(EL-5200/EL-9000) Polynomial interpolation and root finding

[robve]

This EL-5200 (1986) AER program is heavily "optimized" to barely fit within the limits of program size and complexity that EL-5200 AER programming permits. This was an interesting experiment to see if it was possible to combine easy (x,y) data point entry via STAT mode, perform polynomial interpolation, root finding and graphing. This shows what this tiny vintage 1986 machine can do, which is not much, compared to modern calculators. Only 3, 4 or 5 points can be interpolated.

LAGRANGE POLYNOMIAL INTERPOLATION AND ROOT FINDING WITH GRAPHING
For SHARP EL-5200/EL-9000

Select [STAT] then STAT 1 data store mode

Clear all data with [CA] or edit S[] data

Specify 3 to 5 (x,y) points to interpolate by repeating x,y M+

Draw the points of the polynomial:
[G(SD)] [AUTO] [DRAW]

Run the LAGRANGE program:
L [PRO] LAGRANGE [COMP]

[X<->Y] and [left]/[right] to select an x value
[X<->Y] to view y value

Press [SOLVE] repeatedly to find the roots

To zoom the graph:
[AUTO] 100 [ZOOM]

[X<->Y] to select an x value
[X<->Y] to view y value

[ZOOM]
[X<->Y] to select an x value
[X<->Y] to view y value

AER-I (and AER-II) program:

Code:

:LAGRANGE
M:➊Z[1]≠3→N→[➍◣]➋Z[1]≠4→N→[➎◣]➌➏◣
➊:S[1,1]⇒A␣S[1,2]⇒B␣S[1,3]⇒C␣A-B⇒F␣A-C⇒G␣B-C⇒H␣S[2,1]÷FG⇒S␣S[2,2]÷FH⇒T␣S[2,3]÷GH⇒U
➋:S[1,4]⇒D␣A-D⇒I␣B-D⇒J␣C-D⇒K␣S÷I⇒S␣T÷J⇒T␣U÷K⇒U␣S[2,4]÷IJK⇒V
➌:S[1,5]⇒E␣A-E⇒L␣B-E⇒M␣C-E⇒N␣D-E⇒O␣S÷L⇒S␣T÷M⇒T␣U÷N⇒U␣V÷O⇒V␣S[2,5]÷LMNO⇒W
➍:GRAPH S(X-B)(X-C)-T(X-A)(X-C)+U(X-A)(X-B)DRAW
➎:GRAPH S(X-B)(X-C)(X-D)-T(X-A)(X-C)(X-D)+U(X-A)(X-B)(X-D)-V(X-A)(X-B)(X-C)DRAW
➏:GRAPH S(X-B)(X-C)(X-D)(X-E)-T(X-A)(X-C)(X-D)(X-E)+U(X-A)(X-B)(X-D)(X-E)-V(X-A)(X-B)(X-C)(X-E)+W(X-A)(X-B)(X-C)(X-D)DRAW