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14 votes

How can one define a custom data object?

As Michael Pilat explained here it is more robust to use MakeBoxes, rather than Format. Using MakeBoxes: MakeBoxes[diag[m_?MatrixQ], _] ^:= InterpretationBox[RowBox[{"diag", "[", #, ",", #2, "]"} …
Mr.Wizard's user avatar
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8 votes
Accepted

Longest and Shortest won't work in ReplaceList?

To me this is an interesting problem, however I think the question is a misguided one. Briefly: Longest and Shortest only change the order in which an expression is searched for a match. They are not …
Mr.Wizard's user avatar
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5 votes

Opposite of Alternatives

Usually one does not need what you ask for. E.g. a pattern for an even integer greater than 10: x_Integer?EvenQ /; x > 10 (_Integer is not strictly necessary here as only integers will pass EvenQ …
Mr.Wizard's user avatar
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11 votes
Accepted

Permanently extending the behaviour of functions (like decorators)

Based on your requirements I would move the original symbol to a new context. wrapper[fn_, mod_] := Module[{ctxt = Context[fn], name = SymbolName[fn], x}, Context[fn] = "wrapper`" <> ctxt <> To …
Mr.Wizard's user avatar
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93 votes

What does the construct f[x_] := f[x] = ... mean?

Memoization is perhaps the most common application, but it is not the meaning of that construct. More generally it is a construct for a function that redefines itself. This has many uses beyond memo …
Mr.Wizard's user avatar
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4 votes
Accepted

Implement settable properties

Well that's a hairy one. I like it though, as it forced me to think about aspects of evaluation that I am normally oblivious to. Unfortunately that thinking didn't lead to any great insights. My on …
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