[Axiom-developer] [#191 exquo and therefore gcd cannot handle UP(x, EXPR INT)]

[Bill Page]

Changes 
http://page.axiom-developer.org/zope/mathaction/191ExquoAndThereforeGcdCannotHandleUPXEXPRINT/diff
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??changed:
-simplify q
simplify(q::EXPR INT)

--removed:
-
-From wyscc Mon Jul 11 18:18:25 -0500 2005
-From: wyscc
-Date: Mon, 11 Jul 2005 18:18:25 -0500
-Subject: plausible explanation
-Message-ID: <address@hidden>
-
-The problem is 
-
-\begin{axiom}
-r := simplify (x-2^a)*(x+2^a)
-gcd(p,r)
-\end{axiom}
-ends up in EXPR INT, not 'UP(x,EXPR INT)' which is entirely reasonable. But 
then the 'x' in 'r' is no longer the same 'x' in p and hence the 'gcd(p,r)' is 
1. 
-
-I don't think anything should be fixed. Users are responsible when they mix 
variables in nested polynomial domains. Check out the code for 
triangularSystems where careful pushing and pulling of these variables are done.
-
-From wyscc Mon Jul 11 18:54:08 -0500 2005
-From: wyscc
-[30 more lines...]

??changed:
-So Mathaction should give a warning that in using the reply box (instead of 
directly editing the page), a new session of Axiom is initiated.
-
-My analysis of Mon, 11 Jul 2005 18:18:25 -0500 was not supported (but might 
still be the explanation). When done in step by step, Axiom does coerce 'r' 
correctly to what a normal user would expect. So the question is: why would it 
make a difference when everything is put on one line? 
-
-My guess is that when the command is in one line, the arguments are evaluated 
first (supported by the sequence displayed with ')set mess bot on' ) and the 
coercion is done without the benefit of knowledge that 'gcd' is to be involved. 
Without this, the coercion from 'EXPR INT' to 'UP(x,EXPR INT)' is one from the 
coefficient to the univariate polynomial ring. Then the gcd is performed 
without further problem and yields '1'.  In the step by step case, even though 
in 'gcd(p,r)', 'r' has type 'EXPR INT', the Interpreter is looking for a map 
'gcd' and not finding one, will now coerce 'r' to 'UP(x, EXPR INT)' and this 
time, the coercion was done in a different way. Unfortunately, ')set mess bot 
on' does not help here.
-
-
-
-From BillPage Mon Jul 11 21:24:05 -0500 2005
-From: Bill Page
-Date: Mon, 11 Jul 2005 21:24:05 -0500
-Subject: MathAction playing tricks
-Message-ID: <address@hidden>
-
-William Sit wrote:
-
-> When I edit, the entire page is re-rendered and hence the answer
-> is the correct answer (not 1), but when I reply, a new instance
-> of Axiom is started.
-[73 more lines...]
When done in step by step, Axiom does coerce 'r' correctly to what a normal
user would expect. So the question is: why would it make a difference when
everything is put on one line? 

My guess is that when the command is in one line, the arguments are evaluated
first (supported by the sequence displayed with ')set mess bot on' ) and the
coercion is done without the benefit of knowledge that 'gcd' is to be involved.
Without this, the coercion from 'EXPR INT' to 'UP(x,EXPR INT)' is one from the
coefficient to the univariate polynomial ring. Then the gcd is performed without
further problem and yields '1'.  In the step by step case, even though in
'gcd(p,r)', 'r' has type 'EXPR INT', the Interpreter is looking for a map 'gcd'
and not finding one, will now coerce 'r' to 'UP(x, EXPR INT)' and this time,
the coercion was done in a different way. Unfortunately, ')set mess bot on'
does not help here.

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