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Mathematics Mathematica Symbolic Computations

Difference between f1[a_, b_] := a[b]^2 and f2[a_][b_] := a[b]^2 etc.

Tomáš Hruš

Posted 10 years ago

Colleagues, please - it is a difference betwen theese defintifions? It seems to me, that tey are equivalent -- it is true? In[1]:= f1[a_, b_] := a[b]a[2 b] In[2]:= f2[a_][b_] := a[b]a[2 b] In[3]:= f3[a_[b_]] := a[b]*a[2 b] In[4]:= {f1[Func, x], f2[Func][x], f3[Func[x]]} Out[4]= {Func[x] Func[2 x], Func[x] Func[2 x], Func[x] Func[2 x]} Can you give me a link for study this theme? Thanks!

Colleagues, please - it is a difference betwen theese defintifions? It seems to me, that tey are equivalent -- it is true?

In[1]:= f1[a_, b_] := a[b]*a[2 b]

In[2]:= f2[a_][b_] := a[b]*a[2 b]

In[3]:= f3[a_[b_]] := a[b]*a[2 b]

In[4]:= {f1[Func, x], f2[Func][x], f3[Func[x]]}

Out[4]= {Func[x] Func[2 x], Func[x] Func[2 x], Func[x] Func[2 x]}

Can you give me a link for study this theme? Thanks!

POSTED BY: Tomáš Hruš

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Szabolcs Horvát

Posted 10 years ago

The first two accomplish the very same thing, for as long as you keep them in this form. The third one won't always behave the same way though. Consider fun[x_] := x^2 f3[a_[b_]] := a[b]a[2 b] Then `f3[fun[z]]` will evaluate to `f3[z^2]` because `fun[z]` evaluates first. However, if you set `SetAttributes[f3, HoldAll]`, then it will behave more similarly to `f1` and `f2`: `f3[fun[z]]` will now first evaluate to `fun[z]fun[2 z]`, then to `4 z^4`. This is not the complete story, but giving full details is not always educational. So instead I'll leave you with this reference, which (I think) discusses all the relevant issues: http://reference.wolfram.com/mathematica/tutorial/EvaluationOfExpressionsOverview.html In particular, look at the section on Nonstandard Evaluation and the `Hold...` attributes.

POSTED BY: Szabolcs Horvát

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