On Jun 4, 2008, at 8:40 AM, Dan Christensen wrote:
>
> "William Stein" <[EMAIL PROTECTED]> writes:
>
>> Sage Enhancement Proposal: Change comparisons that involve
>> elements of the symbolic ring to return True or False if both sides
>> of the symbolic comparison are constants and the comparison can
>> be definitely determined.
>
> I'm not sure what symbolic equations are currently used for,
Stuff like
sage: solve(x^2 == 5)
[x == -sqrt(5), x == sqrt(5)]
> but
> this kind of special casing can cause problems. If I'm building
> up an equation using inputs that I don't control, my code may
> have unexpected problems if what it thinks is a symbolic equation
> turns into a boolean.
I agree, think we should either always (my preference) or never
return a symbolic equation. "Can be definitely determined" could be
expensive too.
> Maybe the heart of the matter is that we need a separate notation
> for symbolic equations vs. comparison. E.g.
>
> sage: 3 == pi
> False
>
> sage: 3 === pi
> 3 === pi
>
> sage: 1.2 == 1.3
> False
>
> sage: 1.2 === 1.3
> 1.2 === 1.3
>
> Note that this gives you the ability to have symbolic equations
> when the components happen to not be symbolic. (Does this even
> make sense given the current set-up?)
>
> I'm not sure what to do if the user requests a comparison that
> sage can't easily determine:
>
> sage: sqrt(3) + sqrt(8) == sqrt(5) + pi
>
> One idea would be to return a symbolic equation
>
> sqrt(3) + sqrt(8) === sqrt(5) + pi
>
> but probably the best is to raise an exception: if my code is
> expecting a boolean, then a symbolic equation may confuse it.
>
> So my SEP would be that == always returns a boolean or raises
> an exception, and === always returns a symbolic equation.
>
> The notation === is of course a topic for discussion. If ===
> is chosen, it would have to use the pre-processor. Is there
> another operator that would make sense?
This was actually one of the original proposals. One would also have
to come up with operators for <, <=, >=, >, and !=. Also, in the
current system, it is easy to do
sage: bool(3 == pi)
False
sage: if 3 == pi:
print "bad"
....:
sage:
- Robert
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