If you want to carry out operations on the semiring afore mentioned, where adding is OR (not XOR) and multiplying is AND, then you can use floating point arithmetic.
Let Z be 0, and let P be "non-zero positive". Then ordinary multiplication and addition have the following chart ZZ=Z, ZP=Z, PP=P. Z+Z=Z, Z+P=P, P+P=P. So long as you don't overflow/wrap around, you are golden. Of course, you can't invert in this world. The additive identity is Z, but there does not exist an X such that P+X=Z, which is needed for a ring. I'm glad this DLX algorithm is being added to SAGE, now I don't have to implement it myself, and there are wide classes of problems to attack. Here's a challenge: Given a graph, can you find a small subset of vertexes (not edges, but vertexes) such that removing them will partition the graph into two disconnected parts, so that the larger half is at most double the size of the smaller half. If not, then do it be removing edges but they have to be weighted, directed edges, and the removal must be minimal weight. If you can do this, then let me know, I'd be excited. ---Greg --~--~---------~--~----~------------~-------~--~----~ To post to this group, send email to sage-devel@googlegroups.com To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/sage-devel URLs: http://www.sagemath.org -~----------~----~----~----~------~----~------~--~---
