Robert Bradshaw wrote:
>
> On Apr 1, 2008, at 11:59 PM, Jason Grout wrote:
>> Robert Bradshaw wrote:
>>> On Apr 1, 2008, at 9:15 PM, Jason Grout wrote:
>>>
>>>> I'm trying to add _fast_float_ functionality to SymbolicEquation
>>>> objects. However, a perusal of the sage.ext.fast_eval.pyx file
>>>> seems to
>>>> indicate that the operations <, <=, ==, >=, >, and != are not
>>>> supported
>>>> by the fast_float machinery. Is that correct?
>>> That is correct.
>>>
>>>> If so, how do I add
>>>> these operations? If not, then how do I construct a FastDoubleFunc
>>>> object appropriately?
>>>>
>>>> Or, should I just use the python operators and call fast_float on
>>>> each side?
>>> The latter is what I would do--the result of evaluating a symbolic
>>> equation object is a boolean not a float so it would be kind of hard
>>> to hook into this mechanism anyways (well, one could represent True
>>> by one float and False by another, but I don't think that's a very
>>> clean solution).
>>
>> Sorry, Robert, I didn't see your message until just now (after all the
>> work was done). If you want to veto the patch, I understand and
>> I'll do
>> it the way you suggest.
>>
>> The use-case I had in mind called for getting 0 for false and 1 for
>> true, so that is how I implemented it (e.g., contour_plot(x<y,
>> (x,-1,1),
>> (y,-1,1))).
>>
>> Still, it was fun to muck around in the fast_float file. You're
>> amazing!
>
> Thanks.
>
> I put a comment up on trac, but it boils down to
>
> sage: f = (x == 1)
> sage: g = (1 == x)
> sage: bool(f+g)
> True
> sage: ff = f._fast_float_('x') + g._fast_float_('x')
> sage: ff(0)
> 0.0
>
> but I think piecewise functions would be a good way to implement the
> desired functionality.
What sort of interface do you see with piecewise functions and the
_fast_float_ interface (i.e., what sort of opcodes?)
You bring up a good point about the clash between the current semantics
of operations of symbolic equalities and my proposed fast_float
extension. Currently, operations operate on both sides of the equation
if it makes sense (many times it doesn't make sense and an error is
thrown!).
In the patch above, I think of a symbolic equation as a characteristic
function (i.e., 1 where it is true, 0 where it is false). This provides
a very natural, short, and easy notation for such things:
x*(x<1) + (-x)*(x>3) means piecewise([[(-Infinity,1), x], [(1,
Infinity), 0]]) + Piecewise([[(-Infinity, 3), 0], [(3, Infinity), -x]])
and
x*(x<1) + (-x)*(x^2>4) means -- well, I don't know how to express the
constraint that x^2 > 4 using piecewise.
while:
x*(x<1) + (-x*y)*(x^2+y^2<1) -- I'm not sure even how to write this down
using the two variables using piecewise.
Personally, it seems that the characteristic-function approach is more
generally useful (and much nicer notationally) when calling
_fast_float_. Thoughts?
As a middle-ground, how about I implement a SymbolicFormula class that
allows us to express logical combinations of SymbolicEquations. The
SymbolicFormula class, when multiplied under _fast_float_, will act as a
characteristic function.
Jason
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