Saturday, November 26, 2022

HP Prime CAS: Curvature

HP Prime CAS:  Curvature



Introduction


The following CAS functions calculates the curvature of:


functions, y(x)

polar functions, r(t)  (t: Θ)

parametric functions, x(t), y(t)


Let Δα be the angle of rotation angle and Δs is the slight change of distance. Then the radius of curvature is:


K = abs(Δα ÷ Δs) as Δs → 0


And the radius of curvature is the reciprocal of K.  


For circles, the radius of curvature is constant.  Wankel engines and rotary engines have their pistons traveling in a circle.


Calculating the curvature depends on the form of the function.  


Function:  y(x)


K = abs( y''(x) ) ÷ (1 + (y'(x))^2) ^(3/2)


Polar:  r(t)  (t replaces Θ)


K = abs( r(t)^2 + 2 * (r'(t))^2 - r(t) * r''(t) ) ÷ ( r(t)^2 + r'(t)^2 )^(3/2)


Parametric:  x(t), y(t) 


K = abs( x'(t) * y''(t) - y'(t) * x''(t) ) ÷ ( x'(t)^2 + y'(t)^2 )^(3/2)


Radius of Curvature:


r = 1 ÷ K



For the CAS functions, they take the form:


#cas

name(arguments):=

BEGIN

...

END;

#end


Clicking on the CAS checkbox will not put the #cas and #end delimiters.  And these programs will work in CAS mode only.



HP Prime CAS Program: crvfunc


#cas

crvfunc(y,x):=

BEGIN

// curvature

// function

// radius = 1/curvature

LOCAL a,b;

a:=diff(y,x,2);

b:=diff(y,x,1);

RETURN ABS(a)/(1+b^2)^(3/2);

END;

#end






HP Prime CAS Program: crvpol


#cas

crvpol(r,t):=

BEGIN

// curvature

// polar (t: θ)

// radius = 1/curvature

LOCAL a,b,n,d;

a:=diff(r,t,2);

b:=diff(r,t,1);

n:=simplify(r^2+2*b^2-r*a);

d:=r^2+b^2;

RETURN ABS(n)/(d)^(3/2);

END;

#end






HP Prime CAS Program: crvpar


#cas

crvpar(y,x,t):=

BEGIN

// curvature

// parametric

// radius = 1/curvature

LOCAL y1,y2,x1,x2,n,d;

y2:=diff(y,t,2);

y1:=diff(y,t,1);

x2:=diff(x,t,2);

x1:=diff(x,t,1);

n:=simplify(x1*y2-y1*x2);

d:=simplify(x1^2+y1^2); 

RETURN ABS(n)/(d)^(3/2);

END;

#end





Until next time and have a great day, 


Eddie 


Source:


Svirin, Alex Ph.D.      "Curvature and Radius of Curvature" Math24  https://math24.net/curvature-radius.html   2022.  Last Updated September 12, 2022.  


Gratitude to Arno K. and rombio for helping me with derivatives and CAS programs.  

All original content copyright, © 2011-2022.  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. 


Sunday, November 20, 2022

HP 32SII: Some Algorithms For RPN Calculators

HP 32SII:  Some Algorithms For RPN Calculators



Four programs ported to the HP 32SII calculator from algorithms designated for the 1973 HP 45 calculator.  



HP 32SII: Euclid Algorithm - Greatest Common Divisor (GCD)


The HP 45 algorithm is found on page 228 in the Algorithms For RPN Calculators book. (see source below)


This algorithm takes up three labels.


E01 LBL E

E02 INPUT M

E03 ENTER

E04 ENTER

E05 ENTER

E06 INPUT N

E07 x<>y


K01 LBL 1

K02 ÷

K03 FP

K04 ×

K05 1

K06 x>y?

K07 GTO L

K08 R↓

K09 ENTER

K10 ENTER

K11 R↓

K12 R↓

K13 GTO K


L01 LBL L

L02 R↓

L03 R↓

L04 RTN


Sizes and Checksums:

E:  10.5 bytes, 9D4D

K:  19.5 bytes, F8AD

L:  6.0 bytes, C304

Total:  36.0 bytes


Instructions:

Press [ XEQ ] E, enter M and N.   


