Home » Archimedes archive » Acorn User » AU 1995-11.adf » !Regulars » Regulars/StarInfo/Weaver/!Equs/!Help
Regulars/StarInfo/Weaver/!Equs/!Help
This website contains an archive of files for the Acorn Electron, BBC Micro, Acorn Archimedes, Commodore 16 and Commodore 64 computers, which Dominic Ford has rescued from his private collection of floppy disks and cassettes.
Some of these files were originally commercial releases in the 1980s and 1990s, but they are now widely available online. I assume that copyright over them is no longer being asserted. If you own the copyright and would like files to be removed, please contact me.
| Tape/disk: | Home » Archimedes archive » Acorn User » AU 1995-11.adf » !Regulars |
| Filename: | Regulars/StarInfo/Weaver/!Equs/!Help |
| Read OK: | ✔ |
| File size: | 1691 bytes |
| Load address: | 0000 |
| Exec address: | 0000 |
File contents
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# #
# Equs - Simultaneous Equation Solver � Acorn User - 1995 #
# #
# Simon Weaver #
# #
#######################################################################
Purpose
-------
Equs is a program for solving simultaneous linear equations with up to 99
unknown variables. If you do not know what a simultaneous linear equation is
then this program is probably not for you! It is assumed therefore that the
reader is familiar with relevant mathematical terms used in this help text
and if needed a more graphical and less technical introduction to
simultaneous equations is given from the help option within the program
itself.
Use
---
Equs will install on the icon bar and provides full interactive help. The
best way to use the program is to just use it! Before you start you will need
your equation in the form below.
23x + 34y + 6z =32
64x + 23y + 2z =12
0x + y + z =77
The data is then entered into a table and when you click on calculate you are
given the results. In this case:
x = 3.86096
y = -18.5286
z = 95.5286
You can select up to 99 unknowns but you will need the same number of fully
independent equations as the number of unknowns you have.
You can change the number of �significant figures� by clicking the menu
button on the results window. It is also possible to �force� standard form
with the Force EXP option.
Ways of entering numbers
------------------------
As the program uses the operating system�s routines for inputting numbers you
can use any mathematical operators: eg SIN(2*PI)/2*(4/PI)
*, /, +, - : Multiply, divide, add, subtract
a^n : a to the power n
SIN(th), COS(RAD(th)) : SINE of angle in radians, COSINE of angle in degrees
TAN(th) : TANGENT of angle in radians
ASN(n), ACS(n), ATN(n) : Inverse Sin, Cosine, Tangent of n. (in radians)
DEG(rads), RAD(degs) : Converts from radians to degrees and vice-versa
SQR(num), EXP(num) : Square root (num), e^num
LOG(num), LN(num) : LOG of num to base 10/base e respectively
ABS(num), INT(num) : The absolute (positive) value of num, integer of num
SGN(num) : -1 if num is negative, 0 if zero, 1 if positive
Correct algebraic rules are obeyed so division is done before multiplication etc. If in doubt use extra brackets.
A few constants are also defined:
AVOGADRO or MOLE : Avogadro�s constant - 6.022*10^23
GRAV : Acceleration due to gravity - 9.80665
ROOT2 : Square root of two - 1.41421356
ROOT3 : Square root of three - 1.73205081
PI : Pi! - 3.14159265
This allows you to easily type GRAV*ROOT2/2 for ___
G \/ 2 instead of
-------- 9.80665*SQR(2)/2
2
Note that as soon as you press Return the expression is converted into
decimal and all answers are in decimal. You can change or add to the
constants by loading the program into a text editor.
Problems
--------
Because of the way the program calculates the unknown values, when using very
small or large coefficients there may be inaccuracies in the results. So,
after calculating the results the program puts the answers back into the
original equations and calculates the percentage difference with the actual
answer. This will show you how accurate the results are. With more
significant figures the accuracy will be higher.
With most real situation numbers that have been tried, I have had no
problems at all but if you do it may help to swap around some of the lines.
Particularly try to avoid very small/large numbers on the diagonals. The
program won�t work at all if the number in the first cell is 0, but you are
warned if it is.
It may also simply not be possible to calculate the results because the
equations are not independant. For example:
x+y+z = 4
2x+2y+2z = 8
x+2y+3z = 12
With these the second equation is just twice the first and so there are only
really two independent equations so values cannot be worked out. It can be
very difficult to see why the program may fail with the infinite number of
possibilities available and my mathematical knowledge isn�t up to artificial
intelligence programming just yet.
Future?
-------
There are many improvements that could be made to the program but due to a
heavy workload at the moment it could be a while.... that�s if they are ever
made. Risc PC users will notice that the System font is used in some parts of
the program and the outline font in others. Unfortunately I�ve only just
found this out and I�m afraid it�s too hard to correct now! It does mean
that the help text looks awful because it is all over to the left but I have
only very occasional access to a Risc PC. Now if Acorn had released RO3.5
for the older machines....
