declaration symgen : (Symbol,PositiveInteger) -> List 
+--R      Symbol has been added to workspace.
+--R                                                                   Type: Void
+--E 28
+
+--S 29 of 63
+symgen('a,4)
+--R 
+--R   Compiling function symgen with type (Symbol,PositiveInteger) -> List
+--R      Symbol 
+--R
+--R   (29)  [a ,a ,a ,a ]
+--R           4  3  2  1
+--R                                                            Type: List Symbol
+--E 29
+
+\end{chunk}
+
+This is a function to generate the terms for Boutin's Identity.
+Each term is of the form:
+\[sign * (x_n\pm x_{n-1}\\pm \ldots \pm x_1)^n\]
+where the sign is negative if the number of minus signs in the term is odd
+\begin{chunk}{*}
+--S 30 of 63
+term(size:PI,signs:List INT):Polynomial Integer ==
+  syms:=symgen('x,size)
+  t1:POLY(INT):=first syms
+  sign:INT:=if odd? size then 1 else -1
+  for i in 1..#signs repeat
+    if (signs.i = 0)
+      then t1:=t1-syms.(i+1)
+       else ( t1:=t1+syms.(i+1) ; sign:=sign*-1 )
+  sign*(t1^size)
+--R 
+--R   Function declaration term : (PositiveInteger,List Integer) -> 
+--R      Polynomial Integer has been added to workspace.
+--R                                                                   Type: Void
+--E 30
+\end{chunk}
+Now we test it by hand for the case $n=4$
+\begin{chunk}{*}
+
+--S 31 of 63
+factor term(4,[0,0,0])
+--R 
+--R   Compiling function term with type (PositiveInteger,List Integer) -> 
+--R      Polynomial Integer 
+--R
+--R                              4
+--R   (31)  - (x  - x  - x  - x )
+--R             4    3    2    1
+--R                                            Type: Factored Polynomial Integer
+--E 31
+
+--S 32 of 63
+factor term(4,[0,0,1])
+--R 
+--R
+--R                            4
+--R   (32)  (x  - x  - x  + x )
+--R           4    3    2    1
+--R                                            Type: Factored Polynomial Integer
+--E 32
+
+--S 33 of 63
+factor term(4,[0,1,0])
+--R 
+--R
+--R                            4
+--R   (33)  (x  - x  + x  - x )
+--R           4    3    2    1
+--R                                            Type: Factored Polynomial Integer
+--E 33
+
+--S 34 of 63
+factor term(4,[0,1,1])
+--R 
+--R
+--R                              4
+--R   (34)  - (x  - x  + x  + x )
+--R             4    3    2    1
+--R                                            Type: Factored Polynomial Integer
+--E 34
+
+--S 35 of 63
+factor term(4,[1,0,0])
+--R 
+--R
+--R                            4
+--R   (35)  (x  + x  - x  - x )
+--R           4    3    2    1
+--R                                            Type: Factored Polynomial Integer
+--E 35
+
+--S 36 of 63
+factor term(4,[1,0,1])
+--R 
+--R
+--R                              4
+--R   (36)  - (x  + x  - x  + x )
+--R             4    3    2    1
+--R                                            Type: Factored Polynomial Integer
+--E 36
+
+--S 37 of 63
+factor term(4,[1,1,0])
+--R 
+--R
+--R                              4
+--R   (37)  - (x  + x  + x  - x )
+--R             4    3    2    1
+--R                                            Type: Factored Polynomial Integer
+--E 37
+
+--S 38 of 63
+factor term(4,[1,1,1])
+--R 
+--R
+--R                            4
+--R   (38)  (x  + x  + x  + x )
+--R           4    3    2    1
+--R                                            Type: Factored Polynomial Integer
+--E 38
+
+\end{chunk}
+And we test combining the terms using the bitlist function call.
+\begin{chunk}{*}
+--S 39 of 63
+map(x+->factor(term(1,x)),bitlist(1))
+--R 
+--R
+--R   (39)  []
+--R                                       Type: List Factored Polynomial Integer
+--E 39
+
+--S 40 of 63
+map(x+->factor(term(2,x)),bitlist(2))
+--R 
+--R
+--R                     2          2
+--R   (40)  [- (x  - x ) ,(x  + x ) ]
+--R              2    1     2    1
+--R                                       Type: List Factored Polynomial Integer
+--E 40
+
+--S 41 of 63
+map(x+->factor(term(3,x)),bitlist(3))
+--R 
+--R
+--R                        3                 3                 3               3
+--R   (41)  [(x  - x  - x ) ,- (x  - x  + x ) ,- (x  + x  - x ) ,(x  + x  + x ) ]
+--R            3    2    1       3    2    1       3    2    1     3    2    1
+--R                                       Type: List Factored Polynomial Integer
+--E 41
+
+--S 42 of 63
+map(x+->factor(term(4,x)),bitlist(4))
+--R 
+--R
+--R   (42)
+--R                         4                     4                     4
+--R   [- (x  - x  - x  - x ) , (x  - x  - x  + x ) , (x  - x  + x  - x ) ,
+--R        4    3    2    1      4    3    2    1      4    3    2    1
+--R                         4                     4                       4
+--R    - (x  - x  + x  + x ) , (x  + x  - x  - x ) , - (x  + x  - x  + x ) ,
+--R        4    3    2    1      4    3    2    1        4    3    2    1
+--R                         4                     4
+--R    - (x  + x  + x  - x ) , (x  + x  + x  + x ) ]
+--R        4    3    2    1      4    3    2    1
+--R                                       Type: List Factored Polynomial Integer
+--E 42
+
+\end{chunk}
+Next we have two functions, one to create a generic left hand side
+of Boutin's Identity:
+\begin{chunk}{*}
+--S 43 of 63
+lhs(size:PI):POLY(INT) ==
+  size = 1 => 0::POLY(INT)
+  reduce(+,map(x+->term(size,x),bitlist(size)))
+--R 
+--R   Function declaration lhs : PositiveInteger -> Polynomial Integer has
+--R      been added to workspace.
+--R                                                                   Type: Void
+--E 43
+
+\end{chunk}
+and one to create a generic right hand side of Boutin's Identity:
+\begin{chunk}{*}
+--S 44 of 63
+rhs(size:PI):POLY(INT) == 
+ size = 1 => 0
+ bound:PI:=(size-1)
+ factorial(size)*2^bound*reduce(*,symgen('x,size))@POLY(INT)
+--R 
+--R   Function declaration rhs : PositiveInteger -> Polynomial Integer has
+--R      been added to workspace.
+--R                                                                   Type: Void
+--E 44
+
+\end{chunk}
+Now we look at the case where $n=2$, showing the factors, the left
+hand side, the right hand side, and the fact that they are equal
+by subtraction
+\begin{chunk}{*}
+--S 45 of 63
+map(x+->factor term(2,x),bitlist(2))
+--R 
+--R
+--R                     2          2
+--R   (45)  [- (x  - x ) ,(x  + x ) ]
+--R              2    1     2    1
+--R                                       Type: List Factored Polynomial Integer
+--E 45
+
+--S 46 of 63
+lhs(2)
+--R 
+--R   Compiling function lhs with type PositiveInteger -> Polynomial 
+--R      Integer 
+--R
+--R   (46)  4x x
+--R           1 2
+--R                                                     Type: Polynomial Integer
+--E 46
+
+--S 47 of 63
+rhs(2)
+--R 
+--R   Compiling function rhs with type PositiveInteger -> Polynomial 
+--R      Integer 
+--R
+--R   (47)  4x x
+--R           1 2
+--R                                                     Type: Polynomial Integer
+--E 47
+
+--S 48 of 63
+lhs(2)-rhs(2)
+--R 
+--R
+--R   (48)  0
+--R                                                     Type: Polynomial Integer
+--E 48
+
+\end{chunk}
+Now we look at the case where $n=3$, showing the factors, the left
+hand side, the right hand side, and the fact that they are equal
+by subtraction
+\begin{chunk}{*}
+--S 49 of 63
+map(x+->factor term(3,x),bitlist(3))
+--R 
+--R
+--R                        3                 3                 3               3
+--R   (49)  [(x  - x  - x ) ,- (x  - x  + x ) ,- (x  + x  - x ) ,(x  + x  + x ) ]
+--R            3    2    1       3    2    1       3    2    1     3    2    1
+--R                                       Type: List Factored Polynomial Integer
+--E 49
+
+--S 50 of 63
+lhs(3)
+--R 
+--R
+--R   (50)  24x x x
+--R            1 2 3
