Vector as an argument in function definition

Questions
1

Can I somehow specify that G is a vector in function definition so that it won’t complain?

c0[G_, \[Theta]0_, \[CapitalPhi]0_, Q_] := 
 Normal@SeriesCoefficient[Sqrt[
   G[[1]]^2  + G[[2]]^2 - 
    2 Q Sin[\[Theta]] (G[[1]] Cos[\[Phi]] + 
       G[[2]] Sin[\[Phi]])], {\[Theta], \[Theta]0, 
    0}, {\[Phi], \[Phi]0, 0}]
2

You can try with

c0[G_?VectorQ, \[Theta]0_, \[CapitalPhi]0_, Q_]

Beware that using capital letters for variables is not recommended in Mathematica.

3

Doesn’t work.

4

Could you post an example of a complaint?

In[12]:= c0[G_, \[Theta]0_, \[CapitalPhi]0_, Q_] := 
 Normal@SeriesCoefficient[
   Sqrt[G[[1]]^2 + G[[2]]^2 - 
     2 Q Sin[\[Theta]] (G[[1]] Cos[\[Phi]] + 
        G[[2]] Sin[\[Phi]])], {\[Theta], \[Theta]0, 
    0}, {\[Phi], \[Phi]0, 0}]

In[13]:= c0[{a, b}, c, d, e]

Out[13]= Sqrt[a^2 + b^2 - 2 a e Cos[\[Phi]0] Sin[c] - 
 2 b e Sin[c] Sin[\[Phi]0]]
5

You are right, it works with SetDelayed, can we make it work with Set, so that the function will be evaluated right away instead of waiting?

Part::partd: Part specification G[[1]] is longer than depth of object. >>
6

In[17]:= c02[{g1_, g2_}, [Theta]0_, [CapitalPhi]0_, Q_] =
Normal@SeriesCoefficient[
Sqrt[g1^2 + g2^2 -
2 Q Sin[[Theta]] (g1 Cos[[Phi]] +
g2 Sin[[Phi]])], {[Theta], [Theta]0, 0}, {[Phi], [Phi]0,
0}]

Out[17]= Sqrt[g1^2 + g2^2 - 2 g1 Q Cos[\[Phi]0] Sin[\[Theta]0] - 
 2 g2 Q Sin[\[Theta]0] Sin[\[Phi]0]]

In[18]:= c02[{a, b}, c, d, e]

Out[18]= Sqrt[a^2 + b^2 - 2 a e Cos[\[Phi]0] Sin[c] - 
 2 b e Sin[c] Sin[\[Phi]0]]
7

I was just thinking that if G is multidimensional, say 100, there should be a way to pass it as an argument to a function.

8

What function of G do you have in mind? The following works with immediate assignment, but it won’t speed up calculations, I am afraid:

f[u_?VectorQ, v_?VectorQ] = u.v

Using vector notation you may write your function a little more elegantly

c02[g_?VectorQ, \[Theta]0_, \[CapitalPhi]0_, Q_] := 
 Normal@SeriesCoefficient[
   Sqrt[g.g - 
     2 Q Sin[\[Theta]] g.{Cos[\[Phi]], 
        Sin[\[Phi]]}], {\[Theta], \[Theta]0, 0}, {\[Phi], \[Phi]0, 0}]

but it only makes sense for a 2-dimensional g, and it only works with delayed assignment.
Also, I think SeriesCoefficient does not need Normal.

9

There are ways to use Hold to defer evaluation, but I have not encountered many cases where that is preferable to just defering the entire expression with SetDelayed.

In[1]:= tuplesPlus[x_, n_, y_] = Tuples[x, n] + y

During evaluation of In[1]:= Tuples::normal: Nonatomic expression expected at position 1 in Tuples[x,n]. >>

Out[1]= y + Tuples[x, n]

In[2]:= tuplesHeld[x_, n_, y_] = Hold[Tuples[x, n]] + y

Out[2]= y + Hold[Tuples[x, n]]

In[3]:= tuplesHeld[{a, b, c}, 2, d] // ReleaseHold

Out[3]= {{a + d, a + d}, {a + d, b + d}, {a + d, c + d}, {b + d, 
  a + d}, {b + d, b + d}, {b + d, c + d}, {c + d, a + d}, {c + d, 
  b + d}, {c + d, c + d}}