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I was reading this documentation page : http://reference.wolfram.com/language/tutorial/DefiningOutputFormats.html

I really don't understand the point of the Format function.

Indeed, if I take the second example :

Format[xrep[n_]] := StringJoin[Table["x", {n}]]

Calling xrep would give the exact same result as defining things like :

xrep[n_]:=StringJoin[Table["x", {n}]]

So what does the function Format "add of new" here.

Same for the first example, I could write : 

bin[x_, y_] := MatrixForm[{{x}, {y}}]

Instead of :

Format[bin[x_, y_]] := MatrixForm[{{x}, {y}}]

And everything would happen the same.

So I don't get what the Format function allows us to do more ?

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1 Answer 1

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Format allows you to show expression in a nice form while you are still able to work with them as before. By evaluating to _String/_MatrixForm you lose information/flexibility.

Consider:

bin /: bin[x_, y_]^n_. := bin[x, y^n]; Format[bin[x_, y_]] := Row[{"bin[", Panel[Column@{x, y}], "]"}]; bin[2, 2]^3 %^3

enter image description here

while

bin2 /: bin2[x_, y_]^n_. := bin2[x, y^n]; bin2[x_, y_] := Row[{"bin2[", Panel[Column@{x, y}], "]"}]; bin2[2, 2]^3 % ^3

enter image description here

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    $\begingroup$ Just a fast question before I can understand your answer : what does the "bin /: " does before you define your bin function ? Or at least what is the name of the symbol ? $\endgroup$ Commented Apr 26, 2018 at 9:52
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    $\begingroup$ @StarBucK see TagSetDelayed but if you select it and hit F1 it will take you there. $\endgroup$ Commented Apr 26, 2018 at 9:53

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