max and min evaluating symbolic expressions too soon

[Matt Rissler]

So I'm trying to get around the fact that plotting half of an
ellipsoid with plot3d is nigh impossible,

x,y=var('x,y')
plot3d(sqrt(1-(x^2/9+y^2/4)),(x,-3,3),(y,-2,2))

but I stumbled across this problem in the process. Since the problem
is that we can't evaluate at some points lets replace them. So trying
this

sqrt(max(1-(x^2/9+y^2/4),0))

returns this

sqrt(-1/9*x^2 - 1/4*y^2 + 1)

So passing this into plot3d doesn't fix anything.

Is it possible to have max behave as you would expect with a symbolic
expression, i.e. wait until you evaluate it or restrict the domain to
check what is the maximum of the two or more values.

Thanks,
Matt

[Burcin Erocal]

Hi Matt,

On Mon, 14 Sep 2009 05:02:54 -0700 (PDT)
Matt Rissler <disc...@gmail.com> wrote:

> Is it possible to have max behave as you would expect with a symbolic
> expression, i.e. wait until you evaluate it or restrict the domain to
> check what is the maximum of the two or more values.

Below is a quick implementation of a symbolic max function. It seems
to work here:

sage: max_symbolic = MaxSymbolic()
sage: max_symbolic(5,0)
5
sage: max_symbolic(x,0)
max(x, 0)
sage: max_symbolic(x,0).subs(x=5)
5

Is this at all useful? Note that trying to evaluate this many times
might be very very slow.

Cheers,
Burcin

----

from sage.symbolic.function import SFunction

class MaxSymbolic(SFunction):
def __init__(self):
SFunction.__init__(self, 'max', eval_func=self._eval_)

def _eval_(*args):
largs = len(args)
if largs == 0:
raise TypeError, "expected one or more arguments"
if largs == 1:
return args[0]

res = 0
for x in args:
try:
if hasattr(x, 'pyobject'):
pyobj = x.pyobject()
else:
pyobj = x
except TypeError:
return None
res = max(pyobj, res)

return res

[kcrisman]

Might there be a way to do something that doesn't conflict with the
builtin max function in the same way as the (nearly reviewed) #3587
seems to avoid conflict with the builtin sum function? This would be
pretty useful, as currently:

sage: var('x,y')
(x, y)
sage: max(x,y)
x
sage: f(x)=1+x;g(x)=2-x
sage: max(f,g)
x |--> x + 1

which last result is... debatable.

- kcrisman

On Sep 16, 10:34 am, Burcin Erocal <bur...@erocal.org> wrote:
> Hi Matt,
>
> On Mon, 14 Sep 2009 05:02:54 -0700 (PDT)
>

[Burcin Erocal]

On Wed, 16 Sep 2009 08:16:56 -0700 (PDT)
kcrisman <kcri...@gmail.com> wrote:

>
> Might there be a way to do something that doesn't conflict with the
> builtin max function in the same way as the (nearly reviewed) #3587
> seems to avoid conflict with the builtin sum function? This would be
> pretty useful, as currently:
>
> sage: var('x,y')
> (x, y)
> sage: max(x,y)
> x
> sage: f(x)=1+x;g(x)=2-x
> sage: max(f,g)
> x |--> x + 1
>
> which last result is... debatable.

It's not hard to provide symbolic max and min functions, and we should
definitely do this.

http://trac.sagemath.org/sage_trac/ticket/6949

If we can make them as fast as the builtin max and min, we can consider
replacing the builtin ones with the symbolic alternatives.

Cheers,
Burcin

[Matt Rissler]

I finally got back to looking at this thread. That does work, though
it breaks calling plot3d with the following format:

max_symbolic=MaxSymbolic()
f(x,y)=sqrt(max_symbolic(9-x^2-y^2,0))
plot3d(f(x,y),(x,-3,3),(y,-3,3))

However

plot3d(f,(-3,3),(-3,3))

works fine. So it's a fine work around.

Thanks,

Matt

On Sep 16, 9:34 am, Burcin Erocal <bur...@erocal.org> wrote:
> Hi Matt,
>
> On Mon, 14 Sep 2009 05:02:54 -0700 (PDT)
>

[Iwan Lappo-Danilewski]

This is a really nasty bug.. Symbolic maxima and minima are
mathematical standard tools, they should at least be _callable_ in
standard sage. One can see the problem this way:

p = var("p")
show( plot(max(p,3),(p,0,10)) )
show( plot(min(p,3),(p,0,10)) )

Could someone please post a quickhack to define min_symbolic() other
than

max_symbolic(-a,-b)*(-1)