Examples:


Input:  M = 36, N = 28.  Result:  4

Input:  M = 48, N = 126. Result: 6

Input:  M = 115, N = 300.  Result: 5


HP 32SII:  GCD Using One Label - John Kenney 


The program was provided by Ross Barnes, and the algorithm is from the book ENTER by J. Daniel Dodlin and Keith Jarrett (ISBN 0-9615174-2-1, pg. 84).  This is smart, one label program.


Enter both numbers in the stack before running the program.


G01 LBL G

G02 ENTER

G03 ENTER

G04 -

G05 R↓

G06 x<>y

G07 LASTx

G08 /

G09 LASTx

G10 RDN

G11 IP

G12 x

G13 -

G14 x≠0?

G15 GTO G

G16 +

G17 RTN


Size and Checksum:  25.5 bytes, 4E39


Posted with permission.  


HP 32SII:  Tetens Equation


The HP 45 algorithm is found on page 290 in the Algorithms For RPN Calculators book.    The original algorithm took the temperature in Celsius. 


Find the saturation of water vapor (e_m) in mmHg (millimeters of Mercury) given the temperature in °F.


Determined Formulas:

T (in °C) = (T°F - 32) * 5/9

α = T/(236.87 + T)

e_m = 4.579 * 10^(7.49 * α)


T01 LBL T

T02 INPUT T

T03 →°C

T04 ENTER

T05 ENTER

T06 236.87

T07 +

T08 ÷

T09 7.49

T10 ×

T11 10^x

T12 4.579

T13 ×

T14 RTN


Size and Checksum:

45.0 bytes, 404A


Examples:

T = 68 °F, Result: 17.53658 mmHg

T = 99 °F, Result:  47.63501 mmHg




HP 32SII:  Dew Point Given Relative Humidity and Air Temperature


The HP 45 algorithm is found on page 290 in the Algorithms For RPN Calculators book.    The original algorithm took the temperature in Celsius. 


Relativity humidity (F) is to be entered as a decimal.  For instance, instead of 20%, enter 0.20.


Determined Formulas:

T (in °C) = (T°F - 32) * 5/9

A = T/(T + 236.87)

B = 1/(log F/7.49 + A)

TD = 236.87/(B - 1)

TD = TD * 9/5 + 32


D01 LBL D

D02 INPUT T

D03 →°C

D04 ENTER

D05 ENTER

D06 236.87

D07 STO A

D08 +

D09 ÷

D10 INPUT F

D11 LOG

D12 7.49

D13 ÷

D14 +

D15 1/x

D16 1

D17 -

D18 RCL÷ A

D19 1/x

D20 →°F

D21 RTN


Size and Checksum:

47.5 bytes, 8677


Examples:

T = 80, F = 0.64, Result:  66.725

T = 95, F = 0.32, Result:  60.50684



HP 32SII:  Effective Temperature Due to Wind Velocity



The HP 45 algorithm is found on page 291 in the Algorithms For RPN Calculators book.    The original algorithm took the temperature in Fahrenheit. 


Wind velocity is in miles per hour (mph).  


Determined Formulas:

A = 0.634*(0.634 - log V)

ΔT = A*(T - 90)

Effective T = T - ΔT


E01 LBL E

E02 0.634

E03 ENTER

E04 ENTER

E05 INPUT V

E06 LOG

E07 -

E08 ×

E09 INPUT T

E10 ENTER

E11 90

E12 -

E13 ×

E14 RCL T

E15 x<>y

E16 -

E17 RTN


Size and Checksum:

33.5 bytes, 54F7


Examples:

V = 20 mph, T = 15 °F,  Result: -16.71728

V = 15 mph, T = 86 °F,  Result: 84.62526


Source:


Ball, John A.  Algorithms For RPN Calculators  John Wiley & Sons:  New York, NY.  1978. ISBN 0-471-03070-8

For the second GCD program:

Dodin, J. Daniel and Keith Jarrett. ENTER: Reverse Polish Notation Made Easy   Synthetix:  Berkeley, CA   ISBN 0-9612174-2-1  1984.


Special thanks and gratitude to Ross Barnes.  



All original content copyright, © 2011-2022.  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. 


Saturday, November 19, 2022

Casio fx-9750GIII: Integrals with Infinite Limits

Casio fx-9750GIII:  Integrals with Infinite Limits





A Substitution to Get to Infinity... 