Contacting the Author
---------------------
If you have any problems, or praise I would very much like to hear from you.
I can be contacted at:
9 Kingsmill Road
Basingstoke
Hampshire
RG21 3JJ
Tel: 01256 26043
Fax: 01256 57271
e-mail: 100601.2342@compuserve.com
(may not be valid after September 1996)
I would appreciate a stamp if you want a reply!
00000000 0a 20 20 20 23 23 23 23 23 23 23 23 23 23 23 23 |. ############| 00000010 23 23 23 23 23 23 23 23 23 23 23 23 23 23 23 23 |################| * 00000040 23 23 23 23 23 23 23 23 23 23 23 0a 20 20 20 23 |###########. #| 00000050 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 | | * 00000090 20 20 20 20 20 23 0a 20 20 20 23 20 20 20 20 20 | #. # | 000000a0 20 45 71 75 73 20 2d 20 53 69 6d 75 6c 74 61 6e | Equs - Simultan| 000000b0 65 6f 75 73 20 45 71 75 61 74 69 6f 6e 20 53 6f |eous Equation So| 000000c0 6c 76 65 72 20 20 20 a9 20 41 63 6f 72 6e 20 55 |lver . Acorn U| 000000d0 73 65 72 20 2d 20 31 39 39 35 20 20 20 20 20 20 |ser - 1995 | 000000e0 23 0a 20 20 20 23 20 20 20 20 20 20 20 20 20 20 |#. # | 000000f0 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 | | * 00000120 20 20 20 20 20 20 20 20 20 20 20 23 0a 20 20 20 | #. | 00000130 23 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 |# | 00000140 20 20 20 20 20 20 20 20 20 20 20 20 20 53 69 6d | Sim| 00000150 6f 6e 20 57 65 61 76 65 72 20 20 20 20 20 20 20 |on Weaver | 00000160 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 | | 00000170 20 20 20 20 20 20 23 0a 20 20 20 23 20 20 20 20 | #. # | 00000180 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 | | * 000001c0 20 23 0a 20 20 20 23 23 23 23 23 23 23 23 23 23 | #. ##########| 000001d0 23 23 23 23 23 23 23 23 23 23 23 23 23 23 23 23 |################| * 00000200 23 23 23 23 23 23 23 23 23 23 23 23 23 0a 20 20 |#############. | 00000210 0a 50 75 72 70 6f 73 65 20 20 0a 2d 2d 2d 2d 2d |.Purpose .-----| 00000220 2d 2d 0a 45 71 75 73 20 69 73 20 61 20 70 72 6f |--.Equs is a pro| 00000230 67 72 61 6d 20 66 6f 72 20 73 6f 6c 76 69 6e 67 |gram for solving| 00000240 20 73 69 6d 75 6c 74 61 6e 65 6f 75 73 20 6c 69 | simultaneous li| 00000250 6e 65 61 72 20 65 71 75 61 74 69 6f 6e 73 20 77 |near equations w| 00000260 69 74 68 20 75 70 20 74 6f 20 39 39 0a 75 6e 6b |ith up to 99.unk| 00000270 6e 6f 77 6e 20 76 61 72 69 61 62 6c 65 73 2e 20 |nown variables. | 00000280 49 66 20 79 6f 75 20 64 6f 20 6e 6f 74 20 6b 6e |If you do not kn| 00000290 6f 77 20 77 68 61 74 20 61 20 73 69 6d 75 6c 74 |ow what a simult| 000002a0 61 6e 65 6f 75 73 20 6c 69 6e 65 61 72 20 65 71 |aneous linear eq| 000002b0 75 61 74 69 6f 6e 20 69 73 0a 74 68 65 6e 20 74 |uation is.then t| 000002c0 68 69 73 20 70 72 6f 67 72 61 6d 20 69 73 20 70 |his program is p| 000002d0 72 6f 62 61 62 6c 79 20 6e 6f 74 20 66 6f 72 20 |robably not for | 000002e0 79 6f 75 21 20 49 74 20 69 73 20 61 73 73 75 6d |you! It is assum| 000002f0 65 64 20 74 68 65 72 65 66 6f 72 65 20 74 68 61 |ed therefore tha| 00000300 74 20 74 68 65 0a 72 65 61 64 65 72 20 69 73 20 |t the.reader is | 00000310 66 61 6d 69 6c 69 