** Acorn Archimedes mathematical software
for .. (free/ donation  )
       BBC BasicV / 64.  "SeriCalc3  4S".     (25 kbyte BASIC program.)

*** Please Reply to: -

email,    don.mcdonald@paradise.net.nz  (30.4.03, 18 mths currency)

snail mail:
    D.S. (DON) McDONALD,
    63/*3 Hut.chi.son Rd, WELLINGTON 2
    New Zealand. Ph. +64-4- 389-6820 
     
21/4/95.       ref.  > donmcd.calc.submissnaw.Help1.
25.08.96
     
**  MyProg "SERICalc3 4S" offers (approx. 40) customised functions
 for immediate results, as follows:
      (N.B. "*" denotes further input number is required or may be
     prompted for.) 
   ---  
B    Printer ON /OFF / *SPOOL   * 
C    Combination, n C r *
D    list divisors of number
   (includes Perfect nos., abundant/deficient nos. etc.)
E    add exponent of 10  *,  e.g. multiply by 1000. (1E3) 
F    Factorise 
G    fractional part 
H    highest common factor         * 
I    Integer part 
J    -available //  multiples
K    express as Sum of (2) squares 
L    Logarithms, Base e=2.718, Base 10, etc.* 
M    MOD and DIV, remainder of Integer division * 
N    New start 
 
O    Options, list choices 
 
P    Permutation,  n P r           * 
 
Q    Quit. (exit program),   confirm RETURN.
   
R    Reciprocal    1/x
S    Change sign,  +/- 
T    Common Antilog, 10^RES 
U    Poisson discrete probability distribution  (Statistical func.)   
V    Square root      ( SQR 16 = 4.)
W    continued fraction,  rational approximations (E.g. PI = 22/7..)  *
X    Exponential function,  e^x 
Y    powers x^y  and roots  x^(1/y).
Z    Find next  prime number  (or primes tutorial..)
 
A    - Order of Algebra Group * sorry, this one is definitely the most 
                complicated.   (e.g. period of recurring decimal.)
 
, or <CR>  group digits in 3's with comma separators (base 000,)
               display maximum precision

_    underline, delete digits from units place 
 
space,   (Optional) append special calculations, 
               including MOD, DIV, AND, OR, etc.

' apostrophe,  rem. REMark annotation.
    ( innocuous comments also permitted sometimes with input numbers. )
 
Escape         (Exit) or select Instructions/Verbose  
               Y/N, new calc. 
+    plus 
-    minus
*    times 
/    divide by 
^    raise to a power 
!    Factorial.  6! = 6.5.4.3.2.1 
 
()[]   Recall RESults from  stack (0-999) * 
.0123456789     append digits to STR$ value of RES
<,>,=  logical expression (TRUE, FALSE) *
 
~    Hexadecimal display  (Base 16, Base 27.)
&    Hexadecimal (Base 16) input digits, 012..9ABCDEF, (e.g. &BEEB)
 
The scientific and maths functions of BBC Basic are available. 
 
?    help. display some common BASIC arithmetic function keywords, 
E.g.  ATN, LN, LOG, SIN, EXP, COS, EXP,..., ABS, RND. 
@     print format, 
%     percent, 
------------------------------ 

number 
+ number  ___
Result 
x further nos.   ___
Further results. 
    ...

Calculations should show  
working and previous results. 
 
Myprog  "SeriCalc3" does math/arithmetic/number theory/
 statistics  with some common and advanced calculations.
 
The options in my program for Hard Copy are , Printer ON/ OFF, and 
*SPOOL to *ram file.  Or *Save task* window under !Edit.
 
The program offers full error reporting and error trapping.  If an 
illegal calculation is attempted the computer will say what the error 
was e.g. TOO BIG, or square root -ve.   The previous result is still 
stored in variable RES.  A new calculation may be attempted. 
 
The small amount of prompting information is controlled by toggling 
INSTRUCTIONS ESCape. (VERBOSE) from Yes to No etc.


The computer asks for the starting number or expression to be entered. 
 It could be a simple number (5) or a very basic calculation , 2+3.   

*** The next part of the calculation is built on to the first result.  
 ***  (no '?' prompt should be expected, except in cases of advanced
 function calculations.)
 
E.g.  .... + 20*4

(adds 80 to the existing answer.)

Result lines are numbered.
		  E.g.  (1) ... is the 1st result.
		  E.g.  (9) ... is the result of 9th calc step.

The previous result is stored (for obvious reuse) in variable, RES. 

    The trigonometric Sine of RES may be entered by, etc.
 
i)  + SIN(RES),  add to existing result. 
or ii)  N.. new start, expression ?  SIN(RAD(RES)).

The trigonometric and hyperbolic functions are provided
satisfactorily by  Acorn  RISC OS App2.!SciCalc.
  "SeriCalc3" *** strengths are therefore in
arithmetic, combinations, prime number / factors / divisors,
Poisson distribution, printed output,
punctuated nos. with commas, etc.  (rather than in trigonometrics.)
 
Important.  You may often find it helpful / useful to append innocuous 
words, letters, units, etc. to the calculation.  They may be separated 
from the numbers (or functions) by apostrophe ' or space. 
 
------------------ 
I would be pleased to discuss the merits and marketing of my program 
with your principals. 
 
This product will** fill a niche in the educational computing software
market between school-University scientific calculator (without 
printout), and spreadsheet package on personal computer, personal 
digital assistant. 
 
The most advanced mathematical program(s) is "Mathematica."  and "Maple."
 