It is quite a challenge to calculate numerical integrals with infinite limits such as 


∫( f(x) dx, a, ∞)


∫( f(x) dx, -∞, a)


∫( f(x) dx, -∞, ∞)



A trick is to substitute x = tan Θ.  Then:


Θ = arctan x


dx = sec^2 Θ dΘ = cos^-2 Θ dΘ



Note that


lim t→∞ arctan t = π/2


lim t→-∞ arctan t = -π/2  


In this blog, assume that radian angle mode is used in all calculations.


Let's go over some examples and see how it works.  I used a Casio fx-9750GIII, however, this technique should work with all calculators with numerical integral calculations.  Furthermore, changing the integral will allow for Simpson's Rule or Trapezoid Rule approximation.


For the upper limit, I approximate π/2.


A = 1.5708  (π/2 to 4 places)

B = 1.570796  (π/2 to 6 places)

C = 1.57079633 (π/2 to 8 places)



Example 1:  


∫( e^(-x^2) dx, 0, ∞)  


transforms to


∫( e^(-tan^2 Θ)/cos^2 Θ dΘ, 0, ≈π/2)


Calculations (fx-9750GIII):


Upper Limit: A (see above),  Result:  0.8862269255


Upper Limit: B,  Result:  0.8862269255


Upper Limit: C,  Result:  0.8862269255




Example 2:  


∫(x^0.5 * e^(-x) dx, 0, ∞)


transforms to


∫((tan Θ)^0.5 * e^(-tan Θ))/cos^2 Θ dΘ, 0, π/2)


Calculations:


Upper limits A, B, C:  0.862269255


Coincidently, ∫( e^(-x^2) dx, 0, ∞)  = ∫(x^0.5 * e^(-x) dx, 0, ∞) = Γ(1.5) = √(π)/2




Example 3:


∫( e^x*(x^2 + 1) dx, -∞, 0)


transforms to


∫( e^(tan Θ) * (tan^2 Θ + 1)/cos^2 Θ dΘ, -π/2, 0)

=  ∫( e^(tan Θ) * 1/cos^2 Θ * 1/cos^2 Θ dΘ, -π/2, 0)

∫( e^(tan Θ)/cos^4 Θ dΘ, -π/2, 0)


For upper limits A, B, C, the answer returned is 3, which is the exact answer.  


For integrals like this all is needed is a four digit approximation of π/2 = 1.5708.



Let's keep going:


Example 4:


∫( (x^2 + 1)/(x^4 - 1) dx, 0, ∞) 


transforms to


∫( 1/cos^Θ * (tan^2 Θ + 1)/(tan^4 Θ - 1) dΘ, 0, π/2)

= ∫( 1/(sin^4 Θ - cos^4 Θ) dΘ, 0, π/2)


On the fx-9750GIII get MA Error.  



Example 5:


∫( 1/√(x^2 + 3*x + 1) dx, 0, ∞)


transforms to 


∫( 1/(cos^2 Θ * √(tan^2 Θ + 3 * tan Θ + 1)) dΘ, 0, π/2)


like example 4, I get the MA Error.



Observation:  the transformation works best if the integral involves some form of either of the following:


f(x) * e^(g(x))


or 


f(x) * e^(-g(x))



Gamma


The Gamma Function is an excellent candidate for this transformation.  


Γ(t) = ∫( x^(t-1) * e^-x dx, 0, ∞)


transforms to


∫( tan^(t-1) Θ * e^(-tan Θ)/cos^2 Θ dΘ, 0, π/2)



Source


Mier-Jedrzejuwicz, W.A.C. Ph.D.    Tips And Programs for the HP 32S   Synthetix Publication.  Berkeley, CA.  September 1988.  ISBN 0-937637-05-X


Download the book here:  https://literature.hpcalc.org/items/1756




Happy calculating,


Eddie


All original content copyright, © 2011-2022.  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. 


Sunday, November 13, 2022

HP 15C: Weibull Distribution Calculations

HP 15C:  Weibull Distribution Calculations


Introduction


The Weibull probability density distribution function is:


f(x) = (b / Θ) * (x / Θ)^(b-1) * exp(-(x / Θ)^b)


with the lower tail cumulative distribution of (-∞ to x):


Area = 1 - exp(-(x / Θ)^b)


The area function tells us what is the probability a device lasts no more than x time units.  


Area = 1 - Survival


The survival function is the probability a device lasts more than x time units.


Survival = exp(-(x / Θ)^b)


Generally, the higher Θ is, the flatter the Weibull Distribution curve.  