61 72 20 77 69 74 68 20 72 65 |familiar with re| 00000320 6c 65 76 61 6e 74 20 6d 61 74 68 65 6d 61 74 69 |levant mathemati| 00000330 63 61 6c 20 74 65 72 6d 73 20 75 73 65 64 20 69 |cal terms used i| 00000340 6e 20 74 68 69 73 20 68 65 6c 70 20 74 65 78 74 |n this help text| 00000350 0a 61 6e 64 20 69 66 20 6e 65 65 64 65 64 20 61 |.and if needed a| 00000360 20 6d 6f 72 65 20 67 72 61 70 68 69 63 61 6c 20 | more graphical | 00000370 61 6e 64 20 6c 65 73 73 20 74 65 63 68 6e 69 63 |and less technic| 00000380 61 6c 20 69 6e 74 72 6f 64 75 63 74 69 6f 6e 20 |al introduction | 00000390 74 6f 0a 73 69 6d 75 6c 74 61 6e 65 6f 75 73 20 |to.simultaneous | 000003a0 65 71 75 61 74 69 6f 6e 73 20 69 73 20 67 69 76 |equations is giv| 000003b0 65 6e 20 66 72 6f 6d 20 74 68 65 20 68 65 6c 70 |en from the help| 000003c0 20 6f 70 74 69 6f 6e 20 77 69 74 68 69 6e 20 74 | option within t| 000003d0 68 65 20 70 72 6f 67 72 61 6d 0a 69 74 73 65 6c |he program.itsel| 000003e0 66 2e 0a 0a 55 73 65 0a 2d 2d 2d 0a 45 71 75 73 |f...Use.---.Equs| 000003f0 20 77 69 6c 6c 20 69 6e 73 74 61 6c 6c 20 6f 6e | will install on| 00000400 20 74 68 65 20 69 63 6f 6e 20 62 61 72 20 61 6e | the icon bar an| 00000410 64 20 70 72 6f 76 69 64 65 73 20 66 75 6c 6c 20 |d provides full | 00000420 69 6e 74 65 72 61 63 74 69 76 65 20 68 65 6c 70 |interactive help| 00000430 2e 20 54 68 65 0a 62 65 73 74 20 77 61 79 20 74 |. The.best way t| 00000440 6f 20 75 73 65 20 74 68 65 20 70 72 6f 67 72 61 |o use the progra| 00000450 6d 20 69 73 20 74 6f 20 6a 75 73 74 20 75 73 65 |m is to just use| 00000460 20 69 74 21 20 42 65 66 6f 72 65 20 79 6f 75 20 | it! Before you | 00000470 73 74 61 72 74 20 79 6f 75 20 77 69 6c 6c 20 6e |start you will n| 00000480 65 65 64 0a 79 6f 75 72 20 65 71 75 61 74 69 6f |eed.your equatio| 00000490 6e 20 69 6e 20 74 68 65 20 66 6f 72 6d 20 62 65 |n in the form be| 000004a0 6c 6f 77 2e 0a 0a 32 33 78 20 2b 20 33 34 79 20 |low...23x + 34y | 000004b0 2b 20 36 7a 20 3d 33 32 0a 36 34 78 20 2b 20 32 |+ 6z =32.64x + 2| 000004c0 33 79 20 2b 20 32 7a 20 3d 31 32 0a 30 78 20 20 |3y + 2z =12.0x | 000004d0 2b 20 20 20 79 20 2b 20 20 7a 20 3d 37 37 0a 0a |+ y + z =77..| 000004e0 54 68 65 20 64 61 74 61 20 69 73 20 74 68 65 6e |The data is then| 000004f0 20 65 6e 74 65 72 65 64 20 69 6e 74 6f 20 61 20 | entered into a | 00000500 74 61 62 6c 65 20 61 6e 64 20 77 68 65 6e 20 79 |table and when y| 00000510 6f 75 20 63 6c 69 63 6b 20 6f 6e 20 63 61 6c 63 |ou click on calc| 00000520 75 6c 61 74 65 20 79 6f 75 20 61 72 65 0a 67 69 |ulate you are.gi| 00000530 76 65 6e 20 74 68 65 20 72 65 73 75 6c 74 73 2e |ven the results.| 00000540 20 49 6e 20 74 68 69 73 20 63 61 73 65 3a 0a 0a | In this case:..