The Datafile PD-CD 4/DATAFILE_PDCD4.iso/education/help_view/!Help_View/Help/Num_Hlp

Text File | 1995-11-19 | 14.8 KB | 446 lines

Contents
Help for !Numbers  v 1.11
by  <Richard Sharpe>=Author:Numbers>

               <Licence>
               <Introduction>
               <How To Use>

Click on the words in red on any of the pages for more help.
!@#
Introduction
Here, hopefully is an interesting and useful program for stressed out
mathematics teachers who like to muck about with a bit of Number Theory
and want to get their students interested in the subject rather than bored
mindless by the horrors of number crunching.  To anyone else it is probably
the most stupid and tedious program ever devised!

If you are in any doubt as to which category you belong in,  please look
at the accompanying file, "Example" and if the contents interest you or
mean anything to you then you have my sympathy, otherwise take my advice
and continue in bliss and ignorance.

Most of what !Numbers does can be done with a pocket calculator or even a
piece of paper if you have a great deal of time. So if your life in the
classroom is stress free and joyful, !Numbers is definitely not for you.

The program began as a simple BBCBasic set of routines written on and for
an (expletive deleted!) RM Nimbus 186, (single tasking of course) in
response to a Year 7 girl asking me how I really expected her to find all
of the prime palindromics between 10 000 and 20 000.  I said I didn't and
wrote the program.

Later it occured to me that it would be much better to write it in the
Desktop so that the resulting lists could be saved as text files and
printed out.

<Contents>
!@#
How To Use
            Topics
-----------------------------------
   <Getting Started>
   <Lists of numbers/properties>
   <Random Numbers>
   <Factors>
   <Factor Sums>
   <The Kaprekar Process>
   <Digit Reduction>
   <Sums of Diagonals>
   <Big Number Calculator>
-----------------------------------
Happy number crunching!

If you have any suggestions as to how the program could be improved please
let me know.

All correspondence to the <Author>=Author:Numbers>.

<Contents>
!@#
Getting Started
Double click on the !Numbers icon in a filer window, to install it on the
icon bar.

Single click on the icon on the icon bar to open the main window.

There are a number of options to choose from here taking you to a variety
of other windows which do thrilling things.

Each of the subsequent windows has at least three buttons. \<Clear>|,
\<Finish>| and \<OK>|.

\<Clear>| blanks out every writable icon in the window.

\<Finish>| returns you to the main menu window.

\<OK>| sets your calculations going, as does pressing \<Return>|.

<Contents>
!@#
Lists of numbers/properties
First choose your configuration.

This is done using the <Option> buttons on the left and the <Radio>
buttons on the right of the window.

Then type in the number you want to start with in the top writable icon
and the number you want to finish with in the second writable icon
underneath it, pressing \<Return>| after each or by pressing \<Return>|
after entering the start value and pressing the OK button after the
second.  The hourglass will run for a few seconds and then a save box will
be displayed.  Dragging this to a filer window will save the list as a
text file,  which can then be viewed in an Editor.

<How To Use>
!@#
Options
The Option buttons on the left of the window lets you choose the comments
you want appended to the lists.

\<Primes>| will tell you which of the numbers are prime.
\<P'dromes>| will tell you which are Palindromic.
\<Powers>| will tell you which are squares, cubics or quartics.
\<Factorials>| will tell you which are factorial numbers.
\<Fac Sums>| will tell you whether the number is Perfect, Abundant or
Deficient.
\<Kaprekar>| will identify any Kaprekar numbers or constants.
\<Triangle>| will identify any Triangle numbers in the list.

<How To Use>
!@#
Radio
The radio buttons on the right let you choose the type of numbers that are
displayed.

By default every number in your chosen interval is displayed.

If you choose \<Prime>| then only prime numbers are displayed and ditto
with \<Palindromics>| or \<Triangles>|.

<How To Use>
!@#
Random Numbers
When you click on \<Randoms Numbers>| the Main window is closed and a
special random window is opened.

Into the icon marked "Lowest" type the smallest number that you want in
you list.

Into the icon marked "Highest" type the largest number that you want in
your list

Into the icon marked "How Many?" type in the number of random numbers in
the specified range that you require.

<How To Use>
!@#
Factors
When you choose \<Factors>| the Main window is closed and a special
factors window is opened.  Type the number you wish to factorize into the
writable icon at the top and press \<Return>|.  The factors will flow into
the icons down the screen.  Pressing the \<Menu>| button will open a menu
leading to a Save box. This will save the factors to a text file.

<How To Use>
!@#
Factor Sums
This is a starting point for some investigative work.