+--R                                                     Type: Polynomial Integer
+--E 50
+
+--S 51 of 63
+rhs(3)
+--R 
+--R
+--R   (51)  24x x x
+--R            1 2 3
+--R                                                     Type: Polynomial Integer
+--E 51
+
+--S 52 of 63
+lhs(3)-rhs(3)
+--R 
+--R
+--R   (52)  0
+--R                                                     Type: Polynomial Integer
+--E 52
+
+\end{chunk}
+Now we look at the case where $n=4$, showing the factors, the left
+hand side, the right hand side, and the fact that they are equal
+by subtraction
+\begin{chunk}{*}
+--S 53 of 63
+map(x+->factor term(4,x),bitlist(4))
+--R 
+--R
+--R   (53)
+--R                         4                     4                     4
+--R   [- (x  - x  - x  - x ) , (x  - x  - x  + x ) , (x  - x  + x  - x ) ,
+--R        4    3    2    1      4    3    2    1      4    3    2    1
+--R                         4                     4                       4
+--R    - (x  - x  + x  + x ) , (x  + x  - x  - x ) , - (x  + x  - x  + x ) ,
+--R        4    3    2    1      4    3    2    1        4    3    2    1
+--R                         4                     4
+--R    - (x  + x  + x  - x ) , (x  + x  + x  + x ) ]
+--R        4    3    2    1      4    3    2    1
+--R                                       Type: List Factored Polynomial Integer
+--E 53
+
+--S 54 of 63
+lhs(4)
+--R 
+--R
+--R   (54)  192x x x x
+--R             1 2 3 4
+--R                                                     Type: Polynomial Integer
+--E 54
+
+--S 55 of 63
+rhs(4)
+--R 
+--R
+--R   (55)  192x x x x
+--R             1 2 3 4
+--R                                                     Type: Polynomial Integer
+--E 55
+
+--S 56 of 63
+lhs(4)-rhs(4)
+--R 
+--R
+--R   (56)  0
+--R                                                     Type: Polynomial Integer
+--E 56
+
+\end{chunk}
+\subsection{Lagrange's Identity}
+\[\left(\sum a_k^2\right) \left(\sum b_k^2\right) =
+\left(\sum a_k b_k\right)^2 + \sum \left(a_k b_j - a_j b_k\right)^2\]
+
+We need two symbol generation functions. First, we need to generate
+the units for the term
+\[\left(\sum a_k b_k\right)^2\]
+so that \verb|symgen2('a,'b,4)| results in
+\begin{verbatim}
+ [a b ,a b ,a b ,a b ]
+   4 4  3 3  2 2  1 1
+\end{verbatim}
+\begin{chunk}{*}
+--S 57 of 63
+symgen2(var1:Symbol,var2:Symbol,size:PI):List POLY INT ==
+  [(var1.[i]*var2.[i]) for i in size..1 by -1]
+--R 
+--R   Function declaration symgen2 : (Symbol,Symbol,PositiveInteger) -> 
+--R      List Polynomial Integer has been added to workspace.
+--R                                                                   Type: Void
+--E 57
+
+--S 58 of 63
+symgen2('a,'b,4)
+--R 
+--R   Compiling function symgen2 with type (Symbol,Symbol,PositiveInteger)
+--R       -> List Polynomial Integer 
+--R
+--R   (58)  [a b ,a b ,a b ,a b ]
+--R           4 4  3 3  2 2  1 1
+--R                                                Type: List Polynomial Integer
+--E 58
+
+\end{chunk}
+Next we need to generate the units for the term
+\[\sum \left(a_k b_j - a_j b_k\right)^2\]
+so that \verb|symgen3('a,'b,4)| results in
+\begin{verbatim}
+   [0, a b  - a b , a b  - a b , a b  - a b , 0, a b  - a b , a b  - a b , 0,
+        3 4    4 3   2 4    4 2   1 4    4 1      2 3    3 2   1 3    3 1
+    a b  - a b , 0]
+     1 2    2 1
+\end{verbatim}
+\begin{chunk}{*}
+--S 59 of 63
+symgen3(var1:Symbol,var2:Symbol,size:PI):LIST POLY INT == 
+  result:LIST(POLY(INT)):=[]
+  for j in 1..size repeat
+    for k in 1..j repeat
+      p:POLY(INT):=var1.[k]*var2.[j]-var1.[j]*var2.[k]
+      result:=cons(p,result)
+  result
+--R 
+--R   Function declaration symgen3 : (Symbol,Symbol,PositiveInteger) -> 
+--R      List Polynomial Integer has been added to workspace.
+--R                                                                   Type: Void
+--E 59
+
+--S 60 of 63
+symgen3('a,'b,4)
+--R 
+--R   Compiling function symgen3 with type (Symbol,Symbol,PositiveInteger)
+--R       -> List Polynomial Integer 
+--R
+--R   (60)
+--R   [0, a b  - a b , a b  - a b , a b  - a b , 0, a b  - a b , a b  - a b , 0,
+--R        3 4    4 3   2 4    4 2   1 4    4 1      2 3    3 2   1 3    3 1
+--R    a b  - a b , 0]
+--R     1 2    2 1
+--R                                                Type: List Polynomial Integer
+--E 60
+
+\end{chunk}
+Now we are ready to generate and test the Lagrange Identities.
+This function will take a given size and print all of the intermediate
+working results. It eventually creates the left hand side (lhs) and
+the right hand side (rhs) and subtracts them to show that they are equal.
+\begin{chunk}{*}
+--S 61 of 63
+lagrange(size:PI):POLY(INT) ==
+  t1:=factor reduce(+,map(x+->x^2,symgen('a,size)))
+  print ["t1=",t1]
+  t2:=factor reduce(+,map(x+->x^2,symgen('b,size)))
+  print ["t2=",t2]
+  t3:=factor reduce(+,symgen2('a,'b,size))^2
+  print ["t3=",t3]
+  t4:=factor reduce(+,map(x+->x^2,symgen3('a,'b,size)))
+  print ["t4=",t4]
+  lhs:=t1*t2
+  print ["lhs=",lhs]
+  rhs:=t3+t4
+  print ["rhs=",rhs]
+  lhs-rhs
+--R 
+--R   Function declaration lagrange : PositiveInteger -> Polynomial 
+--R      Integer has been added to workspace.
+--R                                                                   Type: Void
+--E 61
+
+\end{chunk}
+Now we test it for the case $n=2$
+\begin{chunk}{*}
+--S 62 of 63
+lagrange(2)
+--R 
+--R   Function definition for lhs is being overwritten.
+--R   Function definition for rhs is being overwritten.
+--R   Compiling function lagrange with type PositiveInteger -> Polynomial 
+--R      Integer 
+--R            2     2
+--R   ["t1=",a   + a  ]
+--R           2     1
+--R            2     2
+--R   ["t2=",b   + b  ]
+--R           2     1
+--R                       2
+--R   ["t3=",(a b  + a b ) ]
+--R            2 2    1 1
+--R                       2
+--R   ["t4=",(a b  - a b ) ]
+--R            1 2    2 1
+--R              2     2    2     2
+--R   ["lhs=",(a   + a  )(b   + b  )]
+--R             2     1    2     1
+--R              2     2   2      2     2   2
+--R   ["rhs=",(a   + a  )b   + (a   + a  )b  ]
+--R             2     1   2      2     1   1
+--R
+--R   (62)  0
+--R                                                     Type: Polynomial Integer
+--E 62
+
+\end{chunk}
+Now we test it for the case $n=3$
+\begin{chunk}{*}
+--S 63 of 63
+lagrange(3)
+--R 
+--R            2     2     2
+--R   ["t1=",a   + a   + a  ]
+--R           3     2     1
+--R            2     2     2
+--R   ["t2=",b   + b   + b  ]
+--R           3     2     1
+--R                              2
+--R   ["t3=",(a b  + a b  + a b ) ]
+--R            3 3    2 2    1 1
+--R   ["t4=",
+--R
+--R          2     2   2                                2     2   2
+--R       (a   + a  )b   + (- 2a a b  - 2a a b )b  + (a   + a  )b   - 2a a b b
+--R         2     1   3         2 3 2     1 3 1  3     3     1   2      1 2 1 2
+--R     + 
+--R          2     2   2
+--R       (a   + a  )b
+--R         3     2   1
+--R     ]
+--R              2     2     2    2     2     2
+--R   ["lhs=",(a   + a   + a  )(b   + b   + b  )]
+--R             3     2     1    3     2     1
+--R              2     2     2   2      2     2     2   2      2     2     2   2
+--R   ["rhs=",(a   + a   + a  )b   + (a   + a   + a  )b   + (a   + a   + a  )b  ]
+--R             3     2     1   3      3     2     1   2      3     2     1   1
+--R
+--R   (63)  0
+--R                                                     Type: Polynomial Integer
+--E 63
+
+)spool 
+)lisp (bye)
+ 
+\end{chunk}
+\eject
+\begin{thebibliography}{99}
+\bibitem{1} T. Piezas, ``A Collection of Algebraic Identities''\\
+{\bf http://sites.google.com/site/tpiezas/001}
+\end{thebibliography}
+\end{document}
+
+
+