What follows are four calculations regarding the Weibull Distribution.  In the following programs, store the following values first prior to running the programs:


R0 = x

R1 = b

R2 = Θ


Use whatever labels you like.  


HP 15C Program:  Lower Tail Probability - Weibull Distribution


CDF = 1 - exp(-(x/Θ)^b)


Keys:


LBL B

1

RCL 0

RCL÷ 2

RCL 1

y^x

CHS

e^x

-

RTN


Key Codes:


42, 21,12

1

45, 0

45, 10, 2

45, 1

14

16

12

30

43, 32


Example:  

b = 1.96, Θ = 420

x = 300, result:  0.4038

x = 400, result:  0.5970

x = 500, result:  0.7552


HP 15C Program:  Failure Rate - Weibull Distribution


FR = b/Θ * (x/Θ)^(b-1) 


Keys:


LBL C

RCL 1

RCL÷ 2

RCL 0

RCL÷ 2

RCL 1

1

-

y^x

*

RTN


Key Codes:


42, 21, 13

45, 0

45, 10, 2

45, 0

45, 10, 2

45, 1

1

30

14

20

43, 32


Example:  

b = 1.96, Θ = 420

x = 300, result:  0.0034

x = 400, result:  0.0045

x = 500, result:  0.0055


HP 15C Program:  Mean of a Weibull Distribution


µ = (1/b)! * Θ


Keys:


LBL D

RCL 1

1/x

x!

RCL× 2

RTN


Key Codes:


42, 21, 14

45, 1

15

42, 0

45, 20, 2

43, 32


Example:  

b = 1.96, Θ = 420

Result:  373.3720


HP 15C Program:  Standard Deviation of a Weibull Distribution


σ = Θ * √((2/b)! - (1/b)!^2)


Keys:


LBL E

2

RCL 1

÷

x!

RCL 1

1/x

x!

x^2

-

RCL× 2

RTN


Key Codes:


42, 21, 15

2

45, 1

10

42, 0

45, 1

15

42, 0

43, 11

30

11

45, 20, 2

43, 32


Example:

b = 1.96, Θ = 420

Result:  198.2208


Sources:


HP55 Statistics Programs  Hewlett Packard Company.  Cupertino, CA.  1975


Ma, Dan.  "The Weibull distribution"  Topics in Actuarial Modeling.  September 28, 2016.   https://actuarialmodelingtopics.wordpress.com/2016/09/28/the-weibull-distribution/  Last Retrieved September 20, 2022.  



Eddie


All original content copyright, © 2011-2022.  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. 


Saturday, November 12, 2022

HP Prime: Reversing an Integer's Digits

HP Prime:  Reversing an Integer's Digits


(Inspired by the HHC 2022 programming contest)


What Should I Add To Reverse the Digits?


Let A, B, C, D, and E be individual digits (0-9) of an integer.   AB would represent a two digit integer with the value of 10 * A + B.  ABC would represent a three digit integer with the value of 100 * A + 10 * B + C.


Reversing a Two Digit Integer


AB + # = BA

10 * A + B + # = 10 * B + A

# = 9 * (B - A)


Example:  Let AB = 76.

A = 7, B = 6

# = 9 * (6 - 7) = -9

76 - 9 = 67


Reversing a Three Digit Integer


ABC + # = CBA

100 * A + 10* B + C + # = 100 * C + 10 * B + A

# = 99 * (C - A)


Example:  ABC = 469

# = 99 * (9 - 4) = 495

469 + 495 = 964


Reversing a Four Digit Integer


ABCD + # = DCBA

1000 * A + 100 * B + 10 * C + D + # = 1000 * D + 100 * C + 10 * B + A

# = 999 * (D - A) + 90 * (C - B)


Example:  ABCD = 7219

# = 999 * (9 - 7) + 90 * (1 - 2) = 1908

7219 + 1908 = 9127


Reversing a Five Digit Integer


ABCDE + # = EDBCA

10000 * A + 1000 * B + 100 * C + 10 * D + E + # =

10000 * E + 1000 * D + 100 * C + 10 * B + A 

# = 9999 * (E - A) + 990 * (D - B)


Example: ABCDE = 52693

# = 9999 * (3 - 5) + 990 * (9 - 2) = -13068

52693 - 13068 = 39625


Having the Calculator Do It


The program REVINT reverses the digits of an integer, up to 11 digits.   The program does not allow numbers that have non-zero fractional parts or integers more than 11 digits.  Instead of solving for # (see above), the program splits the integers into a list in reverse order, and uses list processing to get the final answer. 