If you choose \<Factor Sums>|, the Main window is closed and a special
window is opened.  Type the number in the writable icon at the top and
either press \<Return>| or click on \<OK>|.

!Numbers will then calculate the sum of all the factors of your number
excluding the number itself and then do the whole thing all over again
with the next number.  It will continue like this until it reaches a prime
and goes to 1,  it reaches a Perfect number and repeats itself, or you
click on <Pause>=diff> or press <Escape>=diff>.

If the number gets very big (Greater than 2147483647) everything slows
down considerably as the routine starts to use Nick Craig-Wood's
<Numbers> module which can deal with very large integers.

<How To Use>
!@#
A Peculiarity
Pressing \<Pause>| may take a moment or two to respond but it does give
you the option of taking up where you left off by pressing \<Restart>|.
\<Escape>| stops the loop more quickly but you cannot start again.

(Well actually I lie, you can. It's just that the results are wrong if you
do!  You have been warned!)

<Factor Sums>
!@#
The Kaprekar Process
This is the starting point for some investigative work.

When you choose \<Kaprekar>| the Main window is closed and a special
window is opened.  Type a number into the writable icon at the top and
either press \<Return>|or click on \<OK>|.

The Kaprekar process involves taking a number, putting its digits in
ascending and descending order and subtracting the smaller of the two from
the larger.
The process is then repeated with the resulting number. Try it out for a
few numbers and see what happens. The results are quite surprising.

<How To Use>
!@#
Digit Reduction
This is the starting point for some investigative work.

Choosing \<Digit Reduction> opens a similar window to \<Kaprekar>|. Type a
number into the writable icon at the top and either press \<Return>| or
click on \<OK>|.

Digit Reduction uses that number to create a multiplication table and to
add up the digits of the product until there is just one digit left.

<How To Use>
!@#
Sums of Diagonals
This is the starting point for some investigative work.

\<Diagonals>| opens yet another window and enables you to look at the sums
of different diagonals on a number grid.

Try it out and see if you can figure out the principles.

<How To Use>
!@#
Big Number Calculator
Big Numbers is really just a desktop frontend for <Nick Craig-Wood>'s
NumCalc program which uses his <Numbers> module.

To use the routines type in a calculation as you would in BASIC eg. 48^34
or  (235+45^12)^243

The numbers printed out get as big as you like though very big numbers
take a while to work out and tie up the desktop for a minute or two.

Anything under 10 000 digits should be pretty quick though.

Subsequent calculations will appear one after the other in the display
window and you have the option to save the whole of a session (assuming
you have enough application memory) as a text file by choosing Save from
the display window's menu.

You can finish the session by pressing \<Finish>|.  If you subsequently go
back to the big number calculator you will find that all of the previous
session has been wiped from memory.

<How To Use>
<Big Numbers Instructions>
!@#
Big Numbers Instructions
The following are <Nick Craig-Wood>'s instructions from the original
program.

This is a infinite precision integer calculation program.

Enter your expression in normal infix notation

You may use the following operators (in priority order)

  -a (unary minus), a! (factorial)
  a^b (a to the power of b)
  a*b, a/b, a%b (a modulo b)
  a+b, a-b

And the following functions

  rnd(a)           produces a random number from 0 to a-1
  probablyprime(a) returns 0 if a is composite, or 1 if a is prime with a
                   probability of >=0.75
  gcd(a,b)         returns the greatest common divisor of a and b
  smallfactor(a)   returns a small factor of a, or 0
  sqr(a)           returns the square root of a
  powmod(a,b,c)    computes (a^b) % c using a quick method
  base(a)          sets the base for calculations to a 2-36

A to Z may be used as variables, and @ is the result of the last
calculation done.  Case ignored.
Decimal => Base 10.

Examples of valid usage

 2^64-1"
 a=z*gcd(rnd(10^100),rnd(10^100))
 Q=@*123/W^2 - w%b - (139+1234)*(123^2)
Pressing return repeats the last calculation.
* commands may be used.

<How To Use>
!@#
Licence
This application is SHAREWARE. If you find it useful you are required to
register. (Within 30 days of first using it) You may distribute the
UNREGISTERED version to whoever you like as long as you leave the
application intact and you make the recipient aware of the application's
Shareware status.

** REGISTRATION IS £5.00 for individuals, £10.00 for a school.**

Registration is so that I know who's using the application and hopefully
get some feedback. Also I spent a lot of time on it and want to be
appreciated!