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On Jun 4, 12:35=A0pm, tpie...@gmail.com wrote:
> Hello all,
>
> Here's a nice identity:
>
> (p+q)^4 + (r-s)^4 =3D (p-q)^4 + (r+s)^4
>
> where {p,q,r,s} =3D {a^7+a^5-2a^3+a, 3a^2, a^6-2a^4+a^2+1, 3a^5}
>
> For similar stuff, you may be interested in "A Collection of Algebraic
> Identities":
>
> http://sites.google.com/site/tpiezas/Home
>
> It's a 200+ page book I wrote and made available there. =A0It starts
> with the basics with 2nd powers and goes up to 8th and higher powers.
> Enjoy.
>
> - Titus

I cannot verify the identity on page 001, Form 4, by S.Realis
Is it correct as printed?

Tim Daly



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On Jun 4, 12:35=A0pm, tpie...@gmail.com wrote:
> Hello all,
>
> Here's a nice identity:
>
> (p+q)^4 + (r-s)^4 =3D (p-q)^4 + (r+s)^4
>
> where {p,q,r,s} =3D {a^7+a^5-2a^3+a, 3a^2, a^6-2a^4+a^2+1, 3a^5}
>
> For similar stuff, you may be interested in "A Collection of Algebraic
> Identities":
>
> http://sites.google.com/site/tpiezas/Home
>
> It's a 200+ page book I wrote and made available there. =A0It starts
> with the basics with 2nd powers and goes up to 8th and higher powers.
> Enjoy.
>
> - Titus

on page http://sites.google.com/site/tpiezas/002 you state:

[55,48,73}, {45,28,43}, ....

as pythagorean triples

but it should read

{55,48,73}, {45,28,53} ....

Tim Daly
daly@axiom-developer.org



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On Jun 4, 12:35=A0pm, tpie...@gmail.com wrote:
> Hello all,
>
> Here's a nice identity:
>
> (p+q)^4 + (r-s)^4 =3D (p-q)^4 + (r+s)^4
>
> where {p,q,r,s} =3D {a^7+a^5-2a^3+a, 3a^2, a^6-2a^4+a^2+1, 3a^5}
>
> For similar stuff, you may be interested in "A Collection of Algebraic
> Identities":
>
> http://sites.google.com/site/tpiezas/Home
>
> It's a 200+ page book I wrote and made available there. =A0It starts
> with the basics with 2nd powers and goes up to 8th and higher powers.
> Enjoy.
>
> - Titus

on page http://sites.google.com/site/tpiezas/002

In the section on Euler you state:

(x+1/x)^2 + (y+1/y)^2 =3D z^2

but you never give a value for z



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On Jun 4, 12:35=A0pm, tpie...@gmail.com wrote:
> Hello all,
>
> Here's a nice identity:
>
> (p+q)^4 + (r-s)^4 =3D (p-q)^4 + (r+s)^4
>
> where {p,q,r,s} =3D {a^7+a^5-2a^3+a, 3a^2, a^6-2a^4+a^2+1, 3a^5}
>
> For similar stuff, you may be interested in "A Collection of Algebraic
> Identities":
>
> http://sites.google.com/site/tpiezas/Home
>
> It's a 200+ page book I wrote and made available there. =A0It starts
> with the basics with 2nd powers and goes up to 8th and higher powers.
> Enjoy.
>
> - Titus

On the page http://sites.google.com/site/tpiezas/002

Theorem: If p^2 + (p+1)^2 =3D r^2, then q^2 + (q+1)^2 =3D (p+q+r+1)^2
where q =3D 3p+2r+1

q:=3D3p+2r+1
r:=3Dsqrt(p^2 + (p+1)^2)
q^2 + (q+1)^2 - (p+q+r+1)^2 =3D=3D (-4r -8p -4)sqrt(2p^2+2p+1)+4r^2+(8p+4)
r

which is clearly not zero. What am I missing?

