By the way, I am also +1 for all 4, based on my pull from your github
branch.
Aaron Meurer
On Jul 22, 11:00 am, "Aaron S. Meurer" <asmeu...@gmail.com> wrote:
> On Jul 22, 2009, at 1:10 AM, Fabian Pedregosa wrote:
>
>
>
>
>
>
>
> > Aaron S. Meurer wrote:
> >> How do you actually attach assumptions to variables? The old style
> >> keyword argument to Symbol doesn't seem to work. I know that you can
> >> pass Assume objects to query(), but is there a way to globally define
> >> x as positive?
> >> In [1]: x = Symbol('x', positive=True)
>
> > Hi Aaron. There is a way to define global assumptions, although I
> > haven't used it much:
>
> > In [1]: register_global_assumptions(Assume(x, positive=True))
>
> > In [2]: query(x, positive=True)
> > Out[2]: True
>
> I see. Whenever we get this merged, will Symbol('x', positive=True)
> call register_global_assumptions on x? If so, that will be fine.
>
>
>
>
>
> > you can then clear them with clear_global_assumptions(). I'll add this
> > info to doc/src/modules/queries.txt
>
> >> In [2]: query(x, positive=True)
> >> <returns None>
>
> >> In [3]: Assume(x, positive=True)
> >> Out[3]: Assume(x, positive=True)
>
> >> In [4]: query(x, positive=True)
> >> <returns None>
>
> >> In [5]: sqrt(x**2)
> >> Out[5]: x
>
> >> In [6]: sqrt(y**2)
> >> Out[6]:
> >> ⎽⎽⎽⎽
> >> ╱ 2
> >> ╲╱ y
>
> >> In [9]: Assume(y, positive=True)
> >> Out[9]: Assume(y, positive=True)
>
> >> In [10]: sqrt(y**2)
> >> Out[10]:
> >> ⎽⎽⎽⎽
> >> ╱ 2
> >> ╲╱ y
>
> > The new system won't reduce expressions based on assumptions. This
> > will
> > be done by a function called refine (see mathematica's Refine)
>
> >> So the reduction of sqrt(x**2) comes from the old assumptions, not
> >> the
> >> new ones. I realize that not everything is implemented yet, but it
> >> seems that at least [4] should return True.
>
> > Yes, the price to pay in exchange is a small sacrifice in speed.
> > That is
> > why methods in the core should not use query() directly. They should
> > test properties based on class membership and leave assumption-related
> > simplification to refine().
>
> >> For example, in Maple, typing assume(x, positive) changes the
> >> variable
> >> x to be positive everywhere. You can also use "assuming" to only
> >> assume for one expression:
>
> >>> x;
> >> x
> >>> assume(x, positive);
> >>> x;
> >> x~ (the tilde indicates that x
> >> has an assumption on it)
> >>> is(x, positive);
> >> true
> >>> coulditbe(x, negative);
> >> false
> >>> sqrt(x**2)
> >> x~
> >>> sqrt(y**2) assuming y::positive;
> >> y
> >>> sqrt(y**2);
> >> (1/2)
> >> / 2\
> >> \y /
>
> >> Seehttp://www.maplesoft.com/support/help/view.aspx?path=assumefor
> >> more info on the Maple assumptions system.
>
> >> The actual querying of facts seems to work well when you pass
> >> assumptions to query().
> >> In [1]: Assume(x, negative=True, positive=True)
> >> AssertionError: ('inconsitency between facts', {'real': True,
> >> 'nonzero': True, 'commutative': True, 'nonpositive': False,
> >> 'positive': True, 'negative': False, 'nonnegative': True, 'zero':
> >> False, 'complex': True, 'imaginary': False}, 'negative', True)
>
> >> In [2]: query(x, real=True, assumptions=Assume(x, positive=True)) #
> >> this always bothered me for not working in the old assumption system.
> >> Out [2]: True
>
> >> query() seems to be like the Maple is(). Will we also have something
> >> like Maple's coulditbe()?
>
> > I am not familiar with Maple, but since query() returns None when it
> > can't say, I think coulditbe() is just:
>
> See my link above for more info on Maple's assumptions system.
>
>
>
> > In [1]: def coulditbe(*args, **kwargs):
> > ...: _q = query(*args, **kwargs)
> > ...: if (_q is True) or (_q is None): return True
> > ...: return False
>
> > In [2]: register_global_assumptions(Assume(x, positive=True))
>
> > In [3]: coulditbe(x, negative=True)
> > Out[5]: False
>
> > If this is correct, then I don't think it is worth to implement
> > coulditbe
>
> coulditbe() returns True if there are any values of the variables that
> make the expression true. Maple also has is(), which only returns
> true if all values of the variables make the expression true. about()
> will print the exact assumptions.
> For example in Maple:
> > assume(x, integer);
> > coulditbe(x/2, integer);
> true
> > is(x/2, integer);
> false
> > about(x);
> Originally x, renamed x~:
> is assumed to be: integer
>
> In your branch, query seems to take a middle approach. It returns
> True if it is always True, but None if it is not always True, but not
> always False either (or if it cannot determine), and False if it is
> always False. Is this correct.
>
> In [2]: query(x/2, integer=True, assumptions=Assume(x, integer=True))
> <returns None>
>
> It is also common have inequalities as arguments to coulditbe():
> > assume(x, positive);
> > coulditbe(x < 1);
> true
> > is(x < 1);
> false
> > coulditbe(x < 0);
> false
>
> query() doesn't seem to support this yet, unless I am doing it wrong:
> In [3]: query(Ge(x, 1), assumptions=Assume(x, positive=True))
> KeyError: 'popitem(): dictionary is empty'
>
> I'm trying to think of an example of something that Maple could give
> your more information with its two functions than your single query()
> function. The only thing I can think of is the overloading of None in
> query to mean both that it cannot determine and that it could be True
> or False for different values. What do you think?
>
> Aaron Meurer
>
>
>
>
>
> > Regards,
>
> >> Aaron Meurer
> >> On Jul 21, 2009, at 2:02 PM, Fabian Pedregosa wrote:
>
> >>> In this series of 4 patches, I implement a new query system.
>
> >>> You can also pull from my repo, branch master:
>
> >>> git pullhttp://fseoane.net/git/sympy.gitmaster
>
> > --
> >http://fseoane.net/blog/
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