* should be In [4]: s.complement.complement
On Mon, Nov 12, 2012 at 11:50 AM, Matthew Rocklin <[email protected]>wrote: > Actually, we could give you a set of non-intersecting sets fairly easily. > Your problem can be written as follows > > In [2]: s = Union(Interval(2, 5)*Interval(-oo, oo), Interval(-oo, > oo)*Interval(3, 8)) > In [4]: 2.complement.complement > Out[4]: > (((-∞, 2) ∪ (5, ∞)) × [3, 8]) ∪ ([2, 5] × ((-∞, 3) ∪ (8, ∞))) ∪ ([2, 5] × > [3, 8]) > > Not the prettiest but it should suffice. > > > On Mon, Nov 12, 2012 at 11:46 AM, Matthew Rocklin <[email protected]>wrote: > >> Short answer here is, I think, no. >> >> The short answer *should be* that sympy.stats should be able to handle >> all of this for you at a level higher than sets. It currently errs on this >> sort of question unfortunately. It wouldn't be hard to add though. The >> infrastructure is there. >> >> Sets handles this sort of problem while it computes measures. Sadly it >> assumes a measure with density that is always equal to 1. It would be nice >> if this piece were generalized so that it would integrate a general >> function over the domain. In principle this wouldn't be challenging to >> add. The tedium that you're looking to automate is already solved in the >> various `def _measure` functions in `sympy/core/sets.py`. Unfortunately >> it's tangled up with some too-simple assumptions. You would just need to >> add an argument to all of the `_measure` methods. Presumably at the >> Interval base-layer you would replace `return self.right - self.left` with >> `return integrate(f, self)`. >> >> If you implement this on your own outside of SymPy you might find >> Union._measure helpful. It solves the annoying AuBuC == A + B + C - AB - BC >> + ABC problem generally. If this code were generalized so that >> `blah.measure` were replaced with `foo(blah)` I suspect you would have your >> problem 80% solved. >> >> Your sort of problem is exactly what I would like sympy.stats to be able >> to solve with sympy.core.sets. If I ever get more time I'll work on this. >> Probably not for a while though. >> >> I'm happy to help out if you're willing to fix the problem within >> SymPy.sets. It'd be a nice contribution. >> >> >> >> On Mon, Nov 12, 2012 at 10:59 AM, Simon Clift <[email protected]> wrote: >> >>> Hi folks, >>> >>> I have a straightforward, but tedious probability problem that I need to >>> expand symbolically. Sympy's set and interval material is close, but I >>> can't see how it would work in a multidimensional application. I've used >>> Sympy for some fairly intricate PDE problems, but never for this sort of >>> thing, and I would appreciate any suggestions, please. >>> >>> I have a number of events that appear as, for example 2 < X < 5 and 3 < >>> Y < 8 which have associated probabilities and joint distributions (i.e. are >>> not mutually exclusive). From basic probability and set theory >>> >>> p( 2<X<5 \cup 3<Y<8) = p( 2<X<5 ) + p( 3<Y<8 ) - p( 2<X<5 \cap 3<Y<8 ) >>> >>> and so on. My problems start with about 6 unions that are intersections >>> fo 2 conditions each, all in 3 variables, so requires both the expansion >>> above and reduction for intersecting intervals. It isn't difficult, just >>> tedious (and error-prone). >>> >>> I was about to hand-roll the symbolic algebra as Python classes, but I >>> was wondering if there was a way to approach this with Sympy's intervals >>> module. It's not clear to me, from the docs or from experimentation, that >>> it handles multi-dimensional problems. >>> >>> Best regards >>> -- Simon >>> >>> -- >>> You received this message because you are subscribed to the Google >>> Groups "sympy" group. >>> To view this discussion on the web visit >>> https://groups.google.com/d/msg/sympy/-/qd4-NeUkPzIJ. >>> To post to this group, send email to [email protected]. >>> To unsubscribe from this group, send email to >>> [email protected]. >>> For more options, visit this group at >>> http://groups.google.com/group/sympy?hl=en. >>> >> >> > -- You received this message because you are subscribed to the Google Groups "sympy" group. To post to this group, send email to [email protected]. To unsubscribe from this group, send email to [email protected]. For more options, visit this group at http://groups.google.com/group/sympy?hl=en.