Tim Daly
daly@axiom-developer.org



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From: Tito Piezas <tpiezas@gmail.com>
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--00504502c8be57237e046be8a003
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Hello Tim,

Thank you for the interest.  I just moved to Canada and I am still sorting
out all my stuff.  I will get back to your questions in a few days.  :-)

-Tito

On Sun, Jun 7, 2009 at 8:59 PM, TimDaly <daly@axiom-developer.org> wrote:

> On Jun 4, 12:35 pm, tpie...@gmail.com wrote:
> > Hello all,
> >
> > Here's a nice identity:
> >
> > (p+q)^4 + (r-s)^4 = (p-q)^4 + (r+s)^4
> >
> > where {p,q,r,s} = {a^7+a^5-2a^3+a, 3a^2, a^6-2a^4+a^2+1, 3a^5}
> >
> > For similar stuff, you may be interested in "A Collection of Algebraic
> > Identities":
> >
> > http://sites.google.com/site/tpiezas/Home
> >
> > It's a 200+ page book I wrote and made available there.  It starts
> > with the basics with 2nd powers and goes up to 8th and higher powers.
> > Enjoy.
> >
> > - Titus
>
> On the page http://sites.google.com/site/tpiezas/002
>
> Theorem: If p^2 + (p+1)^2 = r^2, then q^2 + (q+1)^2 = (p+q+r+1)^2
> where q = 3p+2r+1
>
> q:=3p+2r+1
> r:=sqrt(p^2 + (p+1)^2)
> q^2 + (q+1)^2 - (p+q+r+1)^2 == (-4r -8p -4)sqrt(2p^2+2p+1)+4r^2+(8p+4)
> r
>
> which is clearly not zero. What am I missing?
>
> Tim Daly
> daly@axiom-developer.org
>

--00504502c8be57237e046be8a003
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<div>Hello Tim,</div>
<div>=A0</div>
<div>Thank you for the interest.=A0 I just moved to Canada and I am still s=
orting out all my stuff.=A0 I will get back to your questions in a few days=
.=A0 :-)</div>
<div>=A0</div>
<div>-Tito<br><br></div>
<div class=3D"gmail_quote">On Sun, Jun 7, 2009 at 8:59 PM, TimDaly <span di=
r=3D"ltr">&lt;<a href=3D"mailto:daly@axiom-developer.org">daly@axiom-develo=
per.org</a>&gt;</span> wrote:<br>
<blockquote style=3D"BORDER-LEFT: #ccc 1px solid; MARGIN: 0px 0px 0px 0.8ex=
; PADDING-LEFT: 1ex" class=3D"gmail_quote">
<div class=3D"im">On Jun 4, 12:35=A0pm, <a href=3D"mailto:tpie...@gmail.com=
">tpie...@gmail.com</a> wrote:<br>&gt; Hello all,<br>&gt;<br>&gt; Here&#39;=
s a nice identity:<br>&gt;<br>&gt; (p+q)^4 + (r-s)^4 =3D (p-q)^4 + (r+s)^4<=
br>
&gt;<br>&gt; where {p,q,r,s} =3D {a^7+a^5-2a^3+a, 3a^2, a^6-2a^4+a^2+1, 3a^=
5}<br>&gt;<br>&gt; For similar stuff, you may be interested in &quot;A Coll=
ection of Algebraic<br>&gt; Identities&quot;:<br>&gt;<br>&gt; <a href=3D"ht=
tp://sites.google.com/site/tpiezas/Home" target=3D"_blank">http://sites.goo=
gle.com/site/tpiezas/Home</a><br>
&gt;<br>&gt; It&#39;s a 200+ page book I wrote and made available there. =
=A0It starts<br>&gt; with the basics with 2nd powers and goes up to 8th and=
 higher powers.<br>&gt; Enjoy.<br>&gt;<br>&gt; - Titus<br><br></div>On the =
page <a href=3D"http://sites.google.com/site/tpiezas/002" target=3D"_blank"=
>http://sites.google.com/site/tpiezas/002</a><br>
<br>Theorem: If p^2 + (p+1)^2 =3D r^2, then q^2 + (q+1)^2 =3D (p+q+r+1)^2<b=
r>where q =3D 3p+2r+1<br><br>q:=3D3p+2r+1<br>r:=3Dsqrt(p^2 + (p+1)^2)<br>q^=
2 + (q+1)^2 - (p+q+r+1)^2 =3D=3D (-4r -8p -4)sqrt(2p^2+2p+1)+4r^2+(8p+4)<br=
>r<br><br>
which is clearly not zero. What am I missing?<br>
<div>
<div></div>
<div class=3D"h5"><br>Tim Daly<br><a href=3D"mailto:daly@axiom-developer.or=
g">daly@axiom-developer.org</a><br></div></div></blockquote></div><br>

--00504502c8be57237e046be8a003--



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Subject: [Axiom-developer] PostDoc Position
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Research team: Tools for Proofs, MSR-INRIA Joint Centre

The Microsoft Research-INRIA Joint Centre is offering a 2-year position for a post-doctoral researcher to work on a proof development environment for TLA+ in the Tools for Proofs project-team (see http://www.msr-inria.inria.fr).

Research Context

TLA+ is a language for formal specifications and proofs designed by
Leslie Lamport.  It is based on first-order logic, set theory, temporal logic, and a module system.  While the specification part of
TLA+ has existed for over ten years, the proof language is more recent,
and we are developing tools for writing and checking proofs.

The main program of our development environment is called the Proof Manager (PM).  The PM translates TLA+ source files to low-level proofs that are checked by Isabelle.  To this end, the PM calls the Zenon automatic theorem prover to fill in the "trivial" details omitted from proofs at the source level.  Within the Isabelle framework we have an axiomatization of TLA+ (Isabelle/TLA+).  Isabelle provides high assurance by checking all the proofs provided by the user or by Zenon.
The PM also has an interface to SMT solvers, which provides a stronger automatic prover, but with lower assurance of correctness.

The current version of the PM handles only the "action" part of TLA+:
first-order formulas with primed and unprimed variables. Because Isabelle considers a variable to be unrelated to its primed version, the PM can translate first-order formulas to first-order formulas, without the overhead associated with an encoding of temporal logic into first-order logic.  This part of TLA+ is already useful for proving safety properties.

Description of the activity of the post-doc

The task devoted to the post-doc will be to extend the proof manager to deal with the temporal part of TLA+.  To this end, he or she will have to define and implement a new translation into Isabelle to handle the temporal operators in a way that enables the use of TLA+ proof rules whose hypotheses include both temporal-logic formulas and non-temporal theorems proved with the simple translation.

Skills and profile of the candidate

We are looking for a candidate with skills in some or all of the following subjects: parsing and compilation, logic and set theory, Isabelle, OCaml, Eclipse and Java.  Moreover, the applicant must have a good command of the English language.

Location

The Microsoft Research-INRIA Joint Centre is located on the Campus of INRIA Futurs, in South part of Paris, near the Le-Guichet RER station. The Tools for Proofs project-team is composed of Damien Doligez, Leslie Lamport and Stephan Merz.

Ideally, the candidate will start working in september or october, but we can accomodate a later date.

Contact

Candidates should send a resume and the name and e-mail address of one or two references to Damien Doligez <damien.doligez@inria.fr>.






