I am not expecting J to resolve these problems I a merely trying to
ascertain how J has improved from APL and to know its limitations
before thinking of applying it to some problems.
I will need to look up your terminology to understand you. I also
seem to be missing part of the thread of the conversation.
Here are some examples of the class of problems that I am referring
to when I concurred that it might be interesting to know the
difference between 1r3 and 111r333:
The work of Gomory and Hu dates from the 1960’s when they studied a
minimum network creation problem. They modeled a network with a
single commodity that had asynchronous flow requirements. The
problem is to assign sufficient capacity on each edge of the network
to accommodate the flow requirements one at a time, at the minimum
possible cost. They used a special case of uniform costs and ignored
complicated constraints which would make the problem much harder to
solve.
A more complicated example is a network loading problem seeking to
meet point to point demand between paired nodes with capacity at the
edges and with demands to be met simultaneously. There is interest
in for example in finding bottlenecks or in case of failure,
rerouting over subnetworks and other types of sensitivity analysis.
Initial steps can aim to find feasible solutions and then various
methods are used to optimize even if an optimal solution cannot be
proved.
I do not know all the details beyond this because I leave that to
experts.
Thanks
Donna
[EMAIL PROTECTED]
On 28-Jun-06, at 6:49 PM, John Randall wrote:
John Randall wrote:
This corresponds to converting a matrix to Smith normal form over the
integers, versus diagonalizing it over the rationals. I agree
that one
might think of this as the difference between 111r333 and 1r3, but
it does
not really have to do with computer representation of rationals:
it is
more that the integers form a principal ideal domain while the
rationals
do not.
Although I got Donna's point, the above is garbled: obviously Z and
Q are
both PIDs. What I meant to say is:
Given an integer matrix, there may be a difference in its Smith normal
forms when it is considered as a matrix over Z (which corresponds
to the
"111r333-:1r3" case) and as a matrix over Q (which corresponds to
"111r333-:1r3"). From Donna's description, I believe the problem lies
here rather than in representations of rational numbers.
Best wishes,
John
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