#14848: Inconsistencies with FreeAlgebra
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Reporter: ppurka | Owner: AlexGhitza
Type: defect | Status: needs_work
Priority: major | Milestone:
Component: algebra | Resolution:
Keywords: | Merged in:
Authors: | Reviewers:
Report Upstream: N/A | Work issues:
Branch: | Commit:
Dependencies: | Stopgaps:
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Comment (by nbruin):
Regarding point 1: Accessing underscore methods is bound to make your life
hard: the underscore marks that these are methods/attributes for internal
use. The interface is via iteration and using that one can easily
accomplish the task:
{{{
sage: tuple({n[0] for m in g for n in m[1]})
(y, x)
}}}
(i.e., iterate over the terms making up the algebra element, extract the
monomial and iterate over that to extract the variables that occur in
them).
Whether this needs to be wrapped in a method: The operation isn't very
natural: The parent will naturally tell you which variables CAN occur in
in algebra elements. Are the ones that don't have all those variables
really so special that there needs to be a method to query about that?
For polynomials, the same argument holds, but there it was probably added
because some beginners will tend to think of polynomials in terms of SR,
where the variables occurring is really a property of the expression and
not really of SR.
Concerning point 2: The nested operation above shows why it's natural to
return monomials NOT as elements of the algebra: iterating over an algebra
element gives the pairs, iterating over a monomial gives variable-exponent
pairs. The separation actually provides easier access to the underlying
data.
For normal polynomial rings this is probably avoided for efficiency
reasons, but you quickly notice that it's a little inconvenient: you end
up testing quite a bit whether given polynomials are actually monomials,
where doing this via a type check would often in principle be quite
doable.
--
Ticket URL: <http://trac.sagemath.org/ticket/14848#comment:6>
Sage <http://www.sagemath.org>
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