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Subject: [Axiom-developer] Re: [Axiom-mail] Coersion error
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Arnold Doray wrote:
> I'm trying to create a set of orthogonal polynomials using the
> Gram-Schmidt process, but I hit a problem:
>
> dot(f,g) == integrate(f*g*x^2,x=-1..1)
> proj(f,g) == dot(f,g)*f/dot(f,f)
>
> p0 := 1
> p1 := x - proj(p0,x)
> p2 := x^2 - proj(p0,x^2) - proj(p1,x^2)
>
> p0 and p1 evaluate correctly, but p2 hits this error:
>
> ; (DEFUN |*2;dot;5;frame1394| ...) is being compiled.
> ;; The variable |*2;dot;5;frame1394;MV| is undefined.
> ;; The compiler will assume this variable is a global.
>    Internal Error
>    The function coerce with signature OrderedCompletion Integer ->
>       Expression OrderedCompletion Integer is missing from domain
>       Expression(OrderedCompletion (Integer))
>
> I've also tried to define p(n) as a recursive function like so:
>
> p(0) == 1
> p(n | n > 0) == x^n - sum(proj(p(k),x^n),k=0..n-1)
>
> But get a stack overflow: (eg, evaluating p(1))
>
>    OpenAxiom will attempt to step through and interpret the code.
>    Cannot compile map: proj
>    We will attempt to interpret the code.
>    Cannot compile map: p
>    We will attempt to interpret the code.
>
>    >> System error:
>    Bind stack overflow.
>
> I would appreciate any pointers where I am going wrong. I'm an Axiom
> newbie. These calculations were done using open-axiom 1.2.1
>
> Thanks
> Arnold
>
>
>
> _______________________________________________
> Axiom-mail mailing list
> Axiom-mail@nongnu.org
> http://lists.nongnu.org/mailman/listinfo/axiom-mail
>
>   
You are not doing anything wrong. The error message says that there is a 
missing
function (coerce) from one domain to another. I will look at the problem 
and get
back to you.

Tim




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Subject: [Axiom-developer] Re: [Axiom-mail] Re: Coersion error
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Your initial report showed the problem from Open-Axiom
which is not the Axiom project. What command line did you use
to start Open-Axiom?

Your problem is also in Axiom so it is listed as a valid bug report.
It has been assigned bug number 7198.

Tim

Arnold Doray wrote:
> This problem persists in "original" Axiom compiled from the latest
> "Gold" source. My apologies for the confusion -AD
>
>
> On Tue, 2009-06-16 at 16:20 +0800, Arnold Doray wrote:
>   
>> I'm trying to create a set of orthogonal polynomials using the
>> Gram-Schmidt process, but I hit a problem:
>>
>> dot(f,g) == integrate(f*g*x^2,x=-1..1)
>> proj(f,g) == dot(f,g)*f/dot(f,f)
>>
>> p0 := 1
>> p1 := x - proj(p0,x)
>> p2 := x^2 - proj(p0,x^2) - proj(p1,x^2)
>>
>> p0 and p1 evaluate correctly, but p2 hits this error:
>>
>> ; (DEFUN |*2;dot;5;frame1394| ...) is being compiled.
>> ;; The variable |*2;dot;5;frame1394;MV| is undefined.
>> ;; The compiler will assume this variable is a global.
>>    Internal Error
>>    The function coerce with signature OrderedCompletion Integer ->
>>       Expression OrderedCompletion Integer is missing from domain
>>       Expression(OrderedCompletion (Integer))
>>
>>     
>
>
>
>
> _______________________________________________
> Axiom-mail mailing list
> Axiom-mail@nongnu.org
> http://lists.nongnu.org/mailman/listinfo/axiom-mail
>
>   




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Subject: [Axiom-developer] Re: [Axiom-mail] Problem with real/imag/conjugate
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This one is queued as bug number 7199.

When you say the latest "Gold" sources can you tell me the
result of the "Version" and "Timestamp" lines from the Axiom banner?
Where did you get the sources?

Tim


Arnold Doray wrote:
> I get the wrong answer for real/imag for some forms of complex numbers.
> For example:
>
> a := (-1*%i)^(1/2) 
>
> b := (%i)^(3/2)
>
> are both equivalent, but imag/real gives complex (and incorrect) answers
> for "a" (ie, real(a) and imag(a) are both complex), but I get the right
> answers for "b". Also "conjugate" fails on both with an error message.
>
> Am I missing something here? 
>
> I am using Axiom compiled from the latest "Gold" source. 
>
> Thanks,
> Arnold
>
>
>
> _______________________________________________
> Axiom-mail mailing list
> Axiom-mail@nongnu.org
> http://lists.nongnu.org/mailman/listinfo/axiom-mail
>
>   




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--000e0cd4879cb7fe45046c98654e
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Tim,

I think the following patch fixes this problem but I have not yet done
very extensive testing. It might well have some impact on results in
the regression tests.

The patch is against open-axiom sources so you might have to apply it
manually but I do not think this code has changed much in other
versions.

See also comments here:

https://sourceforge.net/tracker/?func=detail&atid=984524&aid=2806053&group_id=203172

----

wspage@debian:~$ svn diff ~/open-axiom-src/src/algebra > itrigmnp.patch
wspage@debian:~$ cat itrigmnp.patch

Index: /home/wspage/open-axiom-src/src/algebra/efstruc.spad.pamphlet
===================================================================
--- /home/wspage/open-axiom-src/src/algebra/efstruc.spad.pamphlet	(revision
1216)
+++ /home/wspage/open-axiom-src/src/algebra/efstruc.spad.pamphlet	(working copy)
@@ -545,6 +545,7 @@
     macro NTHR == 'nthRoot
     ker2explogs: (KG, List KG, List SY) -> FG
     smp2explogs: (PG, List KG, List SY) -> FG
+    nthroot:     (GF,GF) -> GF
     supexp     : (UP, GF, GF, Z) -> GF
     GR2GF      : GR -> GF
     GR2F       : GR -> F
@@ -626,13 +627,23 @@
       map(explogs2trigs(#1::FG),GR2GF, p)$PolynomialCategoryLifting(
                                     IndexedExponents KG, KG, GR, PG, GF)

-    explogs2trigs f ==
-      (m := mainKernel f) case "failed" =>
+    nthroot(a:GF,n:GF):GF ==
+      r := nthRoot(sqrt(norm(a)),retract(n)@Z)
+      e := exp(complex(0, 1)*argument(a)/n)
+      r*e
+
+    explogs2trigs(f:FG):GF ==
+      m := mainKernel f
+      m case "failed" =>
         GR2GF(retract(numer f)@GR) / GR2GF(retract(denom f)@GR)
-      op  := operator(operator(k := m::KG))$F
+      k := m::KG
+      op  := operator(operator(k))$F
       arg := [explogs2trigs x for x in argument k]
       num := univariate(numer f, k)
       den := univariate(denom f, k)
+      is?(op,'nthRoot) =>
+        h := nthroot(first arg, second arg)
+        supexp(num,h,0,0)/supexp(den,h,0,0)
       is?(op,'exp) =>
         e  := exp real first arg
         y  := imag first arg

wspage@debian:~$

----

Regards,
Bill Page.

On Tue, Jun 16, 2009 at 5:45 PM, Tim Daly<daly@axiom-developer.org> wrote:
> This one is queued as bug number 7199.
>
> When you say the latest "Gold" sources can you tell me the
> result of the "Version" and "Timestamp" lines from the Axiom banner?
> Where did you get the sources?
>
> Tim
>
>
> Arnold Doray wrote:
>>
>> I get the wrong answer for real/imag for some forms of complex numbers.
>> For example:
>>
>> a := (-1*%i)^(1/2)
>> b := (%i)^(3/2)
>>
>> are both equivalent, but imag/real gives complex (and incorrect) answers
>> for "a" (ie, real(a) and imag(a) are both complex), but I get the right
>> answers for "b". Also "conjugate" fails on both with an error message.
>>
>> Am I missing something here?
>> I am using Axiom compiled from the latest "Gold" source.
>> Thanks,
>> Arnold
>>

