# http://www.ex-parrot.com/~tom/calcs/calcs/encyc/progs/src/patfind.ctf
# ========================================================================
# Program name: Polynomial Pattern Finder
# 
#      Version: 1.0
#       Author: Tom Lynn
#         Date: 1994-7
#       Models: 9700, 9800
#
#
# Description:
#
# Polynomial pattern finder, based on Babbage's Difference Engine.
# Enter a sequence of numbers, and it outputs the equation which
# generated the sequence, and the projected continuation.
# e.g. 1,4,9,16 gives x^2, continuing 25, 36, etc.
# 
# Originally written for the 7000, this version has been padded out
# a little for clarity.
#


@@ Program "~PATFIND"

"   Pattern Finder"
" "
"Enter terms:"
Mcl
Defm 11
'11 MIN
1->B
?->L
Lbl 7
Isz B
?->K[B]
Lbl 0
1->C
B->D
Lbl 1
C=B-1=>Goto 7
1->E
Lbl 2
F[6C+E]-E[6C+E]->K[6C+E]
Isz E
E<D=>Goto 2
Dsz D
1->E
1->A
Lbl 3
E=D=>Goto 4
K[6C+E]->J
L[6C+E]->K
Abs (Int 1\exp9J-Int 1\exp9K>2)=>0->A
0->K
Isz E
Goto 3
Lbl 4
A=0=>Isz C
A=0=>Goto 1
L[6C]/C!->E[C]
1->E
Lbl 5
K[E]-E[C]*E^C->K[E]
Isz E
E<=B=>Goto 5
1->E
Lbl 6
0->K
Isz E
K[E]->K
J[E]->J
Abs (Int 1\exp9J-Int 1\exp9K<=2)=>9!->K
K=9!=>E<B=>Goto 6
E<>B=>Goto 0
I=0=>Goto A
I_
"                  n^4"
Lbl A
H=0=>Goto B
H_
"                  n^3"
Lbl B
G=0=>Goto C
G_
"                   n\sqr"
Lbl C
F=0=>Goto D
F_
"                    n"
Lbl D
Int 1\exp10L<>0=>L_
" "
"Pattern continues:"
Lbl 9
Isz B
L+FB+GB\sqr+HB^3+IB^4_
Goto 9


# ========================================================================
# CTF compliant.  See http://www.york.ac.uk/~tw104/casio/ for details.
#
# More programs and information at:
#              http://www.ex-parrot.com/~tom/calcs/calcs/encyc/
#
# This file last compiled: Friday, 30 April, 1999
# ========================================================================