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How to remove unneeded constraints
*To*: mathgroup at smc.vnet.net
*Subject*: [mg87904] How to remove unneeded constraints
*From*: Kristian Schmidt <kristian at kreutz.us>
*Date*: Sat, 19 Apr 2008 23:50:19 -0400 (EDT)
Hello
The problem I am working on is a pretty large problem, which I am solving by dividing it into a lot of subproblems.
As such, I have a large list of constraints that apply to the entire problem, but are not relevant for each individual subproblem.
This becomes a problem when I use Refine, as it takes a very long time when you have a lot of conditions, even though the conditions don't pertain to the problem. Example:
In[25]:= Table[Timing@Refine[p>q,Map[Subscript[x,#]>0&,Range[i]]],{i,1000,5000,1000}]
Out[25]= {{0.547,p>q},{1.797,p>q},{3.875,p>q},{8.594,p>q},{10.468,p>q}}
And it only gets worse.
However, for each individual call to Refine I make, I only need a small subset of the total constraints.
So what I want to do is something like this:
expr = some expression of n different variables;
cond = DeleteCases[totalConstraints, all cases which do not contain a variable from expr];
result = Refine[expr,cond];
I have no idea how to construct a pattern powerful enough to do what is required for the DeleteCases call, though.
All of the variables are of the form Subscript[s,_,_,_] or Subscript[b,_,_] and the conditions can also contain expressions of several variables.
I'd be most grateful for any help. Thank you.
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