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Bill Page wrote:
> Tim,
>
> I think the following patch fixes this problem but I have not yet done
> very extensive testing. It might well have some impact on results in
> the regression tests.
>
> The patch is against open-axiom sources so you might have to apply it
> manually but I do not think this code has changed much in other
> versions.
>
> See also comments here:
>
> https://sourceforge.net/tracker/?func=detail&atid=984524&aid=2806053&group_id=203172
>
> ----
>
> wspage@debian:~$ svn diff ~/open-axiom-src/src/algebra > itrigmnp.patch
> wspage@debian:~$ cat itrigmnp.patch
>
> Index: /home/wspage/open-axiom-src/src/algebra/efstruc.spad.pamphlet
> ===================================================================
> --- /home/wspage/open-axiom-src/src/algebra/efstruc.spad.pamphlet	(revision
> 1216)
> +++ /home/wspage/open-axiom-src/src/algebra/efstruc.spad.pamphlet	(working copy)
> @@ -545,6 +545,7 @@
>      macro NTHR == 'nthRoot
>      ker2explogs: (KG, List KG, List SY) -> FG
>      smp2explogs: (PG, List KG, List SY) -> FG
> +    nthroot:     (GF,GF) -> GF
>      supexp     : (UP, GF, GF, Z) -> GF
>      GR2GF      : GR -> GF
>      GR2F       : GR -> F
> @@ -626,13 +627,23 @@
>        map(explogs2trigs(#1::FG),GR2GF, p)$PolynomialCategoryLifting(
>                                      IndexedExponents KG, KG, GR, PG, GF)
>
> -    explogs2trigs f ==
> -      (m := mainKernel f) case "failed" =>
> +    nthroot(a:GF,n:GF):GF ==
> +      r := nthRoot(sqrt(norm(a)),retract(n)@Z)
> +      e := exp(complex(0, 1)*argument(a)/n)
> +      r*e
> +
> +    explogs2trigs(f:FG):GF ==
> +      m := mainKernel f
> +      m case "failed" =>
>          GR2GF(retract(numer f)@GR) / GR2GF(retract(denom f)@GR)
> -      op  := operator(operator(k := m::KG))$F
> +      k := m::KG
> +      op  := operator(operator(k))$F
>        arg := [explogs2trigs x for x in argument k]
>        num := univariate(numer f, k)
>        den := univariate(denom f, k)
> +      is?(op,'nthRoot) =>
> +        h := nthroot(first arg, second arg)
> +        supexp(num,h,0,0)/supexp(den,h,0,0)
>        is?(op,'exp) =>
>          e  := exp real first arg
>          y  := imag first arg
>
> wspage@debian:~$
>
> ----
>
> Regards,
> Bill Page.
>
> On Tue, Jun 16, 2009 at 5:45 PM, Tim Daly<daly@axiom-developer.org> wrote:
>   
>> This one is queued as bug number 7199.
>>
>> When you say the latest "Gold" sources can you tell me the
>> result of the "Version" and "Timestamp" lines from the Axiom banner?
>> Where did you get the sources?
>>
>> Tim
>>
>>
>> Arnold Doray wrote:
>>     
>>> I get the wrong answer for real/imag for some forms of complex numbers.
>>> For example:
>>>
>>> a := (-1*%i)^(1/2)
>>> b := (%i)^(3/2)
>>>
>>> are both equivalent, but imag/real gives complex (and incorrect) answers
>>> for "a" (ie, real(a) and imag(a) are both complex), but I get the right
>>> answers for "b". Also "conjugate" fails on both with an error message.
>>>
>>> Am I missing something here?
>>> I am using Axiom compiled from the latest "Gold" source.
>>> Thanks,
>>> Arnold
>>>
>>>       
>>> ------------------------------------------------------------------------
>>>
>>> _______________________________________________
>>> Axiom-developer mailing list
>>> Axiom-developer@nongnu.org
>>> http://lists.nongnu.org/mailman/listinfo/axiom-developer
>>>       
Excellent. I will try to apply the patch and test it. --Tim




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In a recent report Arnold Doray observed that conjugate sometimes
seems to fail when operating on complicated exact complex numbers:

http://lists.gnu.org/archive/html/axiom-mail/2009-06/msg00027.html

To resolve this problem, the following cumulative patch against FriCAS
adds 'conjugate' and 'norm' for symbolic complex expressions to the to
the patch I sent earlier today.

wspage@debian:~$ svn diff
~/fricas-src/src/algebra/efstruc.spad.pamphlet > ctrigmnp.patch
wspage@debian:~$ cat ctrigmnp.patchIndex:
/home/wspage/fricas-src/src/algebra/efstruc.spad.pamphlet
===================================================================
--- /home/wspage/fricas-src/src/algebra/efstruc.spad.pamphlet	(revision 627)
+++ /home/wspage/fricas-src/src/algebra/efstruc.spad.pamphlet	(working copy)
@@ -767,6 +767,7 @@
   Implementation ==> add
     ker2explogs: (KG, List KG, List SY) -> FG
     smp2explogs: (PG, List KG, List SY) -> FG
+    nthroot:     (GF,GF) -> GF
     supexp     : (UP, GF, GF, Z) -> GF
     GR2GF      : GR -> GF
     GR2F       : GR -> F
@@ -847,13 +848,24 @@
       map(x +-> explogs2trigs(x::FG), GR2GF, p)$PolynomialCategoryLifting(
                                     IndexedExponents KG, KG, GR, PG, GF)

-    explogs2trigs f ==
-      (m := mainKernel f) case "failed" =>
+    -- De Moivre's theorem
+    nthroot(a:GF,n:GF):GF ==
+      r := nthRoot(sqrt(norm(a)),retract(n)@Z)
+      e := exp(complex(0, 1)*argument(a)/n)
+      r*e
+
+    explogs2trigs(f:FG):GF ==
+      m := mainKernel f
+      m case "failed" =>
         GR2GF(retract(numer f)@GR) / GR2GF(retract(denom f)@GR)
-      op  := operator(operator(k := m::KG))$F
+      k := m::KG
+      op  := operator(operator(k))$F
       arg := [explogs2trigs x for x in argument k]
       num := univariate(numer f, k)
       den := univariate(denom f, k)
+      is?(op,'nthRoot) =>
+        h := nthroot(first arg, second arg)
+        supexp(num,h,0,0)/supexp(den,h,0,0)
       is?(op, 'exp) =>
         e  := exp real first arg
         y  := imag first arg
@@ -926,6 +938,10 @@
     imag   : F -> F
       ++ imag(f) returns the imaginary part of \spad{f} where \spad{f}
       ++ is a complex function.
+    conjugate:F-> F
+      ++ conjugate(x+%i*y) returns x-%i*y
+    norm   : F -> F
+      ++ norm(f) returns f*conjugate(f)
     real?  : F -> Boolean
       ++ real?(f) returns \spad{true} if \spad{f = real f}.
     complexForm: F -> Complex F
@@ -952,6 +968,8 @@
     real? f          == empty?(complexKernels(f).ker)
     real f           == real complexForm f
     imag f           == imag complexForm f
+    conjugate f      == real(f) - sqrt(-1) * imag(f)
+    norm f           == f * conjugate(f)

 -- returns [[k1,...,kn], [v1,...,vn]] such that ki should be replaced by vi
     complexKernels f ==
@@ -1067,6 +1085,10 @@
     imag   : F -> FR
       ++ imag(f) returns the imaginary part of \spad{f} where \spad{f}
       ++ is a complex function.
+    conjugate:F-> F
+      ++ conjugate(x+%i*y) returns x-%i*y
+    norm   : F -> FR
+      ++ norm(f) returns f*conjugate(f)
     real?  : F -> Boolean
       ++ real?(f) returns \spad{true} if \spad{f = real f}.
     trigs  : F -> F
@@ -1087,6 +1109,8 @@

     real f        == real complexForm f
     imag f        == imag complexForm f
+    conjugate f      == F2FG real(f) - complex(0,1) * F2FG imag(f)
+    norm f           == FG2F(f * conjugate f)
     rreal? r      == zero? imag r
     kreal? k      == every?(real?, argument k)$List(F)
     complexForm f == explogs2trigs f
wspage@debian:~$

---

Note: These functions treat symbols appearing in values of type
'Expression Complex R' as variables of type R.