| 00000550 78 20 3d 20 20 20 33 2e 38 36 30 39 36 0a 79 20 |x = 3.86096.y | 00000560 3d 20 2d 31 38 2e 35 32 38 36 0a 7a 20 3d 20 20 |= -18.5286.z = | 00000570 39 35 2e 35 32 38 36 0a 0a 59 6f 75 20 63 61 6e |95.5286..You can| 00000580 20 73 65 6c 65 63 74 20 75 70 20 74 6f 20 39 39 | select up to 99| 00000590 20 75 6e 6b 6e 6f 77 6e 73 20 62 75 74 20 79 6f | unknowns but yo| 000005a0 75 20 77 69 6c 6c 20 6e 65 65 64 20 74 68 65 20 |u will need the | 000005b0 73 61 6d 65 20 6e 75 6d 62 65 72 20 6f 66 20 66 |same number of f| 000005c0 75 6c 6c 79 0a 69 6e 64 65 70 65 6e 64 65 6e 74 |ully.independent| 000005d0 20 65 71 75 61 74 69 6f 6e 73 20 61 73 20 74 68 | equations as th| 000005e0 65 20 6e 75 6d 62 65 72 20 6f 66 20 75 6e 6b 6e |e number of unkn| 000005f0 6f 77 6e 73 20 79 6f 75 20 68 61 76 65 2e 0a 0a |owns you have...| 00000600 59 6f 75 20 63 61 6e 20 63 68 61 6e 67 65 20 74 |You can change t| 00000610 68 65 20 6e 75 6d 62 65 72 20 6f 66 20 90 73 69 |he number of .si| 00000620 67 6e 69 66 69 63 61 6e 74 20 66 69 67 75 72 65 |gnificant figure| 00000630 73 91 20 62 79 20 63 6c 69 63 6b 69 6e 67 20 74 |s. by clicking t| 00000640 68 65 20 6d 65 6e 75 0a 62 75 74 74 6f 6e 20 6f |he menu.button o| 00000650 6e 20 74 68 65 20 72 65 73 75 6c 74 73 20 77 69 |n the results wi| 00000660 6e 64 6f 77 2e 20 49 74 20 69 73 20 61 6c 73 6f |ndow. It is also| 00000670 20 70 6f 73 73 69 62 6c 65 20 74 6f 20 90 66 6f | possible to .fo| 00000680 72 63 65 91 20 73 74 61 6e 64 61 72 64 20 66 6f |rce. standard fo| 00000690 72 6d 0a 77 69 74 68 20 74 68 65 20 46 6f 72 63 |rm.with the Forc| 000006a0 65 20 45 58 50 20 6f 70 74 69 6f 6e 2e 20 0a 0a |e EXP option. ..| 000006b0 57 61 79 73 20 6f 66 20 65 6e 74 65 72 69 6e 67 |Ways of entering| 000006c0 20 6e 75 6d 62 65 72 73 0a 2d 2d 2d 2d 2d 2d 2d | numbers.-------| 000006d0 2d 2d 2d 2d 2d 2d 2d 2d 2d 2d 2d 2d 2d 2d 2d 2d |----------------| 000006e0 2d 0a 41 73 20 74 68 65 20 70 72 6f 67 72 61 6d |-.As the program| 000006f0 20 75 73 65 73 20 74 68 65 20 6f 70 65 72 61 74 | uses the operat| 00000700 69 6e 67 20 73 79 73 74 65 6d 91 73 20 72 6f 75 |ing system.s rou| 00000710 74 69 6e 65 73 20 66 6f 72 20 69 6e 70 75 74 74 |tines for inputt| 00000720 69 6e 67 20 6e 75 6d 62 65 72 73 20 79 6f 75 0a |ing numbers you.| 00000730 63 61 6e 20 75 73 65 20 61 6e 79 20 6d 61 74 68 |can use any math| 00000740 65 6d 61 74 69 63 61 6c 20 6f 70 65 72 61 74 6f |ematical operato| 00000750 72 73 3a 20 65 67 20 53 49 4e 28 32 2a 50 49 29 |rs: eg SIN(2*PI)| 00000760 2f 32 2a 28 34 2f 50 49 29 0a 0a 0a 2a 2c 20 2f |/2*(4/PI)...*, /| 00000770 2c 20 2b 2c 20 2d 20 20 20 20 20 20 20 20 20 20 |, +, - | 00000780 20 20 20 3a 20 4d 75 6c 74 69 70 6c 79 2c 20 64 | : Multiply, d| 00000790 69 76 69 64 65 2c 20 61 64 64 2c 20 73 75 62 74 |ivide, add, subt| 000007a0 72 61 63 74 0a 61 5e 6e 20 20 20 20 20 20 20 20 |ract.a^n | 000007b0 20 20 20 20 20 20 20 20 20 20 20 20 3a 20 61 20 | : a | 000007c0 74 6f 20 74 68 65 20 70 6f 77 65 72 20 6e 0a 53 |to the power n.S| 000007d0 49 4e 28 74 68 29 2c 20 43 4f 53 28 52 41 44 28 |IN(th), COS(RAD(| 000007e0 74 68 29 29 20 20 3a 20 53 49 4e 45 20 6f 66 20 |th)) : SINE of | 000007f0 61 6e 67 6c 65 20 69 6e 20 72 61 64 69 61 6e 73 |angle in radians| 00000800 2c 20 43 4f 53 49 4e 45 20 6f 66 20 61 6e 67 6c |, COSINE of angl| 00000810 65 20 69 6e 20 64 65 67 72 65 65 73 0a 54 41 4e |e in degrees.TAN| 00000820 28 74 68 29 20 20 20 20 20 20 20 20 20 20 20 20 |(th) | 00000830 