       Re: How to remove unneeded constraints

• To: mathgroup at smc.vnet.net
• Subject: [mg87965] Re: How to remove unneeded constraints
• From: Jean-Marc Gulliet <jeanmarc.gulliet at gmail.com>
• Date: Mon, 21 Apr 2008 03:27:30 -0400 (EDT)
• Organization: The Open University, Milton Keynes, UK
• References: <fueeo7\$b82\$1@smc.vnet.net>

```Kristian Schmidt wrote:

> 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:= Table[Timing@Refine[p>q,Map[Subscript[x,#]>0&,Range[i]]],{i,1000,5000,1000}]
> Out= {{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.

Hi Kristian,

A possible solution that I would recommend uses *FreeQ[]* for pattern
matching and *Pick[]* to build the list of constraints that do not
contains the unneeded variables.

In:=

(* We make an arbitrary list of constraints *)

conds = {E^(Subscript[s, 1, 1, 2] + Subscript[b, 3, 1]) > 1,
E^(Subscript[s, 1, 1, 3] + Subscript[b, 3, 1])/+Subscript[b, 2, 2]
<= 100,
Abs[Log[Subscript[s, 1, 1, 3]^Sin[Subscript[b, 1, 2] Pi]]] <= 2};

(* We look for any expression that does not have a variable s for which
the third index is 3 *)

FreeQ[#, Subscript[s, _, _, 3] ] & /@ conds

(*We look for any expression that does not have the variable b with
first index equal to 3 *)

FreeQ[#, Subscript[b, 3, _] ] & /@ conds

(* The returned list does not contain any expression that contains the
variable s for which its third index is 3 *)

Pick[conds, FreeQ[#, Subscript[s, _, _, 3] ] & /@ conds]

(* The following examples should be self-explanatory by now *)

Pick[#, FreeQ[#, Subscript[b, ___, 3, ___] ] & /@ #] &@conds

Pick[#, FreeQ[#, Subscript[_, 1, 2, ___] ] & /@ #] &@conds

Pick[#, FreeQ[#, Subscript[b, 1, 2] | Subscript[s, 1, _, 2]] & /@ #] &@conds

Out= {True, False, False}

Out= {False, False, True}

Out=

b    + s
3,1    1,1,2
{E              > 1}

Out=

Sin[Pi b   ]
1,2
{Abs[Log[s                 ]] <= 2}
1,1,3

Out=

b    + s
b    + s             3,1    1,1,3
3,1    1,1,2      E
{E              > 1, -------------- <= 100}
b
2,2

Out=

b    + s
3,1    1,1,3
E
{-------------- <= 100}
b
2,2

Regards,
-- Jean-Marc

```

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