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Re: Re: listing user defined, independent variables

  • To: mathgroup at smc.vnet.net
  • Subject: [mg96876] Re: [mg96819] Re: listing user defined, independent variables
  • From: "Paul Ellsmore" <paul.ellsmore at nanion.co.uk>
  • Date: Thu, 26 Feb 2009 07:59:25 -0500 (EST)
  • References: <go0j0p$mta$1@smc.vnet.net> <200902250907.EAA15875@smc.vnet.net>

Hi Albert,

Thanks for this. I had other replies which mentioned OwnValues. I had never
heard of this function, but it is clearly the kind of thing I need.
Unfortunately, your code doesn't quite do what i need. As an example, here
are two "independent" variables, indVarA and indVarB, and a "dependent"
variable, depVarC. I actually want to get at indVarA and indVarB, but your
code seems to be aimed at getting depVarC:

In[In[26]:=
indVarA=1
indVarB=2
depVarC=indVarA*indVarB

Out[26]=
1

Out[27]=
2

Out[28]=
2


Using your code:

In[29]:=
(*ensure that we can see the symbols, not only the values:*) 

In[30]:=
SetAttributes[dependentQ, HoldFirst]

In[31]:=

(* if we get a symbol which has an OwnValue, extract the unevaluated RHS of
its OwnValue and see whether it contains symbols from the Global
context: *)

In[32]:=
dependentQ[var_Symbol] :=
 If[TrueQ[Length[OwnValues[var]] > 0],
  Not[FreeQ[Extract[OwnValues[var], {1, 2}, Hold],
    s_Symbol /; Context[s] == "Global`"]],
  False
  ]


In[33]:=
(* as a filter for variable names, it is handy if we accept strings as
arguments, too: *) 

In[34]:=
dependentQ[name_String] :=  dependentQ @@ ToExpression[name, InputForm,
Hold]

In[35]:=
 (* use as filter: *)

In[36]:=
Select[Names["Global`*"], dependentQ]

We get a zero length list as output:

Out[36]=
{}


I want to get indVarA and indVarB as output, but if I remove the "Not" from
your code, I get:


In[37]:=
 SetAttributes[dependentQ, HoldFirst]


dependentQ[var_Symbol] :=
 If[TrueQ[Length[OwnValues[var]] > 0],
  FreeQ[Extract[OwnValues[var], {1, 2}, Hold],
    s_Symbol /; Context[s] == "Global`"],
  False
  ]

dependentQ[name_String] :=  dependentQ @@ ToExpression[name, InputForm,
Hold]


Select[Names["Global`*"], dependentQ]


Out[40]=
{depVarC,indVarA,indVarB}


I am not entirely sure I understand your syntax, but I assume that we are
trying to get OwnValues[var_Symbol], without the rhs being evaluated. I
would hope to get OwnValues[depVarC] to be {HoldPattern[depVarC] :> indVarA
+ indVarB}, or something like that, but everything i try gives the evaluated
rhs:

In[41]:=

SetAttributes[myExtract,HoldFirst]
myExtract[var_Symbol]:=Extract[OwnValues[var], {1, 2}, Hold]

In[43]:=

myExtract[depVarC]

Out[43]=
Hold[2]


If I can get the unevaluated rules for each synbol, using OwnValues or any
other function, I will be able to do what I need. Any idea how to do this?

Cheers,

Paul

-----Original Message-----
From: Albert Retey [mailto:awnl at gmx-topmail.de] 
Sent: 25 February 2009 09:07
To: mathgroup at smc.vnet.net
Subject: [mg96876] [mg96819] Re: listing user defined, independent variables

Paul Ellsmore wrote:
> Hi,
> 
>  
> 
> I have a notebook in which there are over 1300 variables (symbols)
defined.
> The vast majority of these are dependent variables. I can get a list of
them
> all with Names["Global`*"], but what I really want is a list of only the
> independent variables. Is there any obvious way to do this? Mathematica
must
> "know" which variables are functions of other symbols, so I was hoping
that
> there would be an "attribute" of a dependent variable that I could use as
a
> filter on Names[]. Any thoughts? I am using V5.1.

I don't think that there is an attribute for that information. The
internals of mathematica are mostly rule based, and OwnValues[] will
give you the information which can be used to determine the dependencies
that you are seeking. I could only think about a rather involved way to
extract that information, since you need to be careful to not evaluate
too early. The following is an approach to determine the dependencies:

(*ensure that we can see the symbols, not only the values:*)
SetAttributes[dependentQ, HoldFirst]

(* if we get a symbol which has an OwnValue, extract the unevaluated RHS
of its OwnValue and see whether it contains symbols from the Global
context: *)
dependentQ[var_Symbol] :=
 If[TrueQ[Length[OwnValues[var]] > 0],
  Not[FreeQ[Extract[OwnValues[var], {1, 2}, Hold],
    s_Symbol /; Context[s] == "Global`"]],
  False
  ]

(* as a filter for variable names, it is handy if we accept strings as
arguments, too: *)
dependentQ[name_String] :=
 dependentQ @@ ToExpression[name, InputForm, Hold]

(* use as filter: *)
Select[Names["Global`*"], dependentQ]

It might well be that there are simpler and/or more efficient ways to do
this, but I can't think of one now and it should be a starting point...

hth,

albert



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