20 20 20 20 3a 20 54 41 4e 47 45 4e 54 20 6f 66 | : TANGENT of| 00000840 20 61 6e 67 6c 65 20 69 6e 20 72 61 64 69 61 6e | angle in radian| 00000850 73 0a 41 53 4e 28 6e 29 2c 20 41 43 53 28 6e 29 |s.ASN(n), ACS(n)| 00000860 2c 20 41 54 4e 28 6e 29 20 3a 20 49 6e 76 65 72 |, ATN(n) : Inver| 00000870 73 65 20 53 69 6e 2c 20 43 6f 73 69 6e 65 2c 20 |se Sin, Cosine, | 00000880 54 61 6e 67 65 6e 74 20 6f 66 20 6e 2e 20 28 69 |Tangent of n. (i| 00000890 6e 20 72 61 64 69 61 6e 73 29 0a 44 45 47 28 72 |n radians).DEG(r| 000008a0 61 64 73 29 2c 20 52 41 44 28 64 65 67 73 29 20 |ads), RAD(degs) | 000008b0 20 20 3a 20 43 6f 6e 76 65 72 74 73 20 66 72 6f | : Converts fro| 000008c0 6d 20 72 61 64 69 61 6e 73 20 74 6f 20 64 65 67 |m radians to deg| 000008d0 72 65 65 73 20 61 6e 64 20 76 69 63 65 2d 76 65 |rees and vice-ve| 000008e0 72 73 61 0a 53 51 52 28 6e 75 6d 29 2c 20 45 58 |rsa.SQR(num), EX| 000008f0 50 28 6e 75 6d 29 20 20 20 20 20 3a 20 53 71 75 |P(num) : Squ| 00000900 61 72 65 20 72 6f 6f 74 20 28 6e 75 6d 29 2c 20 |are root (num), | 00000910 65 5e 6e 75 6d 0a 4c 4f 47 28 6e 75 6d 29 2c 20 |e^num.LOG(num), | 00000920 4c 4e 28 6e 75 6d 29 20 20 20 20 20 20 3a 20 4c |LN(num) : L| 00000930 4f 47 20 6f 66 20 6e 75 6d 20 74 6f 20 62 61 73 |OG of num to bas| 00000940 65 20 31 30 2f 62 61 73 65 20 65 20 72 65 73 70 |e 10/base e resp| 00000950 65 63 74 69 76 65 6c 79 0a 41 42 53 28 6e 75 6d |ectively.ABS(num| 00000960 29 2c 20 49 4e 54 28 6e 75 6d 29 20 20 20 20 20 |), INT(num) | 00000970 3a 20 54 68 65 20 61 62 73 6f 6c 75 74 65 20 28 |: The absolute (| 00000980 70 6f 73 69 74 69 76 65 29 20 76 61 6c 75 65 20 |positive) value | 00000990 6f 66 20 6e 75 6d 2c 20 69 6e 74 65 67 65 72 20 |of num, integer | 000009a0 6f 66 20 6e 75 6d 0a 53 47 4e 28 6e 75 6d 29 20 |of num.SGN(num) | 000009b0 20 20 20 20 20 20 20 20 20 20 20 20 20 20 3a 20 | : | 000009c0 2d 31 20 69 66 20 6e 75 6d 20 69 73 20 6e 65 67 |-1 if num is neg| 000009d0 61 74 69 76 65 2c 20 30 20 69 66 20 7a 65 72 6f |ative, 0 if zero| 000009e0 2c 20 31 20 69 66 20 70 6f 73 69 74 69 76 65 0a |, 1 if positive.| 000009f0 0a 43 6f 72 72 65 63 74 20 61 6c 67 65 62 72 61 |.Correct algebra| 00000a00 69 63 20 72 75 6c 65 73 20 61 72 65 20 6f 62 65 |ic rules are obe| 00000a10 79 65 64 20 73 6f 20 64 69 76 69 73 69 6f 6e 20 |yed so division | 00000a20 69 73 20 64 6f 6e 65 20 62 65 66 6f 72 65 20 6d |is done before m| 00000a30 75 6c 74 69 70 6c 69 63 61 74 69 6f 6e 20 65 74 |ultiplication et| 00000a40 63 2e 20 49 66 20 69 6e 20 64 6f 75 62 74 20 75 |c. If in doubt u| 00000a50 73 65 20 65 78 74 72 61 20 62 72 61 63 6b 65 74 |se extra bracket| 00000a60 73 2e 0a 0a 0a 41 20 66 65 77 20 63 6f 6e 73 74 |s....A few const| 00000a70 61 6e 74 73 20 61 72 65 20 61 6c 73 6f 20 64 65 |ants are also de| 00000a80 66 69 6e 65 64 3a 0a 0a 41 56 4f 47 41 44 52 4f |fined:..AVOGADRO| 00000a90 20 6f 72 20 4d 4f 4c 45 20 20 3a 20 41 76 6f 67 | or MOLE : Avog| 00000aa0 61 64 72 6f 91 73 20 63 6f 6e 73 74 61 6e 74 20 |adro.s constant | 00000ab0 20 20 20 20 20 20 20 20 20 20 2d 20 36 2e 30 32 | - 6.02| 00000ac0 32 