Re: Length of a held expression

*To*: mathgroup at smc.vnet.net*Subject*: [mg96588] Re: Length of a held expression*From*: Nikolaus Rath <Nikolaus at rath.org>*Date*: Mon, 16 Feb 2009 16:41:09 -0500 (EST)*References*: <gn8jdj$7qa$1@smc.vnet.net>

Hi, Nikolaus Rath <Nikolaus at rath.org> writes: > Hello, > > How can I get the length of a list in a Hold[] expression? It seems that in my attempt to produce a short example, I also simplified away the actual problem. So here it comes in slightly longer form. I have written a function that propagates uncertainties in the parameters of a function into the uncertainty of the result. It is used as follows: error[a*b, {a, b}, {aErr, bErr}] --> {a b, Sqrt[Abs[aErr b]^2 + Abs[a bErr]^2]} so it yields the formula again, together with its error. However, usually the parameter already have values assigned to them when I call the function. As was correctly pointed out, I can easily circumvent this problem by packing the call into a Block[]: a = 10; b = 20; aErr = 1; bErr = 2; Block[{a,b}, error[a*b, {a, b}, {aErr, bErr}]] However, I was wondering if it might not be possible to handle this case entirely in the error function, so that I can call a = 10; b = 20; aErr = 1; bErr = 2; error[a*b, {a, b}, {aErr, bErr}] and get the correct result. *So I am not really solving an actual problem here*, I'm just playing with Mathematica's programming model to see if it would allows me to do such a thing. I figured out that, in order to be really able to work with the unevaluated expression I cannot to wrap it in Hold[], but I have to "escape" all the parameters that might otherwise be evaluated. So what I'm doing is this: SetAttributes[error, HoldAll]; error::varno = "There must be the same number of variables and errors"; error[expr_, vars_, errs_] := Module[{safeExpr, safeVars, res, escapeRule, restoreRule, varno}, varno = Length[vars]; If[varno != Length[errs], Message[error::varno]; Throw[$Failed]; ]; (* This replaces the given variables (which may have global definition= s) by local ones *) escapeRule = Table[ Extract[Hold[vars], {1, i}, HoldPattern] -> safeVars[i], {i, varno}]; (* This restores the original values of the variables *) restoreRule = Table[safeVars[i] -> vars[[i]], {i, varno}]; (* Escape variables, so that we can differentiate the expression *) safeExpr = ReleaseHold[Hold[expr] /. escapeRule]; (* Calculate result with error *) {expr, Sqrt[Plus @@ Table[ Abs[D[safeExpr, safeVars[i]] errs[[i]] /. restoreRule ]^2, {i, varno}]]} ] This indeed works nicely, except for one thing: in order to replace all the global variables in the expression by local ones, I have to iterate over the list of parameters, which in turn requires me to know it's length. However, if I'm calculating the length with Length[vars] as above, vars is evaluated first which may, in theory, change its length. (I cannot really come up with an example where this may actually happen, but as I said I'm not trying to solve a real problem anyway). Now that I've written this all up so nicely, I also realize that the solution with Length[Unevaluated[vars]] will also work for this case. I'm mailing this anyway now, since I've already spend so much time writing it. Maybe someone else can come up with a more elegant version to do the above, so this mail wasn't entirely pointless :-). Best, -Nikolaus -- =C2=BBTime flies like an arrow, fruit flies like a Banana.=C2=AB PGP fingerprint: 5B93 61F8 4EA2 E279 ABF6 02CF A9AD B7F8 AE4E 425C

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