[Axiom-developer] [#193 Symbolic values (without variables) are not ordered properly in 'EXPR INT'] Two different orderings mixed up

[wyscc]

Changes 
http://page.axiom-developer.org/zope/mathaction/193SymbolicValuesWithoutVariablesAreNotOrderedProperlyInEXPRINT/diff
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??changed:
-(This is reminescent of FORTRAN: type promotion from INTEGER to REAL). In 
other words, if one wants to test numerical inequalities involving symbolic 
constants, one should work in 'EXPR Float', not 'EXPR Integer' since most 
symbolic constants are not integers. To provide an automatic type promotion 
from 'EXPR INT' to 'EXPR Float' would interfere with the ordering in polynomial 
expressions, unless a symbolic constant can be distinguished from a polynomial 
variable. We cannot overload the operator '<' for two distinct orderings in the 
same domain. I think the suggestion I posted in #47 of a 'SymbolicFloat' domain 
may be worth exploring. In 'SymbolicFloat', we can retain symbolic manipulation 
of expresions with symbolic constants by using the term-ordering of the 
underllying representation, and still use the numerical ordering of the domain 
'SymbolicFloat'. 
(This is reminescent of FORTRAN: type promotion from INTEGER to REAL). In other 
words, if one wants to test numerical inequalities involving symbolic 
constants, one should work in 'EXPR Float', not 'EXPR Integer' since most 
symbolic constants are not integers. To provide an automatic type promotion 
from 'EXPR INT' to 'EXPR Float' would interfere with the ordering in polynomial 
expressions, unless a symbolic constant can be distinguished from a polynomial 
variable. We cannot overload the operator '<' for two distinct orderings in the 
same domain. I think the suggestion I posted in #47 of a 'SymbolicFloat' domain 
may be worth exploring. In 'SymbolicFloat', we can retain symbolic manipulation 
of expressions with symbolic constants by using the term-ordering of the 
underlying representation, and still use the numerical ordering of the domain 
'SymbolicFloat'. 

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