2a 31 30 5e 32 33 0a 47 52 41 56 20 20 20 20 |2*10^23.GRAV | 00000ad0 20 20 20 20 20 20 20 20 20 20 3a 20 41 63 63 65 | : Acce| 00000ae0 6c 65 72 61 74 69 6f 6e 20 64 75 65 20 74 6f 20 |leration due to | 00000af0 67 72 61 76 69 74 79 20 20 20 2d 20 39 2e 38 30 |gravity - 9.80| 00000b00 36 36 35 0a 52 4f 4f 54 32 20 20 20 20 20 20 20 |665.ROOT2 | 00000b10 20 20 20 20 20 20 3a 20 53 71 75 61 72 65 20 72 | : Square r| 00000b20 6f 6f 74 20 6f 66 20 74 77 6f 20 20 20 20 20 20 |oot of two | 00000b30 20 20 20 20 20 20 2d 20 31 2e 34 31 34 32 31 33 | - 1.414213| 00000b40 35 36 0a 52 4f 4f 54 33 20 20 20 20 20 20 20 20 |56.ROOT3 | 00000b50 20 20 20 20 20 3a 20 53 71 75 61 72 65 20 72 6f | : Square ro| 00000b60 6f 74 20 6f 66 20 74 68 72 65 65 20 20 20 20 20 |ot of three | 00000b70 20 20 20 20 20 2d 20 31 2e 37 33 32 30 35 30 38 | - 1.7320508| 00000b80 31 0a 50 49 20 20 20 20 20 20 20 20 20 20 20 20 |1.PI | 00000b90 20 20 20 20 3a 20 50 69 21 20 20 20 20 20 20 20 | : Pi! | 00000ba0 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 | | 00000bb0 20 20 20 20 2d 20 33 2e 31 34 31 35 39 32 36 35 | - 3.14159265| 00000bc0 0a 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 |. | 00000bd0 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 | | * 00000bf0 20 20 20 20 0a 54 68 69 73 20 61 6c 6c 6f 77 73 | .This allows| 00000c00 20 79 6f 75 20 74 6f 20 65 61 73 69 6c 79 20 74 | you to easily t| 00000c10 79 70 65 20 47 52 41 56 2a 52 4f 4f 54 32 2f 32 |ype GRAV*ROOT2/2| 00000c20 20 66 6f 72 20 20 20 20 20 20 20 20 5f 5f 5f 0a | for ___.| 00000c30 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 | | * 00000c60 20 20 20 47 20 5c 2f 20 20 32 20 20 20 20 20 20 | G \/ 2 | 00000c70 20 20 69 6e 73 74 65 61 64 20 6f 66 0a 20 20 20 | instead of. | 00000c80 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 | | * 00000ca0 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 2d | -| 00000cb0 2d 2d 2d 2d 2d 2d 2d 20 20 39 2e 38 30 36 36 35 |------- 9.80665| 00000cc0 2a 53 51 52 28 32 29 2f 32 0a 20 20 20 20 20 20 |*SQR(2)/2. | 00000cd0 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 | | * 00000d00 32 20 20 20 20 20 0a 0a 4e 6f 74 65 20 74 68 61 |2 ..Note tha| 00000d10 74 20 61 73 20 73 6f 6f 6e 20 61 73 20 79 6f 75 |t as soon as you| 00000d20 20 70 72 65 73 73 20 52 65 74 75 72 6e 20 74 68 | press Return th| 00000d30 65 20 65 78 70 72 65 73 73 69 6f 6e 20 69 73 20 |e expression is | 00000d40 63 6f 6e 76 65 72 74 65 64 20 69 6e 74 6f 0a 64 |converted into.d| 00000d50 65 63 69 6d 61 6c 20 61 6e 64 20 61 6c 6c 20 61 |ecimal and all a| 00000d60 6e 73 77 65 72 73 20 61 72 65 20 69 6e 20 64 65 |nswers are in de| 00000d70 63 69 6d 61 6c 2e 20 59 6f 75 20 63 61 6e 20 63 |cimal. You can c| 00000d80 68 61 6e 67 65 20 6f 72 20 61 64 64 20 74 6f 20 |hange or add to | 00000d90 74 68 65 0a 63 6f 6e 73 74 61 6e 74 73 20 62 79 |the.constants by| 00000da0 20 6c 6f 61 64 69 6e 67 20 74 68 65 20 70 72 6f | loading the pro| 00000db0 67 72 61 6d 20 69 6e 74 6f 20 61 20 74 65 78 74 |gram into a text| 00000dc0 20 65 64 69 74 6f 72 2e 0a 0a 50 72 6f 62 6c 65 | editor...Proble| 00000dd0 6d 73 0a 2d 2d 2d 2d 2d 2d 2d 2d 0a 42 65 63 61 |ms.