(50g) Numeric List Commands

08042019, 03:58 PM
Post: #4




RE: (50g) Numeric List Commands
Updating again with two more related programs.
First, the convolution inverse. This is the sequence which, when convolved with the input sequence, produces { 1 0 0 0 ... }, the identity sequence of convolution. The program assumes that you have the program from post #3 above, named DECONV, on your calculator. Code:
Next, the convolution square root. The "convolution square" as defined in the OEIS is the convolution of a sequence with itself. The "convolution square root" is the sequence which must be convolved with itself to produce the input sequence. For example, the triangular numbers { 1 3 6 10 15 21 ... } convolved with themselves (using e.g. the program from post #2 above) returns { 1 6 21 56 126 252 ... }. The convolution square root of this sequence is as expected the triangular numbers. Note that if the input list to this program is not a convolution square, the terms in the output list will not be integers. For instance, the convolution square root of the triangular numbers is { 1 '3/2' '15/8' '35/16' '315/128' '693/256' ... }. Code:
This program will run on the HP48G if PICK3 is replaced with 3 PICK and NIP is replaced with SWAP DROP. The EVAL in the third line can also be removed. 

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(50g) Numeric List Commands  John Keith  01162019, 11:24 PM
RE: (50g) Numeric List Commands  John Keith  01292019, 07:13 PM
RE: (50g) Numeric List Commands  John Keith  05182019, 09:26 PM
RE: (50g) Numeric List Commands  John Keith  08042019 03:58 PM

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