(1) -> conjugate(x+%i*y)

   (1)  - %i y + x
                                           Type: Expression(Complex(Integer))
(2) -> norm(x+%i*y)

         2    2
   (2)  y  + x
                                                    Type: Expression(Integer)
(3) -> conjugate(sqrt(x))

         +-+
   (3)  \|x
                                                    Type: Expression(Integer)
(4) -> conjugate(sqrt(x*%i))

          +--+         +--+
          | 2         4| 2
        (\|x   - %i x)\|x
   (4)  -------------------
                  +--+
              +-+ | 2
             \|2 \|x
                                           Type: Expression(Complex(Integer))
(5) ->

Further testing is encouraged.

Regards,
Bill Page.

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Bill,

Do you have an input file of test cases?

Tim


Bill Page wrote:
> In a recent report Arnold Doray observed that conjugate sometimes
> seems to fail when operating on complicated exact complex numbers:
>
> http://lists.gnu.org/archive/html/axiom-mail/2009-06/msg00027.html
>
> To resolve this problem, the following cumulative patch against FriCAS
> adds 'conjugate' and 'norm' for symbolic complex expressions to the to
> the patch I sent earlier today.
>
> wspage@debian:~$ svn diff
> ~/fricas-src/src/algebra/efstruc.spad.pamphlet > ctrigmnp.patch
> wspage@debian:~$ cat ctrigmnp.patchIndex:
> /home/wspage/fricas-src/src/algebra/efstruc.spad.pamphlet
> ===================================================================
> --- /home/wspage/fricas-src/src/algebra/efstruc.spad.pamphlet	(revision 627)
> +++ /home/wspage/fricas-src/src/algebra/efstruc.spad.pamphlet	(working copy)
> @@ -767,6 +767,7 @@
>    Implementation ==> add
>      ker2explogs: (KG, List KG, List SY) -> FG
>      smp2explogs: (PG, List KG, List SY) -> FG
> +    nthroot:     (GF,GF) -> GF
>      supexp     : (UP, GF, GF, Z) -> GF
>      GR2GF      : GR -> GF
>      GR2F       : GR -> F
> @@ -847,13 +848,24 @@
>        map(x +-> explogs2trigs(x::FG), GR2GF, p)$PolynomialCategoryLifting(
>                                      IndexedExponents KG, KG, GR, PG, GF)
>
> -    explogs2trigs f ==
> -      (m := mainKernel f) case "failed" =>
> +    -- De Moivre's theorem
> +    nthroot(a:GF,n:GF):GF ==
> +      r := nthRoot(sqrt(norm(a)),retract(n)@Z)
> +      e := exp(complex(0, 1)*argument(a)/n)
> +      r*e
> +
> +    explogs2trigs(f:FG):GF ==
> +      m := mainKernel f
> +      m case "failed" =>
>          GR2GF(retract(numer f)@GR) / GR2GF(retract(denom f)@GR)
> -      op  := operator(operator(k := m::KG))$F
> +      k := m::KG
> +      op  := operator(operator(k))$F
>        arg := [explogs2trigs x for x in argument k]
>        num := univariate(numer f, k)
>        den := univariate(denom f, k)
> +      is?(op,'nthRoot) =>
> +        h := nthroot(first arg, second arg)
> +        supexp(num,h,0,0)/supexp(den,h,0,0)
>        is?(op, 'exp) =>
>          e  := exp real first arg
>          y  := imag first arg
> @@ -926,6 +938,10 @@
>      imag   : F -> F
>        ++ imag(f) returns the imaginary part of \spad{f} where \spad{f}
>        ++ is a complex function.
> +    conjugate:F-> F
> +      ++ conjugate(x+%i*y) returns x-%i*y
> +    norm   : F -> F
> +      ++ norm(f) returns f*conjugate(f)
>      real?  : F -> Boolean
>        ++ real?(f) returns \spad{true} if \spad{f = real f}.
>      complexForm: F -> Complex F
> @@ -952,6 +968,8 @@
>      real? f          == empty?(complexKernels(f).ker)
>      real f           == real complexForm f
>      imag f           == imag complexForm f
> +    conjugate f      == real(f) - sqrt(-1) * imag(f)
> +    norm f           == f * conjugate(f)
>
>  -- returns [[k1,...,kn], [v1,...,vn]] such that ki should be replaced by vi
>      complexKernels f ==
> @@ -1067,6 +1085,10 @@
>      imag   : F -> FR
>        ++ imag(f) returns the imaginary part of \spad{f} where \spad{f}
>        ++ is a complex function.
> +    conjugate:F-> F
> +      ++ conjugate(x+%i*y) returns x-%i*y
> +    norm   : F -> FR
> +      ++ norm(f) returns f*conjugate(f)
>      real?  : F -> Boolean
>        ++ real?(f) returns \spad{true} if \spad{f = real f}.
>      trigs  : F -> F
> @@ -1087,6 +1109,8 @@
>
>      real f        == real complexForm f
>      imag f        == imag complexForm f
> +    conjugate f      == F2FG real(f) - complex(0,1) * F2FG imag(f)
> +    norm f           == FG2F(f * conjugate f)
>      rreal? r      == zero? imag r
>      kreal? k      == every?(real?, argument k)$List(F)
>      complexForm f == explogs2trigs f
> wspage@debian:~$
>
> ---
>
> Note: These functions treat symbols appearing in values of type
> 'Expression Complex R' as variables of type R.
>
> (1) -> conjugate(x+%i*y)
>
>    (1)  - %i y + x
>                                            Type: Expression(Complex(Integer))
> (2) -> norm(x+%i*y)
>
>          2    2
>    (2)  y  + x
>                                                     Type: Expression(Integer)
> (3) -> conjugate(sqrt(x))
>
>          +-+
>    (3)  \|x
>                                                     Type: Expression(Integer)
> (4) -> conjugate(sqrt(x*%i))
>
>           +--+         +--+
>           | 2         4| 2
>         (\|x   - %i x)\|x
>    (4)  -------------------
>                   +--+
>               +-+ | 2
>              \|2 \|x
>                                            Type: Expression(Complex(Integer))
> (5) ->
>
> Further testing is encouraged.
>
> Regards,
> Bill Page.
>   
> ------------------------------------------------------------------------
>
> _______________________________________________
> Axiom-developer mailing list
> Axiom-developer@nongnu.org
> http://lists.nongnu.org/mailman/listinfo/axiom-developer
>   




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Version: Axiom (July 2008)

Source downloaded from:
http://axiom.axiom-developer.org/axiom-website/downloads/axiom-july2008-src.tgz

Just realized that the latest source is actually Nov 2008. I will try
again with the Nov 2008 version. 

