Composite Program (CurveP - Accurate TVM - Hg vapour standard - RainGaugeCalP - Parallel resistances - Quadratic equation solve - Convert to Fraction - Solve a System of Linear Equations - EbikeMax - Bike Power - Bike Development - Function tests)

Description

J E Patterson - jepspectro.com - 20180429

This program works with the DM15C series of calculators by SwissMicros. The extended memory firmware should be installed. The hp15c Simulator by Torsten Manz can be used as well if the DM15C preferences are set to 229 registers. The programs are self-contained so they can be extracted as separate programs.

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CurveP J E Patterson - jepspectro.com - version 20151017

CurveP starts at line 1 and finishes at line 158.

The program fits data that may be linear at low x,y amplitudes but y falls off at higher x values.
This is a common issue in many physical systems. x1, y1 should preferably be on the linear part of the curve.
CurveP is not a regression. It assumes that the data is reasonably precise. Linear and power curves can be fitted, as well.

The equation used is y = scale*xorder + slope*x*e-factor*x. See Curve Fitting at jepspectro.com.


Originally chart recorders were used to obtain data which occupied the y axis, leaving interpreted results naturally plotted on the x axis, when graphed on the same paper.
Here we are using y as the equation output axis.

x is first normalised, the equation solved and un-normalised to get y.
The equation parameters, scale, order, slope and factor are found by entering some standard data.

y1 ENTER, y2 ENTER, y3 f A
x1 ENTER, x2 ENTER, x3 f B

Do not press ENTER after y3 or x3.
y3>y2>y1 and x3>x2>x1.
After normalisation y3 = x3 = 10 so x3 is not saved. y3 is used instead in the program.

The curve runs through the origin and three points (x1,y1) (x2,y2) (x3,y3).
The order of the upper part of the curve is displayed.

y input to GSB C to get x. This uses SOLVE to run GSB D - y until zero, the solution x is obtained.
x input to GSB D to get y.

If there is a blank value, enter it and subtract the answers.
Enter f USER to avoid the f key during data input.

Test [x,y] data sets [2,2 4,5 5,8] [1,1 2,4 3,9] [1,1 2,2 3,3] [20,3.69 30,8.64 47,22.16]
Enter y data in A and x data in B. eg. y1 ENTER y2 ENTER y3 GSB A, x1 ENTER x2 ENTER x3 GSB B.
The last data set relates an element's atomic number to its X-ray fluorescence k line energy in keV - see Moseley's Law.

In this update I have improved the starting values for the iteration and added a refined guess to the stack for Solve. Order is limited to 10.

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TVM - Accurate TVM usage instructions - Jeff Kearns

TVM starts at line 159 and finishes at line 198.

(15C) Accurate TVM for HP-15C

1. Store 4 of the following 5 variables, using appropriate cash flow conventions as follows:
N STO 1 --- Number of compounding periods
I STO 2 --- Interest rate (periodic) expressed as a %
B STO 3 --- Initial Balance or Present Value
P STO 4 --- Periodic Payment
F STO 5 --- Future Value
and store the appropriate value (1 for Annuity Due or 0 for Regular Annuity) as
B/E STO 6 --- Begin/End Mode. The default is 0 for regular annuity or End Mode.

2. Store the register number containing the floating variable to the indirect storage register I.

3. f SOLVE E

Example from the HP-15C Advanced Functions Handbook -

"Many Pennies (alternatively known as A Penny for Your Thoughts):

A corporation retains Susan as a scientific and engineering consultant.
Her fee is one penny per second for her thoughts, paid every second of every day for a year.
Rather than distract her with the sounds of pennies dropping, the corporation proposes to deposit them for her into a bank account.
Interest accrues at the rate of 11.25 percent per annum compounded every second.
At year's end these pennies will accumulate to a sum

total = (payment) X ((1+i/n)n-1)/(i/n)

where payment = $0.01 = one penny per second,
i = 0.1125 = 11.25 percent per annum interest rate,
n = 60 X 60 X 24 X 365 = number of seconds in a year.

Using her HP-15C, Susan reckons that the total will be $376,877.67.
But at year's end the bank account is found to hold $333,783.35 .
Is Susan entitled to the $43,094.32 difference?"

31,536,000 STO 1
(11.25/31,536,000) STO 2
0 STO 3
- 0 . 0 1 STO 4
5 STO I
f SOLVE E

The HP-15C now gives the correct result: $333,783.35.