*** I would be pleased to discuss the merits and marketing or 
development of my program with your principals. 
    
**    Yours ,		Donald  S  McDonald.
    ===================== 

SeriHelp,  Help description for program "SeriCalC3", serious
Maths-Science Serial printout calculator,  by Don S  McDonald, 
Wellington, NZ. 
 
Basic math functions. 
 
+ - * / ^  +/- 
 
rem.  Simple cutdown program "DispCommas" also included separately. 
 
INTEGER functions. 
 
Integer part 
Fractional part 
Quotient / Remainder  (DIV - MOD) 
Delete last digit (units place). 
 
Extra math functions. 
 
Reciprocal 1/x,  e^x, 10^x, ln, log 10, sqrt, %, PI, TIME 
add digits, add exponent, BASIC V Standard Functions. 
   Powers and roots.   n.b.  not HYP.
    
FACTORIAL Functions.

(Best uses BASIC 64.  click on !SciCalc,
*basic64, CHAIN"sericalc3"..*quit)
x!,  nCr,  nPr,  Combination - Permutation. 
	Results correct e.g.  1000 nCr 500.

Number Theory functions. 
 
Factorise      (least prime factor at each step.)
Divisors         (Abundant nos., deficient nos. , multi-perfect nos.)
Find Next  prime    (twin primes, prime triple, Sophie Germain primes,
		Mersenne Primes, Fermat Primes, tutorial.)
HCF, highest common factor 
Continued fraction      (Rational approximations.  p/q, integers.)
Sum of Squares 
 
ALGEBRA 
 
Order of Group 
(Period of recurring decimal reciprocal) 
     
STATISTICAL Analysis.
 
Poisson discrete probability distribution.  (parameter, key  'U'.)
 
Print Options. 
 
Printer On / Off 
*Spool 
(If Program SeriCalC3 should be run in a
TASK WINDOW, then a log of
the entire session may be saved under !EDIT.) 
 
CONTROL Options. 


New Calculation       (N)
Escape  (Instructions Y / N.) 
Quit    (Confirm / Resume.) 
Recall results  (list latest 24 results
     or recall from 999 memories.)   [,]
OPTIONS              (letter 'O')
?  Help,  Keywords, remarks
@  Printout format..  Check / Change .
 
BASE Conversions. 
 
& Input Hex (e.g.  &BEEB) 
~ Display Hex 
,  Base 1000, insert commas    (,000) 
 
---------------------------- 
 
Differences from Acorn !SciCalc.
 
No GOTO's necessary.      (If line nos. present they are due
    to StrongEdII editor and could be stripped off if desired.)
Online Serial printout (ON/ OFF) or SPOOL available. 
40 column print display.  (2 columns on A4 page.) 
 
BASIC V and BASIC 64. 
     
Output numbers range +- 0 to  1E308,  etc.
Permutations up to  2E9 nPr 33   = 1E308
Combinations up to 1024 nCr 512, etc.  or 2E9 nCr 33 = 1E308
        (these are a very big improvement on Acorn's !SciCalc.)

FULL ERROR TRAPPING and reporting for illegal calculations. 
Prime number functions 
Recall 999 numbered memories 
POISSON Probability tables   , U.
One Key Qwerty keyboard functions A- Z  (Prompt for second number as 
necessary.) 
No mouse input needed 
Basic Keywords  (E.g. 'NEW' calculation,  SIN(RAD(RES)),  -No  HYP)
Comma formatting of numeric results, Base 1,000.
Display all significant figures     (up to 16 signif. figs.) 
Remarks 
HELPS. 
 
  =========================================================== 
    Abstract.
 
A cheap calculator that you use with a cheque book has + x - / =. 
Sometimes also square root v,  percent %, or memory M. 
 
From there you can go on to a printout calculator using a paper roll, 
or a scientific calculator (many models and functions options.) 
 
[ x, 1/x, powers x^y, logs, exponentials e^x, trigonometric functions
tan, sin, cos, base conversions hex, factorials !, change sign +/-, 
combinations and permutations, highest common factor, programmable, 
graphics display, etc. 
 
 
Acorn Archimedes RISC OS provides a simple calculator and a scientific 
calculator under  Apps or   $.App2.!SciCalc. 
 
[These may be used by clicking the mouse on a simulated calculator on 
the screen - copy the results onto your sheet of paper !!@#$%$#@!! ugggh!]
 
Don McDonald's new program, "Seri(al)Calc", which he is revealing at
this month's (JUNE 93) meeting, displays calculation results and 
allows the add on of the next calculator step(s). 
 
At its simplest it could be a bank statement balancer.  [ where each 
step is adding or subtracting 1 deposit or withdrawal transaction. ] 
 
Of course such a program as SeriCalc3 allows all the arithmetic and
logical expressions and functions of BBC Basic V to be evaluated plus 
many maths, engineering, and prime number functions. 
 
Note that the Serial results of the whole calculation can be turned on 
to a printer and turned off when you do or do not desire a printout.  
The last 1000 results at any time are available to be recalled (any 1 
result, or a short table of the last 24 numbers calculated.) 
 
-----------------------------
 
Note, if the number is very big the display may be like "1E6".  This 
means 1 followed by 6 'zeroes'. 
    
I have even proved Combination, "1024 nCr 512" in one quarter of a
second using SeriCalc3 on BASIC64.  Imagine a 'Lotto' game with 1000
balls in the barrel where the player had to choose 500 of them 
correctly to win.!  It has 307 digits. 

--------
An original one-liner BASIC serial calculator..

*KEY8INPUT R:REP.:I.SPC4; A$:A$=STR$(R)+A$:R=EVAL(A$):PRINT"= ";R;:U.FA.|M

by ..
Don S McDonald
#.
don.mcdonald@paradise.net.nz