JR=John Randall, DB=me
JR> Given that the xth Chebyshev polynomial evaluated at y can be written
JR> cos x*arccos y
JR> is there a way to write it using inverses?
DB> I'd be tempted to write:
DB> cheb0 =: 2 _2 */ .o. ,
DB> If you were asking if there's a way to write
DB> this with &. (under), I think the answer is no.
JR> I was thinking along these lines:
JR> t3=:0 _3 0 4&p.
JR> T3=:13 : 'cos 3&* arccos y'
JR> f =:3&* &. arccos
Ah, I see I misunderstood your original question. You wrote cos x*arccos y
intending it to be read as J, but I read it as math notation. Which is to say,
the code I posted solves the wrong problem (i.e. my cheb verbs give (cos
x)*(arccos y) instead of cos(x * arccos y) ). Sorry about that.
JR> What I can't do is make the 3 a parameter. As you indicate, it may be
JR> impossible in a verb.
Correct (I hope my explanation of why is still clear, despite my
misunderstanding).
JR> Perhaps if one really wanted to do this, one should
JR> use an adverb instead.
Of course, you could do this pretty easily, i.e.:
F =: (&*) (&. arccos)
3 F
3&*&.arccos
But adverbial solutions have serious drawbacks (unless the arguments are pretty
static and known in advance, adverbs & conjs are hard to use; it's hard to
slice-and-dice arguments to them).
Coincidentally, Tracy Harms and I were having a discussion on just this topic
not too long ago, on RosettaCode:
http://www.rosettacode.org/wiki/Talk:Forward_difference#J:_verb_vs_adverb
-Dan
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