Thanks to Thomas Klemm for debugging the routine.
The code has been edited to reflect Thomas's suggested changes.

Jeff Kearns

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HgCalP - J E Patterson - jepspectro.com - version 20151017

HgCalP starts at line 199 and finishes at line 224.

The concentration of mercury vapour in air, above liquid mercury, depends on the temperature.
A good calibration curve can be obtained using a simplified Dumarey equation.
Reference: R. Dumarey, E. Temmerman, R. Dams, J. Hoste, Analyt. Chim. Acta 170, 337 (1985).

Enter the temperature in °C of the mercury calibration vessel, then GSB 1
The mercury vapour concentration in the calibration vessel is displayed in ng/ml

The equation is Hg ng/ml = 10(-3229/(T+273.16)+14.6 - Log(T +273.16)).
At 20°C mercury saturated air has a mercury concentration of 13.14 ng/ml

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RGCalP - J E Patterson - jepspectro.com - version 20151017

RGCalP starts at line 225 and finishes at line 247.

RAIN GAUGE calibration in mm per bucket tip, given the number of bucket tips, the diameter of funnel in mm and the calibration volume of water in ml.

Number of tips ENTER
Diameter of funnel in mm ENTER
Water volume in ml GSB 2
mm per tip is displayed.

A tipping bucket rain-gauge has a funnel diameter of 79 mm.
200 ml of slowly added water generates 81 tips.

8 1 ENTER
7 9 ENTER
2 0 0 GSB 2
The result in x = 0.50 mm of rain per tip.

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Parallel Resistances - J E Patterson - jepspectro.com - version 20151017

Parallel Resistances starts at line 248 and finishes at line 260.

First resistance, press ENTER, second resistance.
GSB 3 for parallel resistance result.
R/S returns first entry for the next try.
Enter a second value and press R/S for a new result.

R1 = 15 ohms and R2 = 10 ohms.
1 5 ENTER
1 0 GSB 3
The parallel resistance R = 6 ohms is displayed in x.

R/S returns R1=15 ohms to x.
1 2 R/S calculates R = 6.7 ohms.
R/S to return R1 = 15 ohms to x.
1 0 R/S calculates R = 6 ohms, etc.

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Quadratic Equation Solver program for the HP-15C - from Torsten Manz

This program starts at line 261 and finishes at line 354.

This program finds the roots of a quadratic equation of the form ax2 + bx + c = 0.
Push a, b, and c into the Z, Y, and X registers of the stack respectively, then press GSB 4.
The discriminant b2 - 4ac is displayed briefly.
If it is positive there are two real roots.
If is zero there is one real root.
If it is negative there are two complex roots.
The roots of the equation will appear in the X and Y registers.
Use X<>Y to view the second root.
If the "C" indicator appears then the roots are complex.
f (i) can be used to temporarily view the imaginary parts.
Press g CF 8 to clear this flag before running the routine again.

Example: a = 1, b = 2, c = 3.
1 ENTER
2 ENTER
3 GSB 4
Roots are in x and y.
x= -1 - √2i
press f (i) to view the imaginary part.
X<>Y
y = -1 + √2i
press f (i) to view the imaginary part.

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Convert to Fraction - Guido Socher

This program starts at line 355 and finishes at line 378.

Let's say you would like to know what 0.15625 as a fraction is.
You type: 0.15625.
GSB 5
The display shows "running" and then you see first 5, and then a second later, 32
The fraction is therefore 5/32 (numerator = 5 and denominator = 32).
32 remains in X (display) after the program finishes and 5 remains in Y.

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Solve a System of Linear Equations - J E Patterson - jepspectro.com - version 20170531

This program starts at line 379 and finishes at line 413.

N GSB 6 where N is the number of equations (8 or less).

A N N is displayed.
Matrix [A] has a dimension of NxN.

Enter the coefficients of xi where i has values from 1 to N
Press R/S after each is entered.

B N 1 is displayed.
Matrix [B] has a dimension of Nx1.

Enter the constants.
Press R/S after each is entered.

C N 1 is displayed.
Matrix [C] has a dimension of Nx1.

Values for xi are read out in turn by pressing R/S.