--------.Beca| 00000de0 75 73 65 20 6f 66 20 74 68 65 20 77 61 79 20 74 |use of the way t| 00000df0 68 65 20 70 72 6f 67 72 61 6d 20 63 61 6c 63 75 |he program calcu| 00000e00 6c 61 74 65 73 20 74 68 65 20 75 6e 6b 6e 6f 77 |lates the unknow| 00000e10 6e 20 76 61 6c 75 65 73 2c 20 77 68 65 6e 20 75 |n values, when u| 00000e20 73 69 6e 67 20 76 65 72 79 0a 73 6d 61 6c 6c 20 |sing very.small | 00000e30 6f 72 20 6c 61 72 67 65 20 63 6f 65 66 66 69 63 |or large coeffic| 00000e40 69 65 6e 74 73 20 74 68 65 72 65 20 6d 61 79 20 |ients there may | 00000e50 62 65 20 69 6e 61 63 63 75 72 61 63 69 65 73 20 |be inaccuracies | 00000e60 69 6e 20 74 68 65 20 72 65 73 75 6c 74 73 2e 20 |in the results. | 00000e70 53 6f 2c 20 0a 61 66 74 65 72 20 63 61 6c 63 75 |So, .after calcu| 00000e80 6c 61 74 69 6e 67 20 74 68 65 20 72 65 73 75 6c |lating the resul| 00000e90 74 73 20 74 68 65 20 70 72 6f 67 72 61 6d 20 70 |ts the program p| 00000ea0 75 74 73 20 74 68 65 20 61 6e 73 77 65 72 73 20 |uts the answers | 00000eb0 62 61 63 6b 20 69 6e 74 6f 20 74 68 65 0a 6f 72 |back into the.or| 00000ec0 69 67 69 6e 61 6c 20 65 71 75 61 74 69 6f 6e 73 |iginal equations| 00000ed0 20 61 6e 64 20 63 61 6c 63 75 6c 61 74 65 73 20 | and calculates | 00000ee0 74 68 65 20 70 65 72 63 65 6e 74 61 67 65 20 64 |the percentage d| 00000ef0 69 66 66 65 72 65 6e 63 65 20 77 69 74 68 20 74 |ifference with t| 00000f00 68 65 20 61 63 74 75 61 6c 0a 61 6e 73 77 65 72 |he actual.answer| 00000f10 2e 20 54 68 69 73 20 77 69 6c 6c 20 73 68 6f 77 |. This will show| 00000f20 20 79 6f 75 20 68 6f 77 20 61 63 63 75 72 61 74 | you how accurat| 00000f30 65 20 74 68 65 20 72 65 73 75 6c 74 73 20 61 72 |e the results ar| 00000f40 65 2e 20 57 69 74 68 20 6d 6f 72 65 0a 73 69 67 |e. 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Fo| 00001120 72 20 65 78 61 6d 70 6c 65 3a 0a 0a 20 20 20 20 |r example:.. | 00001130 20 20 20 20 20 20 20 20 20 78 2b 79 2b 7a 20 20 | x+y+z | 00001140 20 20 3d 20 34 0a 20 20 20 20 20 20 20 20 20 20 | = 4. | 00001150 20 20 20 32 78 2b 32 79 2b 32 7a 20 3d 20 38 0a | 2x+2y+2z = 8.| 00001160 20 20 20 20 20 20 20 20 20 20 20 20 20 78 2b 32 | x+2| 00001170 79 2b 33 7a 20 20 3d 20 31 32 0a 0a 57 69 74 68 |y+3z = 12..With| 00001180 20 74 68 65 73 65 20 74 68 65 20 73 65 63 6f 6e | these the secon| 00001190 64 20 65 71 75 61 74 69 6f 6e 20 69 73 20 6a 75 |d equation is ju| 000011a0 73 74 20 74 77 69 63 65 20 74 68 65 20 66 69 72 |st twice the fir| 000011b0 73 74 20 61 6e 64 20 73 6f 20 74 68 65 72 65 20 |st and so there | 000011c0 61 72 65 20 6f 6e 6c 79 0a 72 65 61 6c 6c 79 20 |are only.really | 000011d0 74 77 6f 20 69 6e 64 65 70 65 6e 64 65 6e 74 20 |two independent | 000011e0 65 71 75 61 74 69 6f 6e 73 20 73 6f 20 76 61 6c |equations so val| 000011f0 75 65 73 20 63 61 6e 6e 6f 74 20 62 65 20 77 6f |ues cannot be wo| 00001200 72 6b 65 64 20 6f 75 74 2e 20 49 74 20 63 61 6e |rked out. 