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  1. PO
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    <p>This is recipe from Stan Wagon's book...use it when built-in Plot behaves erratically due to lack of precision</p> <pre><code>Options[PrecisePlot] = {PrecisionGoal -&gt; 6}; PrecisePlot[f_, {x_, a_, b_}, opts___] := Module[{g, pg}, pg = PrecisionGoal /. {opts} /. Options[PrecisePlot]; SetAttributes[g, NumericFunction]; g[z_?InexactNumberQ] := Evaluate[f /. x -&gt; z]; Plot[N[g[SetPrecision[y, \[Infinity]]], pg], {y, a, b}, Evaluate[Sequence @@ FilterRules[{opts}, Options[Plot]]]]]; </code></pre> <p>I often use the following trick from Kristjan Kannike's when I need "dictionary-like" behavior from Mathematica's downvalues</p> <pre><code>index[downvalue_, dict_] := (downvalue[[1]] /. HoldPattern[dict[x_]] -&gt; x) // ReleaseHold; value[downvalue_] := downvalue[[-1]]; indices[dict_] := Map[#[[1]] /. {HoldPattern[dict[x_]] -&gt; x} &amp;, DownValues[dict]] // ReleaseHold; values[dict_] := Map[#[[-1]] &amp;, DownValues[dict]]; items[dict_] := Map[{index[#, dict], value[#]} &amp;, DownValues[dict]]; indexQ[dict_, index_] := If[MatchQ[dict[index], HoldPattern[dict[index]]], False, True]; (* Usage example: *) (* Count number of times each subexpression occurs in an expression *) expr = Cos[x + Cos[Cos[x] + Sin[x]]] + Cos[Cos[x] + Sin[x]] Map[(counts[#] = If[indexQ[counts, #], counts[#] + 1, 1]; #) &amp;, expr, Infinity]; items[counts] </code></pre> <p>When evaluation results are confusing, sometimes it helps to dump evaluation steps into a text file</p> <pre><code>SetAttributes[recordSteps, HoldAll]; recordSteps[expr_] := Block[{$Output = List@OpenWrite["~/temp/msgStream.m"]}, TracePrint[Unevaluated[expr], _?(FreeQ[#, Off] &amp;), TraceInternal -&gt; True]; Close /@ $Output; Thread[Union@ Cases[ReadList["~/temp/msgStream.m", HoldComplete[Expression]], symb_Symbol /; AtomQ@Unevaluated@symb &amp;&amp; Context@Unevaluated@symb === "System`" :&gt; HoldComplete@symb, {0, Infinity}, Heads -&gt; True], HoldComplete] ] (* Usage example: *) (* puts steps of evaluation of 1+2+Sin[5]) into ~/temp/msgStream.m *) recordSteps[1+2+Sin[5]] </code></pre>
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    1. POWhat is in your Mathematica tool bag?
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    1. USYaroslav Bulatov
    1. USYaroslav Bulatov
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      1. VTUpMod
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    1. COAn usage sample would be great. Try to post one when you have time.
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      1. USDr. belisarius
    2. CODo you know Kristjan? I used to work in the same group with him in Helsinki. Nice guy, small world.
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      1. USTimo
    3. CONope, found his code on the web. Actually, tried to email him to fix a small bug in the code, but the email on his webpage no longer works
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      1. USYaroslav Bulatov
 

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