Casio fx-3900Pv: Linear System, Poisson Kernel, Normal Distribution, 3 x 3 Matrix Determinant
Today, we feature four programs for the classic Casio fx-3900Pv calculator. The fx-3900Pv has 300 steps.
My review from 2023: https://edspi31415.blogspot.com/2023/05/retro-review-casio-fx-3900pv.html
One of the great features of the early “inexpensive” algebraic keystroke programmable calculators (1980s) is that the programs can be seen and edited.
The programs listed will require inputs to be stored in to the memory registers prior to running the program by using the [ Kin ] key.
Casio fx-3900Pv: 2 x 2 Systems
This program solves 2 x 2 linear systems. The Constant memory registers (K1 – K6) are mapped as follows:
K4 * x + K5 * y = K6
K1 * x + K2 * y = K3
The equations are solved as follows:
x = (K2 * K6 – K5 * K3) / M
y = (-K1 * K6 + K4 * K3) / M
where M = (K4 * K2 – K1 * K5)
This program takes 36 steps.
Code:
Kout 4 (determinant)
×
Kout 2
-
Kout 1
×
Kout 5
=
Min
HLT (Pause program, shows determinant. We want a nonzero-determinant.)
(
Kout 2
×
Kout 6
-
Kout 5
×
Kout 3
)
÷
MR
=
HLT (Solve for x)
(
Kout 1
+/-
×
Kout 6
+
Kout 4
×
Kout 3
)
÷
MR
= (Solve for y)
Examples
Example 1
x – y = 5
x + 3 * y = 9
Store the parameters: 1 Kin 4, -1 Kin 5, 5 Kin 6; 1 Kin 1, 3 Kin 2, 9 Kin 3
Results: det = 4, x = 6, y = 1
Example 2
3 * x + 16 * y = 49
5 * x – 2 * y = 22
Store the parameters: 3 Kin 4, 16 Kin 5, 49 Kin 6; 5 Kin 1, -2 Kin 2, 22 Kin 3
Results: det = -86, x = 5.23255814, y = 2.081395349
Casio fx-3900Pv: Poisson Kernel
The program calculates the kernel using the formula:
Pr(θ) = (1 – r^2) / (1 – 2 * r * cos θ + r^2),
0 ≤ r < 1, -π < θ ≤ π
This program takes 22 steps.
Store r in register 1, θ in register 2.
Code:
Rad (Mode 5)
(
1
-
Kout 1
x^2
)
÷
(
1
-
2
×
Kout 1
×
Kout 2
cos
+
Kout 1
x^2
)
=
Examples
Example 1:
r = 0.5, θ = 2.1
0.5 Kin 1, 2.1 Kin 2
Result: 0.4273879049
Example 2:
r = 0.268, θ = 0.842
0.268 Kin 1, 0.842 Kin 2
Result: 1.298397221
Source:
“Poisson Kernel” Wikipedia. May 28, 2024. https://en.wikipedia.org/wiki/Poisson_kernel
Retrieved November 26, 2024
Casio fx-3900Pv: Normal Distribution (Integration)
The program, which is ran in Integration Mode (Mode 1):
∫( e^(-t^2 / 2) / √(2 * π) dt, a, b)
To calculate, really approximate the integral:
MODE 1 P#
Store a level n (1-9), SHIFT RUN
Lower limit RUN
Upper limit RUN
The level n corresponds to the integration intervals 2^n. The higher n is, the longer the calculation takes but the accurate the integral is.
The integrated variable is stored in memory M. Start the function using Min.
Code:
Min
(
MR
x^2
+/-
÷
2
)
e^x
÷
(
2
×
π
)
√
=
Examples
The following examples will use n = 4.
Example 1: lower limit = 0, upper limit = 3. Result: 0.49865
(actual ≈ 0.4986501019)
Example 2: lower limit = -1, upper limit = 1. Result: 0.6827
(actual ≈ 0.6826894921)
Example 3: lower limit = -2, upper limit = 1.5. Result: 0.910443
(actual ≈ 0.910 4426667)
Casio fx-3900Pv: 3 x 3 Determinant
This program calculates the determinant of a 3 x 3 matrix. How are we to do this with only seven memory registers?
The program sets the matrix as:
[ [ 1st input, 2nd input, 3rd input ] [ K4, K5, K6 ], [ K1, K2, K3 ] ]
The user will be stop execution three times. At each time, enter the element corresponding to the top row.
For example:
[ [ 1, 2, 3 ] [ 4, 5, 6 ] [ 7, 8, 9 ] ]
Store 4 in K4, 5 in K5, 6 in K6; 7 in K1, 8 in K2, 9 in K3. While running, enter 1, 2, then 3 during program execution.
The determinant is stored to memory M. This program takes 40 steps.
Code:
(
Kout 5
×
Kout 3
-
Kout 2
×
Kout 6
)
×
ENT # (enter a legitimate number to continue, prompt for row 1, column 1)
=
Min
(
Kout 4
×
Kout 3
-
Kout 6
×
Kout 1
)
×
ENT # (prompt for row 1, column 2)
=
M-
(
Kout 4
×
Kout 2
-
Kout 5
×
Kout 1
)
×
ENT # (prompt for row 1, column 3)
=
M+
MR
Examples
Example 1:
[ [ 1, 5, 6 ] [ 2, 7, 8 ] [ 11, 4, 3 ] ]
Store:
(2nd row) 2 Kin 4, 7 Kin 5, 8 Kin 6
(3rd row) 11 Kin 1, 4 Kin 2, 3 Kin 3
Run the program (P1-P4): 1 RUN, 5 RUN, 6 RUN
Result: -15
Example 2:
[ [ -3, 0, 9 ] [ 0 , -3, 9 ] [ 9, -3, 0 ] ]
Store:
(2nd row) 0 Kin 4, -3 Kin 5, 9 Kin 6
(3rd row) 9 Kin 1, -3 Kin 2, 0 Kin 3
Run the program (P1-P4): -3 RUN, 0 RUN, 9 RUN
Result: 162
Until next time,
Eddie
All original content copyright, © 2011-2025. Edward Shore. Unauthorized use and/or unauthorized distribution for commercial purposes without express and written permission from the author is strictly prohibited. This blog entry may be distributed for noncommercial purposes, provided that full credit is given to the author.
