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To explain better what I mean I'll give an example of what I want the symbol to do. I want a symbol that wraps around a unit vector to use it as head for further calculations.

Something like:

UnitVector[{1,0,0}]
UnitVector[{1,1,0}]
(* UnitVector[{1,0,0}] *)
(* $Fail *)

so after I can use it in a function like:

RandomStuff[arg_UnitVector]:=(* Some procedure that requires the argument to be a unit vector *)

I know this can be easily done with a wrapper function that just returns a UnitVector, but I would also like to know how to do this and if it is considered a good or bad practice.

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    $\begingroup$ Probably it should be something like this mathematica.stackexchange.com/a/79891/82074 but without all the fancy box stuff. $\endgroup$
    – AmadoC
    Commented yesterday
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    $\begingroup$ Normally I would do something like unitVectorQ[v_?VectorQ] := TrueQ@Simplify[Norm[v] == 1]; unitVectorQ[_] := False; f[arg_?unitVectorQ] := (*etc*). I can't call to mind a use-case in which having a wrapper head on a standard sort of object like a vector would be convenient. I imagine my code would have to check, add, and remove the wrapper all the time. (Compare for example all the complaints on this site gets about MatrixForm.) $\endgroup$
    – Michael E2
    Commented yesterday
  • $\begingroup$ Thanks, I over simplified my use case from what I really want to do. My problem is that I need to write vectors in two different notations, one is something like an SparseArray but with a different coodinate system and an standard vector. The first one is easier to write as user and the second one is easier to operate, that is why I want a head wraper. $\endgroup$
    – AmadoC
    Commented 22 hours ago

1 Answer 1

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As suggested in the comments you first need a validation function, something like

unitVectorQ[l:{_,_,_}] := SameQ[Norm[l], 1]
unitVectorQ[___] := False

Then write one down value for unitVector

unitVector[in_ /; !unitVectorQ[in]] := $Failed

and it works as expected

In[101]:= unitVector[{1, 0, 0}]

Out[101]= unitVector[{1, 0, 0}]

In[102]:= unitVector[{1, 1, 0}]

Out[102]= $Failed

Now you are guaranteed anything wrapped in unitVector is really a 3-dimensional unit vector.

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