#13378: Do not cache the non-existence of coerce/convert map too often, and do
not
pretend that there is a conversion where it doesn't make sense at all
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Reporter: SimonKing | Owner: robertwb
Type: defect | Status: new
Priority: major | Milestone: sage-5.3
Component: coercion | Resolution:
Keywords: coercion conversion object cache | Work issues:
Report Upstream: N/A | Reviewers:
Authors: | Merged in:
Dependencies: | Stopgaps:
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Comment (by nbruin):
> ZZ has no parent, it ''is'' a parent. Elements have a parent, but
parents have a category.
Ah yes, keeping that distinction strict is probably a good idea, even if
it's
not always desirable from a strictly mathematical point of view:
{{{
sage: I=ZZ.ideal(3)
sage: I(6)
TypeError: 'Ideal_pid' object is not callable
sage: parent(I)
Monoid of ideals of Integer Ring
sage: category(I)
Category of ring ideals in Integer Ring
}}}
so an ideal is an element and not a parent (although mathematically it's
also a
a non-unitary ring and at the very least a ZZ-module). What's that
category
doing on `I` though? Do elements have a parent ''as well as'' a category?
{{{
sage: V=FreeModule(ZZ,1)
sage: W=V.span([3*V.0])
sage: parent(W)
<class 'sage.modules.free_module.FreeModule_submodule_pid_with_category'>
sage: category(W)
Category of modules with basis over Integer Ring
}}}
And here we're not getting a parent "... of submodules of V", whatever the
...
should be.
Along these lines, by the way:
{{{
sage: NumberField(x^2+1,name='i').ideal(3)
Fractional ideal (3)
sage: QQ.ideal(3)
Principal ideal (1) of Rational Field
}}}
illustrating the usual schism between algebraists and number theorists.
I don't think I'm really trying to make any point here. I'm just checking
to
what degree Sage agrees with my mathematical intuition.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/13378#comment:5>
Sage <http://www.sagemath.org>
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