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How to create functions of arbitrary number of variables?

i want to use a Function f[] with different set of arguments. example: f[{x,y,z}] as well as f[{x1,y1,z1},{x2,y2,z2},...,{xn,yn,zn}]. How do i write its definition to accept Both type of calls.

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marked as duplicate by Jens, whuber, rcollyer, Yves Klett, Artes Dec 20 '12 at 14:45

This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.

This could be considered a duplicate of How to create functions of arbitrary number of variables? – Jens Dec 19 '12 at 18:47

The pattern matching in Mathematica gives you a powerful way to define recursive functions.

For example if you'd like to write a function which takes a Mathematica function definition and generates C-Code from it:

<< SymbolicC`
SetAttributes[toSymbolicC, {HoldAll}]
toSymbolicC[x_List] := toSymbolicC /@ x
toSymbolicC[(op : (Plus | Times))[args___]] := 
           COperator[op, toSymbolicC[{args}]]
toSymbolicC[(op : (Cos | Sin))[x_]] := 
           CStandardMathOperator[op, toSymbolicC[x]]
toSymbolicC[x_] := x

I know this should be more elaborated but for the sake brevity I just defined functions for lists, two commutative operators, Cos and his imaginary friend ;).

You'd use it in that way:

toSymbolicC[Cos[x] + Sin[x]]

which yields:

COperator[Plus, {CStandardMathOperator[Cos, x], CStandardMathOperator[Sin, x]}]

to convert this into a regular C-Expression you'd use (of course you could've done this in postfix form)


Hope this gave an idea about the power of pattern matching, especially in symbolic programming languages like Mathematica.

Patterns in Mathematica

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You simply write them:

f[{x_,y_,z_}]:= definition1
f[{x_,y_,z_},{x1_,y1_,z1_},{x2_,y2_,z2_}]:= definition2

Of if you want to match this pattern one or more times you can use the Repeated pattern operator .., and bind the sequence of matches to a single variable p:

f[p:({_,_,_}..)] := definition3

Mathematica will use the most specific pattern that matches a call.

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@jVincentMy definitions of f[] depend on number of Arguments, How do i know how many arguments have been passed ? – santhosh Dec 19 '12 at 10:11
@user4972 In the above you know for certain that definition 1 has one passed, and definition 2 has three passed. In the last definition, the matched p be equal to Sequence[{x,y,z},{x1,y1,z1},...,{xN,yN,zN}], so you can find the length using Length[{p}]. Note that {} is needed due to the way Sequence works. – jVincent Dec 19 '12 at 10:15
So instead Of 1st 2 definitions, i can directly use last one and use Length[{p}] for number of times to execute my operations right ? – santhosh Dec 19 '12 at 10:26
@user4972 Yes, the first two examples where to highlight how you would go about if you knew exactly what numbers it should work for. – jVincent Dec 19 '12 at 10:58
okay.And how do i identify each set of arguments and work on them ? Can i find it like p[[i]] till length[{p}] ? – santhosh Dec 19 '12 at 11:46

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