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EbikeMax - Ebike maximum speed from motor rpm - J E Patterson - jepspectro.com - version 20160210

The program starts at line 414 and ends at line 447

Enter motor rpm
Enter wheel size in inches or mm - the program works out if the units are inches or mm from the magnitude
GSB 7

The maximum speed at 36 volts is displayed.
Press R/S.
The maximum speed at 42 volts is displayed.

speed km/h = 4.79E-3 x motor rpm x wheel size in inches at 42 volts
25.4 x pi x 60 / E^6 = 4.79E-3.

Speed is proportional to the battery voltage and the wheel diameter.
Speed is limited by hills and wind.
For a 20 inch wheel the bike speed in km/h at 42 volts is approximately motor rpm/10.

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Bike Power - J E Patterson - jepspectro.com - version 20160119

This program starts at line 448 and ends at line 527

This program calculates the power required for a given bike speed.

Enter total weight W (kg), STO 1. This weight W includes the bike plus rider.
Enter the grade G (%) of the road, STO 2. For a flat road enter 0 STO 2
Enter V (km/h)
GSB 8
The required power P (watts) to reach a bike speed V (km/h) is displayed.

Enter a head wind speed in km/h. This is an optional step..
Press R/S
The power Pw required to maintain the same speed into the head wind is displayed.

Stored results:
R4 = Power required to overcome air drag resistance, Pd
R6 = Power required to overcome rolling resistance, Pr
R7 = Power required to overcome % grade G, Ps
R8 = The total required power, P = (Pd + Pr + Ps) * 1.0309
R9 = The power required into a head wind, Pw = (R4 * (Va/Vr)^2 + R6 + R7) * 1.0309

There are constants in the program:
1.0309 = 1/(1 - 3/100) compensates for a 3% drive-train loss.
0.2778 = 1000/3600 converts km/h to m/s
0.2626 = 0.5 x (Air Density (1.226) * Drag coefficient Cd (0.63) * Frontal area (0.68))
Reduce this constant in proportion for a more streamlined setup

0.0490 = g (9.8067) * Coefficient of rolling resistance Crr (0.005)
9.8067 = g acceleration due to gravity (m/s²)

Equations:
Pd = Vr * 0.5 * rho * Va^2 * Cd * A
Pr = Vr * m * g * cos(arctan(s)) * Crr
Ps = Vr * m * g * sin(arctan(s))
P = (Pd + Pr + Ps) * 1.0309

Va = Vr + head-wind speed (m/s)
Vr = Va in still air.
Pw = (R4 * (Va/Vr)² + R6 + R7) * 1.0309

Terms:
rho = air density = 1.226 kg/m³
Cd = drag coefficient 0.63
A = frontal area 0.68 m² - upright riding style
m = mass kg = W
g = acceleration due to gravity = 9.8607 m/s²
Crr = coefficient rolling resistance 0.005
s = slope = G/100
Vr = bike road speed (m/s)
Va = bike air speed (m/s)

References:
Bicycle Performance
Bike Calculator

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Bike Development - J E Patterson - jepspectro.com - version 20160210

This program starts at line 528 and finishes at line 567

Enter wheel diameter in inches or mm - the program works out if the units are inches or mm from the magnitude
Enter front sprocket teeth number
Enter rear sprocket teeth number

GSB 9 returns Gear-Inches
R/S returns Metres-Development
R/S returns Gain-Ratio for a 170 mm crank arm

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Function tests - J E patterson - jepspectro.com - version 20151017

This program starts at line 568 and ends at line 609

N STO 2
GSB 0 for N iterations.
N is the number of iterations required otherwise there is only one iteration.

The Simulator result is 3736036.572 with 10,000 iterations in 56 seconds.
The DM15 result is 3736036.611 with 100 iterations in 67 seconds.

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Program Resources

Labels

Name Description Name Description Name Description
 A CurveP - Enter y inputs  3 Parallel resistances .2 CurveP - RCL .5 1/x STO .5
 B CurveP - Enter x inputs  4 Quadratic equation solver .3 CurveP - GSB D-x =0 for SOLVE
 C CurveP - Enter y to get x  5 Convert to Fraction .4 Convert to fraction - loop and test
 D CurveP - Enter x to get y  6 Solve a System of Linear Equations .5 Linear equations - coefficients of xi storage loop
 E TVM SOLVE  7 Electric bike speed .6 Linear Equations - constant storage loop
 0 Function tests  8 Bike Power .7 Linear equations - result display
 1 Mercury - Enter temperature( (°C) for ng/l Hg in air  9 Bike development .8 Quadratic equation - subroutine
 2 Millimetres of rain per tip .1 CurveP - loop .9 Quadratic equation - subroutine