The advantages of Registering and paying the far from exorbitant fee are
as follows:

  1.   You will not be breaking the law.
  2.   You will encourage me to write more educational software at low
       cost.
  3.   You will make me ecstatically happy.
  4.   You will be entitled to free upgrades (for a while at least!)
  5.   You will have the opportunity to tell me how to make the program
       better!
  6.   You will have the opportunity to suggest other projects that you
       desire an author for.

<Contents>
!@#
Distribution
You may distribute the UNREGISTERED version of this program to anyone you
like so long as you pass on the whole application including ALL of the
files in the application directory.

You may not alter any of the files in any way nor may you claim to have
written any of the code.

Send your money, name, address, telephone number, comment, criticisms and
anything else you like to the <Author>=Author:Numbers>.

<Contents>
!@#
Credits
The Wimp Procedure Library that I used was written by <Paul Hobbs> and is
part of his excellent <!EventShell>=EventShell> package.

I appended it to the program using <!Blib>=Blib> which is likewise a very
fine piece of work by <Ian Palmer>=Blib>.

It was then well and truly squashed using <!BasShrink>=John Wallace> by <John Wallace>.

The <Numbers> Module and some of the associated coding are by
<Nick Craig-Wood> so any number that the program chucks out that is
longer than the usual allowable number of digits is down to him.

<Contents>
!@#
Nick Craig-Wood
Chalk barton
Shere Road
West Horsley
Leatherhead
Surrey
KT24 6EW

Email: [e-mail]

<Credits>
!@#
Paul Hobbs
Rheinpfalzstrasse 2
85049 Ingolstadt
Germany

Tel:    [phone]
Fax:    [phone]
EMail:    [e-mail]

<Credits>
!@#
Author:  !EventShell
This program has been written using the routines supplied with the
EvntShell library which is copyright <Paul Hobbs>.

EvntShell is a starting point for developing your own applications that
run under the RISC-OS wimp system. The EvntShell library contains code to
handle most of the 'Events' (i.e. opening a menu, closing a window etc)
that can occur, and all your application has to do is inform the library
what it should do when certain events occur. For example a menu can be
attached to a window or to an icon - the library will open the menu for
you (in the correct position!) when the MENU button on the mouse is used.

Normally writing a wimp application is a very complex business, involving
much reading of the Programmers Reference Manuals, magazine articles and
examining other applications. The aim of the EvntShell library is to
reduce the need for this and to enable the speedy creation of easily
maintained and robust applications.

<Credits>
!@#
Distribution Licence (EvntShell)
You have permission to use any part or the whole library in any Public
Domain/ShareWare project ONCE YOUR COPY HAS BEEN REGISTERED, as long as I
am fully credited (via the inclusion of this file in the program
documentation). If you wish to use these routines in a program that is for
sale (for however much and for whatever reasons) or released as copyright
material then my express permission in writing must be obtained. I
maintain copyright on all the material supplied as part of the EvntShell
system (except where noted below) and reserve the right to amend these
conditions in cases where I deem misuse.

The library code is supplied free of charge to everyone 'as is'. There is
no guarantee that it is free from bugs and no warranty is given about its
suitability for use.

Further details about EvntShell may be obtained from the <author>=Paul Hobbs>:

<Credits>
!@#
Heap Manager
The heap manager routines used by EvntShell are copyright Risc User. and
are used with permission.

<Credits>
!@#
John Wallace
John Wallace (Architype SoftWare)
Supplier of !BasShrink which costs £5.00p. !BasShrink_PD is the
Public Domain version and is available from various PD libraries.

John Wallace, Architype Software, 54 Parkes Hall Road, Woodsetton,
Dudley, West Midlands, DY1 3SR ENGLAND.

<Credits>
!@#
Numbers
Please see the accompanying textfile NumModTxt in the Docs directory
inside !Numbers

<Credits>
!@#
!EventShell
This is the most comprehensive Basic Wimp library available.
It is SHAREWARE so if you do get hold of a copy and find it useful, do pay
the registration fee which for what you get is very little indeed. £10.00
is a lot cheaper than !WimpGen.
It is written by <Paul Hobbs> and is available from most P.D. libraries or
from the author. (Despite the address he is English but you can write in
English or German.)

<Click here>=Author:  !EventShell> for what <Paul Hobbs> wants to say about his very
excellent work.

<Credits>
!@#
Blib
A Basic library linker by Ian Palmer available from various P.D. libraries.

<Credits>
!@#
Author:Numbers
Richard Sharpe
5 Camberwell Terrace
Leamington Spa
Warwickshire
CV31 1LP

Tel:  [phone]

<Contents>
!@#