Benjamin Jones <benjaminfjo...@gmail.com> writes:
> On Mon, Dec 17, 2012 at 9:32 PM, P Purkayastha <ppu...@gmail.com>
> 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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