Jason Grout wrote:
> Wilfried_Huss wrote:
>>
>> On 19 Mrz., 16:47, Jason Grout <[email protected]> wrote:
>>> [email protected] wrote:
>>>> Hello, this command produces one half of a cirle, not 1/4 as excepted.
>>>> I think that this is a bug in sage 3.4
>>>> Robert
>>>> region_plot([y>0,x>0,x^2+y^2<3], (-3, 3), (-3,
>>>> 3),plot_points=100,incol='gray').show(aspect_ratio=1)
>>> I get a quarter-circle on my sage 3.4 and on sagenb.org. Can you try on
>>> sagenb.org?
>> This works:
>> sage: var('x,y')
>> sage: region_plot([y>0,x>0,x^2+y^2<3], (x, -3, 3), (y, -3,3))
>>
>> But if one leaves out the variables, one gets an half circle:
>> sage: region_plot([y>0,x>0,x^2+y^2<3], (-3, 3), (-3,3))
>>
>> I've written a patch which fixes this:
>> http://trac.sagemath.org/sage_trac/ticket/5567
>
>
> Ah, yes, good catch. For those that want to know, Sage was interpreting
> the first two constraints as functions of one variable, so when it
> plugged in two numbers, Sage behaved as though you had typed x>0, x>0.
> When I did my example, I explicitly put in the variable names (it's a
> good habit to be explicit in plotting), so I got the right plot.
>
> There should be a standard function that takes a tuple of functions and
> returns a list of variables for all the functions. This is used all
> over the plotting code, the fast_callable code, now this code, etc.
> Basically, there should be a function that, treating a tuple of
> functions as a vector-valued function, returns the variables used in the
> vector-valued function.
>
> Also, I wonder why fast_float is not used? It could drastically speed
> up plots. You could just replace the lines like:
>
> s = symbolic_expression(f.rhs() - f.lhs()).function(*variables)
>
> with
>
> s = fast_float(f.rhs() - f.lhs(), *vars)
>
> and you'd probably see at least an order of magnitude speedup. (make
> sure to do "from sage.ext.fast_eval import fast_float" first).
>
Actually, I believe that the call to setup_eval_on_grid automatically
does the call to fast_float, so it's probably already happening and we
don't have to worry about anything.
In fact, I think the root of the problem is in
plot/plot3d/parametric_plot3d.py in the adapt_to_callable function (this
is called by setup_for_eval_on_grid, which is in turn called by
region_plot). Observe (and please pardon my debugging in public :)
sage: from sage.plot.plot3d.parametric_plot3d import adapt_to_callable
sage: var('x,y')
(x, y)
sage: funcs = [x,y]
sage: adapt_to_callable(funcs,2)
((<sage.ext.interpreters.wrapper_rdf.Wrapper_rdf object at 0xa9b1d9c>,
<sage.ext.interpreters.wrapper_rdf.Wrapper_rdf object at 0xa9d916c>),
(y, x))
First of all, why in the world are the arguments y, then x? I thought
the convention was alphabetical ordering if an ordering wasn't specified.
Well, the problem is in this line of adapt_to_callable:
tuple(sorted(set(sum( [z.variables() for z in f], ()) )))
Note:
sage: sorted(set(sum([z.variables() for z in funcs],())))
[y, x]
and even
sage: sorted(list(set(sum([z.variables() for z in funcs],()))))
[y, x]
For some reason, sorting the list [y,x] doesn't make it [x,y]:
sage: sorted([y,x])
[y, x]
There seem to be other problems too:
sage: funcs=[x,y,1]
sage: adapt_to_callable(funcs,2)
---------------------------------------------------------------------------
TypeError Traceback (most recent call last)
/home/jason/.sage/temp/littleone/16993/_home_jason__sage_init_sage_0.py
in <module>()
/home/jason/sage/local/lib/python2.5/site-packages/sage/plot/plot3d/parametric_plot3d.pyc
in adapt_to_callable(f, nargs)
620 except TypeError:
621 vars = ()
--> 622 f = [fast_float_constant(x) for x in f]
623
624 if nargs is not None and len(vars) != nargs:
/home/jason/sage/local/lib/python2.5/site-packages/sage/ext/fast_eval.so
in sage.ext.fast_eval.fast_float_constant (sage/ext/fast_eval.c:6827)()
/home/jason/sage/local/lib/python2.5/site-packages/sage/ext/fast_eval.so
in sage.ext.fast_eval.FastDoubleFunc.__init__ (sage/ext/fast_eval.c:2781)()
TypeError: a float is required
This comes from assuming that if any of the functions doesn't have a
.variables() method, then *all* of the functions must be constants.
That seems a bit silly...
So I think it not a coincidence that this function has no doctests. I
think this is yet another example of code that doesn't have doctests
that (not surprisingly) is broken.
Wilfried, can you take a look at this function (adapt_to_callable)? I
think fixing it will fix probably lots of other bugs as well, since it
is called from lots of plotting code.
Thanks,
Jason
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