Jason Grout wrote:
> William Stein wrote:
>> On Wed, May 14, 2008 at 6:57 AM, David Joyner <[EMAIL PROTECTED]> wrote:
>>> On Wed, May 14, 2008 at 8:54 AM, Pedro Patricio <[EMAIL PROTECTED]> wrote:
>>>> nope, booleans means 1+1=1.
>>>> take + as OR and * as AND in the propositional calculus.
>> So 1+1 = 1 and 1*1 = 1 and 1*0 = 0 and 1+0 = 1 and 0+0=0?
>> That's *not* a ring, so you shouldn't make matrices over it in
>> Sage, since in Sage all matrices are over rings.
>>
>> You could "fake things" by creating a new "the booleans" data
>> type but then you are asking for trouble since they aren't a ring.
>>
>> You could also just make a very simple boolean type with
>> the properties you want and make a numpy matrix with
>> entries that type. What do you actually want to *do* with
>> your boolean matrix?
>>
>
> From your post on sage-edu, it sounds like you just want the adjacency
> matrix of the transitive closure of a digraph; is that right? If so,
> you might use the transitive closure function. I can't remember if it
> is defined for digraphs, but it should be easy to extend.
Sorry, I wasn't thinking. Of course the transitive closure function is
defined for digraphs: that's the only case where it's actually interesting.
sage: g=DiGraph({0:[1,2], 1:[3], 2:[5,6]})
sage: g.transitive_closure().adjacency_matrix()
[0 1 1 1 1 1]
[0 0 0 1 0 0]
[0 0 0 0 1 1]
[0 0 0 0 0 0]
[0 0 0 0 0 0]
[0 0 0 0 0 0]
The transitive closure function isn't very smart right now. It ought to
be sped up by looking at the strongly connected components (I don't know
if we already have a function to do that, though).
Jason
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