HP Prime Program:  REVINT


Caution:  Integers that end or begin with zero may not return accurate results.   My suggestion is not use 0s with this program.  See examples below for more details.  


EXPORT REVINT(N)

BEGIN

// 2022-09-18 EWS

// reverse the integer N

// up to 12 digits

LOCAL D,P,A,I,M,L;

L:={};

P:=XPON(N);


// check size 

  IF P>11 THEN

  RETURN "TOO BIG";

  KILL;

  END;

 

// check type

  IF FP(N) THEN

  RETURN "NOT AN INTEGER";

  KILL;

  END;

   

D:=N;


// loop

  FOR I FROM P DOWNTO 0 DO

  A:=D/ALOG(I);

  L:=CONCAT({IP(A)},L);

  D:=D-IP(A)*ALOG(I); 

  END;

  

// rebuild 

M:=ΣLIST(MAKELIST(ALOG(X),X,P,0,−1)*L);

RETURN M; 

END;


Examples:


REVINT(4321) returns 1234


REVINT(56765) returns 56765   (56765 is a palindrome, reversing the digits results in the same number)


REVINT(42910) returns 1924 (01924 - be aware about integers ending or beginning with 0)


REVINT(67.28) returns "NOT AN INTEGER" (error)



Eddie


All original content copyright, © 2011-2022.  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. 


Monday, November 7, 2022

Retro Review: Texas Instruments TI SR-51-II

 Retro Review:   Texas Instruments TI SR-51-II



Quick Facts


Model:  SR-51-II

Company:  Texas Instruments

Years:  1976

Type:  Scientific 

Batteries: 1 × BP6, with AC-Adapter**

Operating Modes:  AOS

Number of Registers: 3

Display:  10 digit - red seven segment digits

Leather Case


** I purchased the calculator on eBay not to long ago from night_owl_items, who made it so the SR-51 II can run on two AA batteries, making it one of the kind and extend it's life.


Features


*  Trigonometric functions and inverses

*  Hyperbolic functions and inverses

*  Logarithms and exponentials

*  Factorials of positive integers

*  Percent and percent change

*  Arithmetic, powers, and roots







Conversions


There are eight conversions:


* in · mm

* gal · l

* lb · kg

* °F · °C

* D · R  (degrees - radians)

* G · R  (grads - radians)

* DMS · DD (degrees-minutes-seconds - decimal degrees)

* P → R (polar - rectangular conversions)


The [ 2nd ] key sequence converts left to right


The [ 2nd ] [ INV ] key sequence converts right to left



Angle Modes


The SR-51-II has the three customary angle modes:  degrees, radians, and grads.  Unfortunately there is no angle mode indicator.   The way to:


Degrees Mode:  0.5 sin^-1 returns 30

Radians Mode:  0.5 sin^-1 returns .5235987756

Grads Mode:  0.5 sin^-1 returns 33.33333333



Storage and Storage Registers


The SR-51-II has three memory registers.   The calculator also has storage arithmetic:


SUM:  STO+

INV SUM:  STO-

PROD:  STO×

INV PROD:  STO÷



The CONST Function


The CONST is an access to common scientific functions, but allows the user to do a short arithmetic calculation, includes roots, powers, and percent change.  


Example:  Subtract 100 from 290, 370, and 480 respectively.


100 [ - ] [ 2nd ] (CONST) 

290 [ = ] returns 190

370 [ = ] returns 270

480 [ = ] returns 380


Example 2: Multiply 172, 288, and 382 by 6 respectively.


6 [ × ] [ 2nd ] (CONST)

172 [ = ] returns 1032

288 [ = ] returns 1728

382 [ = ] returns 2292



Statistics


The statistics modes have one and two variable statistics.  What is unique of the SR-51-II is that the y-variable is primary. However, entering two variable statistics remain the usual:  x [ x<>y ] y [ Σ+ ].