Storage Registers

Name Description Name Description Name Description
 0 Fraction, decimal input value  7 xscale, Ps .4 scale
 1 y1, N, °K, Funnel area, R1+R2, Result, Speed 36V,W,GI  8 yscale, Pt .5 temp1
 2 y2, I, Hg conc, Number of tips, R1, Count, Speed 42V,G,25.4  9 slope, Pw .6 temp2
 3 y3, PV, ml water used, V m/s, 25.4,front/rearT .0 absolute decimal number for fraction .7 temp3
 4 order, PMT, Pd, Wheel size in inches .1 x1 .8 xinput
 5 factor, FV,Tan-1(G/100) .2 x2 .9 yinput
 6 count, B/E 1/0, Pr .3 order first guess (i) Register of TVM value required

Flags

Number Description
8 Indicates, by showing "C" in the display, that the roots are complex numbers

Program

Line Display Key Sequence Line Display Key Sequence Line Display Key Sequence
000 204 1 1 408 42,21, .7 f LBL . 7
001 42,21,11 f LBL A 205 6 6 409 31 R/S
002 44 8 STO 8 206 40 + 410 u 45 13 USER RCL C
003 33 R⬇ 207 44 1 STO 1 411 22 .7 GTO . 7
004 44 2 STO 2 208 3 3 412 42,16, 0 f MATRIX 0
005 33 R⬇ 209 2 2 413 43 32 g RTN
006 44 1 STO 1 210 2 2 414 42,21, 7 f LBL 7
007 45 8 RCL 8 211 9 9 415 2 2
008 1 1 212 16 CHS 416 5 5
009 0 0 213 45,10, 1 RCL ÷ 1 417 48 .
010 44 3 STO 3 214 1 1 418 4 4
011 10 ÷ 215 4 4 419 44 3 STO 3
012 44,10, 2 STO ÷ 2 216 48 . 420 33 R⬇
013 44,10, 1 STO ÷ 1 217 6 6 421 2 2
014 43 32 g RTN 218 40 + 422 0 0
015 42,21,12 f LBL B 219 45 1 RCL 1 423 0 0
016 44 7 STO 7 220 43 13 g LOG 424 34 x↔y
017 33 R⬇ 221 30 425 43,30, 7 g TEST x>y
018 44 .2 STO . 2 222 13 10ˣ 426 45,10, 3 RCL ÷ 3
019 33 R⬇ 223 44 2 STO 2 427 44 4 STO 4
020 44 .1 STO . 1 224 43 32 g RTN 428 33 R⬇
021 45 7 RCL 7 225 42,21, 2 f LBL 2 429 33 R⬇
022 45 3 RCL 3 226 44 1 STO 1 430 4 4
023 10 ÷ 227 33 R⬇ 431 48 .
024 44,10, .2 STO ÷ . 2 228 44 2 STO 2 432 7 7
025 44,10, .1 STO ÷ . 1 229 33 R⬇ 433 9 9
026 45 3 RCL 3 230 44 3 STO 3 434 26 EEX
027 45 2 RCL 2 231 33 R⬇ 435 16 CHS
028 10 ÷ 232 45 2 RCL 2 436 3 3
029 43 12 g LN 233 2 2 437 45,20, 4 RCL × 4
030 45 3 RCL 3 234 10 ÷ 438 20 ×
031 45 .2 RCL . 2 235 43 11 g 439 44 1 STO 1
032 10 ÷ 236 43 26 g π 440 31 R/S
033 43 12 g LN 237 20 × 441 48 .
034 10 ÷ 238 44 2 STO 2 442 8 8
035 44 4 STO 4 239 45 1 RCL 1 443 5 5
036 44 .3 STO . 3 240 45 2 RCL 2 444 7 7
037 1 1 241 10 ÷ 445 10 ÷
038 44 5 STO 5 242 45 3 RCL 3 446 44 2 STO 2
039 0 0 243 10 ÷ 447 43 32 g RTN
040 44 6 STO 6 244 26 EEX 448 42,21, 8 f LBL 8