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Unfortunatel| 00001400 79 20 49 91 76 65 20 6f 6e 6c 79 20 6a 75 73 74 |y I.ve only just| 00001410 0a 66 6f 75 6e 64 20 74 68 69 73 20 6f 75 74 20 |.found this out | 00001420 61 6e 64 20 49 91 6d 20 61 66 72 61 69 64 20 69 |and I.m afraid i| 00001430 74 91 73 20 74 6f 6f 20 68 61 72 64 20 74 6f 20 |t.s too hard to | 00001440 63 6f 72 72 65 63 74 20 6e 6f 77 21 20 49 74 20 |correct now! It | 00001450 64 6f 65 73 20 6d 65 61 6e 0a 74 68 61 74 20 74 |does mean.that t| 00001460 68 65 20 68 65 6c 70 20 74 65 78 74 20 6c 6f 6f |he help text loo| 00001470 6b 73 20 61 77 66 75 6c 20 62 65 63 61 75 73 65 |ks awful because| 00001480 20 69 74 20 69 73 20 61 6c 6c 20 6f 76 65 72 20 | it is all over | 00001490 74 6f 20 74 68 65 20 6c 65 66 74 20 62 75 74 20 |to the left but | 000014a0 49 20 68 61 76 65 0a 6f 6e 6c 79 20 76 65 72 79 |I have.only very| 000014b0 20 6f 63 63 61 73 69 6f 6e 61 6c 20 61 63 63 65 | occasional acce| 000014c0 73 73 20 74 6f 20 61 20 52 69 73 63 20 50 43 2e |ss to a Risc PC.| 000014d0 20 4e 6f 77 20 69 66 20 41 63 6f 72 6e 20 68 61 | Now if Acorn ha| 000014e0 64 20 72 65 6c 65 61 73 65 64 20 52 4f 33 2e 35 |d released RO3.5| 000014f0 0a 66 6f 72 20 74 68 65 20 6f 6c 64 65 72 20 6d |.for the older m| 00001500 61 63 68 69 6e 65 73 2e 2e 2e 2e 0a 0a 43 6f 6e |achines......Con| 00001510 74 61 63 74 69 6e 67 20 74 68 65 20 41 75 74 68 |tacting the Auth| 00001520 6f 72 0a 2d 2d 2d 2d 2d 2d 2d 2d 2d 2d 2d 2d 2d |or.-------------| 00001530 2d 2d 2d 2d 2d 2d 2d 2d 0a 49 66 20 79 6f 75 20 |--------.If you | 00001540 68 61 76 65 20 61 6e 79 20 70 72 6f 62 6c 65 6d |have any problem| 00001550 73 2c 20 6f 72 20 70 72 61 69 73 65 20 49 20 77 |s, or praise I w| 00001560 6f 75 6c 64 20 76 65 72 79 20 6d 75 63 68 20 6c |ould very much l| 00001570 69 6b 65 20 74 6f 20 68 65 61 72 20 66 72 6f 6d |ike to hear from| 00001580 20 79 6f 75 2e 0a 0a 49 20 63 61 6e 20 62 65 20 | you...I can be | 00001590 63 6f 6e 74 61 63 74 65 64 20 61 74 3a 0a 0a 20 |contacted at:.. | 000015a0 20 20 20 39 20 4b 69 6e 67 73 6d 69 6c 6c 20 52 | 9 Kingsmill R| 000015b0 6f 61 64 0a 20 20 20 20 42 61 73 69 6e 67 73 74 |oad. Basingst| 000015c0 6f 6b 65 0a 20 20 20 20 48 61 6d 70 73 68 69 72 |oke. Hampshir| 000015d0 65 0a 20 20 20 20 52 47 32 31 20 33 4a 4a 0a 20 |e. RG21 3JJ. | 000015e0 0a 20 20 20 20 54 65 6c 3a 20 30 31 32 35 36 20 |. Tel: 01256 | 000015f0 32 36 30 34 33 0a 20 20 20 20 46 61 78 3a 20 30 |26043. Fax: 0| 00001600 31 32 35 36 20 35 37 32 37 31 0a 20 65 2d 6d 61 |1256 57271. e-ma| 00001610 69 6c 3a 20 31 30 30 36 30 31 2e 32 33 34 32 40 |il: 100601.2342@| 00001620 63 6f 6d 70 75 73 65 72 76 65 2e 63 6f 6d 0a 20 |compuserve.com. | 00001630 20 20 20 20 20 20 20 20 28 6d 61 79 20 6e 6f 74 | (may not| 00001640 20 62 65 20 76 61 6c 69 64 20 61 66 74 65 72 20 | be valid after | 00001650 53 65 70 74 65 6d 62 65 72 20 31 39 39 36 29 0a |September 1996).| 00001660 0a 49 20 77 6f 75 6c 64 20 61 70 70 72 65 63 69 |.I would appreci| 00001670 61 74 65 20 61 20 73 74 61 6d 70 20 69 66 20 79 |ate a stamp if y| 00001680 6f 75 20 77 61 6e 74 20 61 20 72 65 70 6c 79 21 |ou want a reply!| 00001690 0a |.| 00001691
.