[ 2nd ] (MEAN):  mean of y data;  [ INV ] [ 2nd ] (MEAN):  mean of x data


[ 2nd ] (S.DEV):  standard deviation of y data; 

[ INV ] [ 2nd ] (S.DEV):  standard deviation of x data


[ 2nd ] (VAR):  population variance of y data;

[ INV ] [ 2nd ] (VAR):  population variance of x data



Solid calculator.  I wish the SR-51-II had a random number function and angle mode indicator.  


Source:


Woerner, Joerg.  "Texas Instruments SR-51-II" Datamath.  December 5, 2001.   Last Retrieved November 1, 2022.  http://www.datamath.org/Sci/MAJESTIC/sr-51-II.htm


Eddie


All original content copyright, © 2011-2022.  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. 


Sunday, November 6, 2022

hp 9g: Sample Programs

hp 9g:  Sample Programs


Introduction


As I mentioned in yesterday's blog, today's blog will have some sample programs for the hp 9g.   


The hp 9g's programming language is a mix of C and Basic, and is unique from the rest of the Hewlett Packard calculators.    The hp 9g has 400 steps of programming memory to be allocated among 10 program files, P0 through P9.   


The 9g has 26 variables, but can be extended up to 53 variables at the cost of program steps.  The square brackets indicate indirect addressing.  The number in the square brackets is the number of steps away from the variable.   Any variable beyond Z (Z[0], A[25]) must be addressed in this fashion.  


Example: 

A[0] calls up A

A[1] calls up B

...

A[25] calls up Z. 


We can use any letter, but I recommend using either A or Z. 



hp 9g Program:  Integer Division


This program gives the quotient and remainder of N ÷ D.  The program here assumes you enter positive integers, and some code can be entered for checking inputs.  


INPUT N

INPUT D

Q=INT(N/D)

R=N-Q*D

PRINT Q," R",R

END


Examples:


N = 4379, D = 8;  Result:  547 R3


N = 5884, D = 29;  Result:  202 R26



Note:  The PRINT command converts variable values to strings automatically, without the need for a string or STR$ command.


hp 9g Program:  Arithmetic-Geometric Mean


This program determines the AGM given two numbers A and G.


INPUT A

INPUT B

PRINT "ACC. 10^-8"

Lbl 0:

X=.5(A+G)

Y=√(AG)

If (ABS(X-Y)<10^(-8))

Then {Goto 1}

A=X

G=Y

Goto 0

Lbl 1:

Print "ANS= ", X


Examples:


A = 1.3, G = 1.5,   Result:  ANS ≈ 1.39821143


A = 20, G = 45,  Result:  ANS ≈ 31.23749374



Notes:  


10^ is from [ 2nd ] (10^x) the antilog function.


The label command must have the colon character after the label number, or a syntax error occurs.  


If you run a program from the Main mode by the [ PROG ] key, you will be transferred to Program mode when the program finishes.


hp 9G Program: The Maximum Value of A through X



Y = maximum value

Z = counter variable


PRINT "MAX(A:X)"; ◢

FOR(Z=2;Z<23;Z++){

IF(A[Z]>Y)

THEN{Y=A[Z]}};

PRINT "MAX=",Y;

END


Example:  


Clear all variable in the MAIN mode by CL-VAR

Set up variables: 


A = 12, D = 24, E = 37, G = 40, S = 19, T = 16, U = 7

Result:  MAX= 40


Notes:   


++ is from the Instruction menu, it is a smaller-jointed double plus.


When the program encounters a run/stop instruction (◢), the last message is displayed.  Continue execution by pressing the equals key [ = ].  


hp 9g Program:  Plotting y = A * sin(B * x + C) + D


The programming mode does not offer a lot of support when it comes to graphs.  


PRINT "SINE"

SLEEP(.5)

INPUT A,B,C,D

RANGE(-2π,2π,π/4,-A,A,1)

Graph Y=A*sin(BX+C)+D

PRINT "PRESS G<>T"

END




A = 1, B = 1, C = 0, D = 0



Notes:


Prior to running the program, set the angle mode to Radians through the [DRG] key.  Also, press [ 2nd ] [ → ] (CLS) to clear the graph screen.  Unfortunately, neither of these commands can be programmed.  


Plots from programs cannot be traced.


When the program ends, you will need to switch to Main mode, press [G<>T] to show the graph.   Not a very efficient way of showing a graph.  



That is a sample of the programs for the hp 9g.  Good for number crunching, kind of a little bit to be desired for graphics.


Until next time,


Eddie 



All original content copyright, © 2011-2022.  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. 


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