041 45 1 RCL 1 245 3 3 449 48 .
042 45,10, .1 RCL ÷ . 1 246 20 × 450 2 2
043 44 9 STO 9 247 43 32 g RTN 451 7 7
044 42,21, .1 f LBL . 1 248 42,21, 3 f LBL 3 452 7 7
045 1 1 249 44 1 STO 1 453 8 8
046 44,40, 6 STO + 6 250 33 R⬇ 454 20 ×
047 45 3 RCL 3 251 44 2 STO 2 455 44 3 STO 3
048 45 4 RCL 4 252 44,40, 1 STO + 1 456 3 3
049 43,30, 7 g TEST x>y 253 43 33 g R⬆ 457 14
050 45 .3 RCL . 3 254 20 × 458 48 .
051 44 4 STO 4 255 45,10, 1 RCL ÷ 1 459 2 2
052 45 3 RCL 3 256 31 R/S 460 6 6
053 45 5 RCL 5 257 45 2 RCL 2 461 2 2
054 45,20, 3 RCL × 3 258 31 R/S 462 6 6
055 16 CHS 259 22 3 GTO 3 463 20 ×
056 12 260 43 32 g RTN 464 44 4 STO 4
057 45,20, 3 RCL × 3 261 42,21, 4 f LBL 4 465 45 2 RCL 2
058 45,20, 9 RCL × 9 262 43, 6, 8 g F? 8 466 26 EEX
059 30 263 22 .9 GTO . 9 467 2 2
060 45 3 RCL 3 264 44 3 STO 3 468 10 ÷
061 45 4 RCL 4 265 33 R⬇ 469 43 25 g TAN-¹
062 43,30, 2 g TEST x<0 266 16 CHS 470 44 5 STO 5
063 45 .3 RCL . 3 267 44 2 STO 2 471 24 COS
064 44 4 STO 4 268 43 11 g 472 48 .
065 14 269 34 x↔y 473 0 0
066 10 ÷ 270 2 2 474 4 4
067 44 .4 STO . 4 271 20 × 475 9 9
068 45,10, 1 RCL ÷ 1 272 44 1 STO 1 476 0 0
069 45 .1 RCL . 1 273 45,20, 3 RCL × 3 477 20 ×
070 45 4 RCL 4 274 2 2 478 45,20, 1 RCL × 1
071 14 275 20 × 479 45,20, 3 RCL × 3
072 20 × 276 30 480 44 6 STO 6
073 44 .5 STO . 5 277 42 31 f PSE 481 45 5 RCL 5
074 1 1 278 43,30, 2 g TEST x<0 482 23 SIN
075 43,30, 8 g TEST x<y 279 22 .8 GTO . 8 483 45,20, 1 RCL × 1
076 32 .2 GSB . 2 280 11 √x̅ 484 45,20, 3 RCL × 3
077 1 1 281 44 0 STO 0 485 9 9
078 45 .5 RCL . 5 282 45,40, 2 RCL + 2 486 48 .
079 30 283 45,10, 1 RCL ÷ 1 487 8 8
080 43 12 g LN 284 45 2 RCL 2 488 0 0
081 16 CHS 285 45,30, 0 RCL 0 489 6 6
082 45,10, .1 RCL ÷ . 1 286 45,10, 1 RCL ÷ 1 490 7 7
083 44 5 STO 5 287 43 32 g RTN 491 20 ×
084 45,20, .2 RCL × . 2 288 42,21, .8 f LBL . 8 492 44 7 STO 7
085 16 CHS 289 43, 4, 8 g SF 8 493 45 4 RCL 4
086 12 290 11 √x̅ 494 45,40, 6 RCL + 6
087 45,20, .2 RCL × . 2 291 42 30 f Re↔Im 495 45,40, 7 RCL + 7
088 45,20, 9 RCL × 9 292 45,10, 1 RCL ÷ 1 496 1 1
089 45 .4 RCL . 4 293 44 .0 STO . 0 497 48 .
090 45 .2 RCL . 2 294 45 2 RCL 2 498 0 0
091 45 4 RCL 4 295 45,10, 1 RCL ÷ 1 499 3 3
092 14 296 42 25 f I 500 0 0
093 20 × 297 42 30 f Re↔Im 501 9 9
094 40 + 298 45 2 RCL 2 502 20 ×
095 44 .6 STO . 6 299 45,10, 1 RCL ÷ 1 503 44 8 STO 8
