Re: Re: Crossreference, code documentation

• To: mathgroup at christensen.cybernetics.net
• Subject: [mg1673] Re: [mg1633] Re: Crossreference, code documentation
• From: Allan Hayes <hay%haystack at christensen.cybernetics.net>
• Date: Tue, 11 Jul 1995 05:37:19 -0400

```Levent Kitis <lk3a at kelvin.seas.virginia.edu>
wrote in [mg1633] Re: Crossreference, code documentation

>In Message-ID: <3tahhp\$6bb at news0.cybernetics.net>
>wagner at bullwinkle.cs.Colorado.EDU (Dave Wagner) writes:

>> This function finds all symbols in an
>> expression without allowing anything to evaluate:
>>
>> 	SetAttributes[FindSymbols, HoldFirst]
>> 	FindSymbols[expr_] :=
>> 	    String | Integer | Real | Complex | Rational, {},
>> 	    Symbol, {HoldForm[expr]},
>> 	    _,  Union[Flatten[ReleaseHold[
>> 				Map[FindSymbols,
>> 				    Apply[List, Hold[expr], {1}],
>> 				    {2}] ]],
>> 		      FindSymbols @@ HeldPart[Hold[expr], 1, 0]
>> 		]
>> 	]
>>
>
>This functionality is more simply achieved, without resorting to
>recursion, by the function  findsym  :
>
>--------------------------------------------------------------------->
>  SetAttributes[{findsym, WrapAll}, HoldAll]
>
>  findsym[expr_] :=
>      Union[
>         Cases[
>	    Level[ WrapAll[expr], {0, Infinity}, Heads -> True],
>            Hold[x_Symbol] :> HoldForm[x]
>	 ]
>      ]
>
>  WrapAll[expr_] := First[Map[ Hold, Hold[expr], Infinity, Heads
-> > True ]]
---------------------------------------------------------------------

Some further simplification and speed up seems possible:

SetAttributes[findsym2, HoldAll]

findsym2[expr_] :=
Union[
Cases[ Unevaluated[expr],
x_Symbol -> HoldForm[x],
{-1},
]
]

EXAMPLES:

{  findsym[1/0] == findsym2[1/0],
Do[ findsym[1/0],{100}]//Timing//First,
Do[findsym2[1/0],{100}]//Timing//First
}

{True, 0.466667 Second, 0.15 Second}

{a, b, c, f, g} = {1, 2, 3, func1, func2};
{  findsym[f[a][ b, g[c]]] === findsym[f[a][ b, g[c]]],
Do[ findsym[f[a][ b, g[c]]],{100}]//Timing//First,
Do[findsym2[f[a][ b, g[c]]],{100}]//Timing//First
}

{True, 0.533333 Second, 0.216667 Second}

test := findsym[P[{x, f[f[g[a], b], b, h[c], f]}] +
Sin[x + Pi y] Log[c] Exp[I x + u]/(9 Integrate[Pi x, {x, 0, 2}])]
test2 := findsym2[P[{x, f[f[g[a], b], b, h[c], f]}] +
Sin[x + Pi y] Log[c] Exp[I x + u]/(9 Integrate[Pi x, {x, 0, 2}])]
{   test === test2,
Do[test,{100}]//Timing//First,
Do[test2,{100}]//Timing//First
}

{True, 2.21667 Second, 1. Second}

findsym[Infinity/0 + "string"/0 + (3 + I u)/Infinity] ===
findsym2[Infinity/0 + "string"/0 + (3 + I u)/Infinity]

True

Allan Hayes
De Monfort University, Leicester, UK
hay at haystack.demon.co.uk

```

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