Arnold

On Tue, 2009-06-16 at 17:45 -0400, Tim Daly wrote:
> This one is queued as bug number 7199.
> 
> When you say the latest "Gold" sources can you tell me the
> result of the "Version" and "Timestamp" lines from the Axiom banner?
> Where did you get the sources?
> 
> Tim
> 





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The command I used was "open-axiom" to start Open Axiom. I had compiled
this from their latest stable source too, but did not run the checks.
-AD


On Tue, 2009-06-16 at 17:40 -0400, Tim Daly wrote:
> Your initial report showed the problem from Open-Axiom
> which is not the Axiom project. What command line did you use
> to start Open-Axiom?
> 
> Your problem is also in Axiom so it is listed as a valid bug report.
> It has been assigned bug number 7198.
> 
> Tim





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Subject: [Axiom-developer] Mandriva axiom install
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I was unaware that there was a Mandriva rpm of Axiom anywhere.

All working versions of Axiom are available at:
http://axiom-developer.org/axiom-website/download.html
One of the fedora versions is likely to work fine, especially
since Mandriva is a derivative of the RedHat line.

I will build a Mandriva machine and an Axiom build.

Tim


URL:
  <http://savannah.nongnu.org/support/?106905>

                 Summary: cannot get axiom to work
                 Project: Axiom Computer Algebra System
            Submitted by: None
            Submitted on: Sun 21 Jun 2009 02:28:50 AM UTC
                Category: None
                Priority: 5 - Normal
                Severity: 3 - Normal
                  Status: None
                 Privacy: Public
             Assigned to: None
        Originator Email: ekhaya.lindsay@gmail.com
             Open/Closed: Open
         Discussion Lock: Any
        Operating System: GNU/Linux

    _______________________________________________________

Details:

I am running Mandriva Spring 2009, on a Gnome desktop.
I first installed axiom from the Mandriva rpm installer. 
At the console, absolutely nothing happened when I typed axiom. It simply
returned to my directory. 

I then downloaded and installed the binary file "redhat9" and followed all
the instructions. 
This time an error message of a missing shared library is generated. 
The library referred to is:
libreadline.so.4

I have checked, and note that I have libreadline.so.6

I presume some line in the code has to change. 
How do I do this, so there is a correct reference to libreadline version 6?

Otherwise, I have to give up on trying to use axiom




    _______________________________________________________

Reply to this item at:

  <http://savannah.nongnu.org/support/?106905>

_______________________________________________
  Message sent via/by Savannah
  http://savannah.nongnu.org/




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    Hi,
   =20
    the may-2009 release compiles without problems, but some regression =
tests
    failed.


.....
.....
.....
45 Makefile.linux called
46 Environment : PLF=3DLINUXplatform CCF=3D-O2 -fno-strength-reduce =
-Wall -D_GNU_SOU
RCE -DLINUXplatform -I/usr/X11/include LDF=3D -L/usr/lib =
/usr/lib/libXpm.a  CC=3Dgcc
 AWK=3Dgawk RANLIB=3Dranlib TOUCH=3Dtouch TAR=3Dtar =
AXIOMXLROOT=3D/home/michael/Builds/axi
om/mnt/opensuse/compiler O=3Do BYE=3Dbye LISP=3Dlsp =
DAASE=3D/home/michael/Builds/axiom/s
rc/share XLIB=3D/usr/lib GCLOPTS=3D--enable-vssize=3D65536*2 =
--enable-locbfd --disable
-dynsysbfd --disable-statsysbfd --enable-maxpage=3D512*1024 =
--disable-xgcl --disab
le-tkconfig SRCDIRS=3Dbootdir interpdir sharedir algebradir etcdir =
clefdir docdir=20
graphdir smandir hyperdir browserdir inputdir PATCH=3Dpatch
int/input/DoubleFloat.regress:regression result FAILED 2 of 10 stanzas =
file Doub
leFloat
int/input/FileName.regress:regression result FAILED 2 of 18 stanzas file =
FileNam
e
int/input/TextFile.regress:regression result FAILED 2 of 10 stanzas file =
TextFil
e
int/input/constant.regress:regression result FAILED 1 of 37 stanzas file =
constan
t
int/input/dfloat.regress:regression result FAILED 2 of 10 stanzas file =
dfloat
int/input/e1.regress:regression result FAILED 4 of 7 stanzas file e1
int/input/easter.regress:regression result FAILED 1 of 200 stanzas file =
easter
int/input/ei.regress:regression result FAILED 10 of 20 stanzas file ei
int/input/elemnum.regress:regression result FAILED 16 of 50 stanzas file =
elemnum
int/input/en.regress:regression result FAILED 6 of 7 stanzas file en
int/input/fname.regress:regression result FAILED 1 of 9 stanzas file =
fname
int/input/fname1.regress:regression result FAILED 2 of 18 stanzas file =
fname1
int/input/gamma.regress:regression result FAILED 4 of 12 stanzas file =
gamma
int/input/grpthry.regress:regression result FAILED 3 of 68 stanzas file =
grpthry
int/input/gstbl.regress:regression result FAILED 1 of 1 stanzas file =
gstbl
int/input/ico.regress:regression result FAILED 11 of 65 stanzas file ico
int/input/repa6.regress:regression result FAILED 4 of 33 stanzas file =
repa6
int/input/textfile.regress:regression result FAILED 2 of 10 stanzas file =
textfil
e
int/input/unittest2.regress:regression result FAILED 1 of 236 stanzas =
file unitt
est2



         M.Becker
        =20





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Date: Mon, 22 Jun 2009 02:51:21 -0400
From: Tim Daly <daly@axiom-developer.org>
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Subject: [Axiom-developer] Re: Mandriva axiom install
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Please visit the Axiom download webpage at:
http://axiom-developer.org/axiom-website/download.html

In the download table you can download the binary for a
Mandriva 2009 Spring version of Axiom

Tim


Tim Daly wrote:
> I was unaware that there was a Mandriva rpm of Axiom anywhere.
>
> All working versions of Axiom are available at:
> http://axiom-developer.org/axiom-website/download.html
> One of the fedora versions is likely to work fine, especially
> since Mandriva is a derivative of the RedHat line.
>
> I will build a Mandriva machine and an Axiom build.
>
> Tim
>
>
> URL:
>  <http://savannah.nongnu.org/support/?106905>
>
>                 Summary: cannot get axiom to work
>                 Project: Axiom Computer Algebra System
>            Submitted by: None
>            Submitted on: Sun 21 Jun 2009 02:28:50 AM UTC
>                Category: None
>                Priority: 5 - Normal
>                Severity: 3 - Normal
>                  Status: None
>                 Privacy: Public
>             Assigned to: None
>        Originator Email: ekhaya.lindsay@gmail.com
>             Open/Closed: Open
>         Discussion Lock: Any
>        Operating System: GNU/Linux
>
>    _______________________________________________________
>
> Details:
>
> I am running Mandriva Spring 2009, on a Gnome desktop.
> I first installed axiom from the Mandriva rpm installer. At the 
> console, absolutely nothing happened when I typed axiom. It simply
> returned to my directory.
> I then downloaded and installed the binary file "redhat9" and followed 
> all
> the instructions. This time an error message of a missing shared 
> library is generated. The library referred to is:
> libreadline.so.4
>
> I have checked, and note that I have libreadline.so.6
>
> I presume some line in the code has to change. How do I do this, so 
> there is a correct reference to libreadline version 6?
>
> Otherwise, I have to give up on trying to use axiom
>
>
>
>
>    _______________________________________________________
>
> Reply to this item at:
>
>  <http://savannah.nongnu.org/support/?106905>
>
> _______________________________________________
>  Message sent via/by Savannah
>  http://savannah.nongnu.org/
>