096 45 2 RCL 2 300 45 .0 RCL . 0 504 31 R/S
097 45,10, 3 RCL ÷ 3 301 16 CHS 505 48 .
098 3 3 302 42 25 f I 506 2 2
099 0 0 303 43 32 g RTN 507 7 7
100 20 × 304 42,21, .9 f LBL . 9 508 7 7
101 45,10, 6 RCL ÷ 6 305 44 3 STO 3 509 8 8
102 11 √x̅ 306 42 30 f Re↔Im 510 20 ×
103 45,20, .6 RCL × . 6 307 44 .3 STO . 3 511 45 3 RCL 3
104 45 .6 RCL . 6 308 33 R⬇ 512 40 +
105 45,30, 2 RCL 2 309 16 CHS 513 45,10, 3 RCL ÷ 3
106 10 ÷ 310 44 2 STO 2 514 43 11 g
107 15 1/x 311 42 30 f Re↔Im 515 45 4 RCL 4
108 1 1 312 16 CHS 516 20 ×
109 40 + 313 44 .2 STO . 2 517 45,40, 6 RCL + 6
110 44 .7 STO . 7 314 42 30 f Re↔Im 518 45,40, 7 RCL + 7
111 45,20, 4 RCL × 4 315 11 √x̅ 519 1 1
112 44 4 STO 4 316 34 x↔y 520 48 .
113 45 .7 RCL . 7 317 2 2 521 0 0
114 1 1 318 20 × 522 3 3
115 30 319 44 1 STO 1 523 0 0
116 43 16 g ABS 320 42 30 f Re↔Im 524 9 9
117 1 1 321 44 .1 STO . 1 525 20 ×
118 26 EEX 322 42 30 f Re↔Im 526 44 9 STO 9
119 16 CHS 323 45 3 RCL 3 527 43 32 g RTN
120 6 6 324 45 .3 RCL . 3 528 42,21, 9 f LBL 9
121 43,30, 8 g TEST x<y 325 42 25 f I 529 10 ÷
122 22 .1 GTO . 1 326 20 × 530 44 3 STO 3
123 45 4 RCL 4 327 2 2 531 20 ×
124 43 32 g RTN 328 20 × 532 44 1 STO 1
125 42,21,14 f LBL D 329 30 533 2 2
126 44 .8 STO . 8 330 42 31 f PSE 534 5 5
127 45,10, 7 RCL ÷ 7 331 42 30 f Re↔Im 535 48 .
128 45 3 RCL 3 332 42 31 f PSE 536 4 4
129 20 × 333 42 30 f Re↔Im 537 44 2 STO 2
130 44 .8 STO . 8 334 11 √x̅ 538 2 2
131 45 4 RCL 4 335 44 0 STO 0 539 0 0
132 14 336 42 30 f Re↔Im 540 0 0
133 45,20, .4 RCL × . 4 337 44 .0 STO . 0 541 45 1 RCL 1
134 45 5 RCL 5 338 45,40, .2 RCL + . 2 542 45 3 RCL 3
135 45,20, .8 RCL × . 8 339 42 30 f Re↔Im 543 10 ÷
136 16 CHS 340 45,40, 2 RCL + 2 544 43,30, 7 g TEST x>y
137 12 341 45 1 RCL 1 545 45,10, 2 RCL ÷ 2
138 45,20, .8 RCL × . 8 342 45 .1 RCL . 1 546 45 3 RCL 3
139 45,20, 9 RCL × 9 343 42 25 f I 547 20 ×
140 40 + 344 10 ÷ 548 44 3 STO 3
141 45,20, 8 RCL × 8 345 45 2 RCL 2 549 45 2 RCL 2
142 45 3 RCL 3 346 45,30, 0 RCL 0 550 20 ×
143 10 ÷ 347 45 .2 RCL . 2 551 44 1 STO 1
144 43 32 g RTN 348 45,30, .0 RCL . 0 552 45 2 RCL 2
145 42,21,13 f LBL C 349 42 25 f I 553 10 ÷
146 44 .9 STO . 9 350 45 1 RCL 1 554 31 R/S
147 36 ENTER 351 45 .1 RCL . 1 555 45 1 RCL 1
148 42,10, .3 f SOLVE . 3 352 42 25 f I 556 43 26 g π
149 43 32 g RTN 353 10 ÷ 557 20 ×
150 42,21, .2 f LBL . 2 354 43 32 g RTN 558 26 EEX
