On Monday, 7 January 2013 14:04:36 UTC-7, Benjamin Jones wrote:
>
> On Mon, Jan 7, 2013 at 10:53 AM, Keshav Kini
> <kesha...@gmail.com<javascript:>>
> wrote:
> > Benjamin Jones <benjami...@gmail.com <javascript:>> writes:
> >
> >> On Mon, Dec 17, 2012 at 9:32 PM, P Purkayastha
> >> <ppu...@gmail.com<javascript:>>
>
> >> wrote:
> >>
> >> On 12/18/2012 10:10 AM, Benjamin Jones wrote:
> >>
> >> if y > 0 is true,
> >> is x*(y > 0) true or false?
> >>
> >>
> >> Why is this kind of operation (+,-,*, etc) distributive over
> >> comparison operators? Is this distributive operation well defined
> >> in general, maybe according to some theory?
> >>
> >>
> >>
> >> If you think about the comparison operators as type constructors (for
> >> the SR type), it's useful for them to be functors. In other words,
> >> it's useful to be able to map over them, e.g. map the function that
> >> is multiplication by a constant element of SR over a comparison:
> >>
> >> sage: y = var('y')
> >> sage: x * (y > 0)
> >> x*y > 0
> >>
> >> Just like applying the operator (x*_) over a list [ y, 0 ].
> >
> > Couldn't you apply the same logic to "*" as well? Now (a * b) * c
> > becomes (a * c) * (b * c), which is obviously not what we want.
> >
> > Certainly it's nice to be able to map over things. I would think that
> > there should be some actual syntax for this, though, rather than just
> > implicitly distributing all operations over relational operators. As far
> > as I can see, the only thing that's special here about relational
> > operators as opposed to arithmetic operators is that we don't currently
> > have a coherent way of resolving the application of other operators to
> > relational expressions. I don't think that should mean that by default
> > we just distribute.
> >
> > See also http://trac.sagemath.org/sage_trac/ticket/7660#comment:8 .
> >
> > -Keshav
> >
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> >
>
> I agree that an explicit syntax for mapping over relations would be
> better than having it done implicitly. But, then again, it would be
> nice to implicitly map over equality, there would be no confusion
> there.
>
> So, what should x*(y > 0) do, raise a NotImplementedError? And x*(y ==
> 0)? I guess we just special case inequalities.
>
> --
> Benjamin Jones
>
Or rather equalities may have special case behaviour while others throw an
error?
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