[Axiom-developer] [#47 complexForm(log(%i) - log(-%i))]

[wyscc]

Changes 
http://page.axiom-developer.org/zope/mathaction/47ComplexFormLogILogI/diff
--

??changed:
-half: ()-> EXPR INT
myhalf: ()-> EXPR INT

??changed:
-Note, I think the current return of  'argument(0::Complex EXPR INT)' and 
'argument(0::Complex INT)' as '%pi/2' are wrong. 
Note, I think the current returns by 'argument(0::Complex EXPR INT)' and 
'argument(0::Complex INT)' as '%pi/2' are wrong. 

??changed:
-Even 'POLY INT' does not have 'OrderedRing' and the reason given was to allow 
'EXPR' to implement 'abs'. I thought about this briefly and wonder what 'abs' 
of a polynomial really should be and find no satisfactory answer (one 
possibility is to define it relative to a term-ordering as the 'abs' of the 
leading coefficient). You probably noted that 'OrderedRing' is not the same as 
'Join(OrderedSet, Ring)'. One use of 'ORDRING' is to step through a segment. 
Clearly, there is no canonical meaning to stepping from one expression (or 
polynomial) to another (since some term-orderings like pure lex is not 
*sequential* because there may be infinitely number of monomials between two).
Even 'POLY INT' does not have 'OrderedRing' and the reason given was to allow 
'EXPR' to implement 'abs'. I thought about this briefly and wonder what 'abs' 
of a polynomial really should be and find no satisfactory answer (one 
possibility is to define it relative to a term-ordering as the 'abs' of the 
leading coefficient). You probably noted that 'OrderedRing' is not the same as 
'Join(OrderedSet, Ring)'. One use of 'ORDRING' is to step through a segment. 
Clearly, there is no canonical meaning to stepping from one expression (or 
polynomial) to another (since some term-orderings like pure lex is not 
*sequential* because there may be infinitely many monomials between two).

--
forwarded from http://page.axiom-developer.org/zope/mathaction/address@hidden