151 45 .5 RCL . 5 355 42,21, 5 f LBL 5 559 3 3
152 15 1/x 356 43 16 g ABS 560 10 ÷
153 44 .5 STO . 5 357 44 0 STO 0 561 31 R/S
154 43 32 g RTN 358 1 1 562 45 1 RCL 1
155 42,21, .3 f LBL . 3 359 44 1 STO 1 563 3 3
156 32 14 GSB D 360 42,21, .4 f LBL . 4 564 4 4
157 45,30, .9 RCL . 9 361 33 R⬇ 565 0 0
158 43 32 g RTN 362 15 1/x 566 10 ÷
159 42,21,15 f LBL E 363 44,20, 1 STO × 1 567 43 32 g RTN
160 44 24 STO (i) 364 36 ENTER 568 42,21, 0 f LBL 0
161 45 2 RCL 2 365 43 44 g INT 569 2 2
162 26 EEX 366 30 570 36 ENTER
163 2 2 367 4 4 571 36 ENTER
164 10 ÷ 368 16 CHS 572 4 4
165 36 ENTER 369 13 10ˣ 573 14
166 36 ENTER 370 43 10 g x≤y 574 15 1/x
167 1 1 371 22 .4 GTO . 4 575 11 √x̅
168 40 + 372 45 0 RCL 0 576 12
169 43 12 g LN 373 45 1 RCL 1 577 13 10ˣ
170 34 x↔y 374 43 44 g INT 578 43 11 g
171 43 36 g LSTx 375 20 × 579 43 12 g LN
172 1 1 376 42 31 f PSE 580 43 13 g LOG
173 43,30, 6 g TEST x≠y 377 43 36 g LSTx 581 43 14 g %
174 30 378 43 32 g RTN 582 43 15 g Δ%
175 10 ÷ 379 42,21, 6 f LBL 6 583 43 16 g ABS
176 20 × 380 43, 5, 8 g CF 8 584 16 CHS
177 45,20, 1 RCL × 1 381 42,16, 0 f MATRIX 0 585 23 SIN
178 36 ENTER 382 36 ENTER 586 24 COS
179 12 383 42,23,11 f DIM A 587 25 TAN
180 45,20, 3 RCL × 3 384 42,16, 1 f MATRIX 1 588 43 25 g TAN-¹
181 34 x↔y 385 45,16,11 RCL MATRIX A 589 43 24 g COS-¹
182 2 2 386 42 31 f PSE 590 43 23 g SIN-¹
183 10 ÷ 387 42,21, .5 f LBL . 5 591 15 1/x
184 42,22,23 f HYP SIN 388 31 R/S 592 42,22,23 f HYP SIN
185 43 36 g LSTx 389 u 44 11 USER STO A 593 42,22,24 f HYP COS
186 12 390 22 .5 GTO . 5 594 42,22,25 f HYP TAN
187 20 × 391 45,23,11 RCL DIM A 595 43,22,25 g HYP-¹ TAN
188 2 2 392 42,16, 1 f MATRIX 1 596 43,22,24 g HYP-¹ COS
189 20 × 393 1 1 597 43,22,23 g HYP-¹ SIN
190 45,20, 4 RCL × 4 394 42,23,12 f DIM B 598 1 1
191 26 EEX 395 45,16,12 RCL MATRIX B 599 0 0
192 2 2 396 42 31 f PSE 600 40 +
193 45,10, 2 RCL ÷ 2 397 42,21, .6 f LBL . 6 601 42 0 f x !
194 45,40, 6 RCL + 6 398 31 R/S 602 44 1 STO 1
195 20 × 399 u 44 12 USER STO B 603 1 1
196 40 + 400 22 .6 GTO . 6 604 44,30, 2 STO 2
197 45,40, 5 RCL + 5 401 3 3 605 45 2 RCL 2
198 43 32 g RTN 402 45,16,12 RCL MATRIX B 606 43,30, 1 g TEST x>0
199 42,21, 1 f LBL 1 403 42 31 f PSE 607 22 0 GTO 0
200 2 2 404 45,16,11 RCL MATRIX A 608 45 1 RCL 1
201 7 7 405 42,26,13 f RESULT C 609 43 32 g RTN
202 3 3 406 10 ÷
203 48 . 407 42,16, 1 f MATRIX 1