Hello my friends
A program for polynomial extrapolation can be written
etc=.{.&.:(t :.t=.[: {."1 (2-/\])^:([: i. #))
For example, the first 21 square numbers are extrapolated from 3 square numbers
like this.
21 etc 0 1 4
0 1 4 9 16 25 36 49 64 81 100 121 144 169 196 225 256 289 324 361 400
My first question is this: Can the program be written without naming the
intermediate verb (t) ?
Note that t is an involution:
t t 0 1 4
0 1 4
and the etc program just pads zeroes
21 {. t 0 1 4
0 _1 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
before transforming back.
t 21 {. t 0 1 4
0 1 4 9 16 25 36 49 64 81 100 121 144 169 196 225 256 289 324 361 400
The transformation (t) creates a space-consuming intermediate matrix
(2-/\])^:([: i. #) 1 4 9
1 4 9
_3 _5 0
2 0 0
where only the first row is input and only the first column is output. I want
to compute in-place to save space:
1, 4 9 --> 1 _3, _5 --> 1 _3 2
My second question: How is that done?
Venlig hilsen, Bo
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