3 5 14 50 Version 1.0
>
>
>*****************
>** SUB_CAL **
>*****************
>A subset of
>EL_CAL
>The Elementary Calculator
>by J.Andrzej Wrotniak
>Distributed by Debonair Software
>
>To view a page, click on its top-right corner.
>To change volume or to rearrange pages,
>click on the proper volume number.
---- Page 1
>ABOUT THIS PROGRAM
This is a simplified version of El_Cal: The
Elementary (heh-heh!) Calculator.
It calculates arithmetic expressions, plots
functions, computes integrals and derivatives,
finds roots of polynomial equations (up to cubic)
and solves equations numerically.
>
Sub_Cal can be distributed freely at no cost as
long as all the accompanying files remain intact.
The full version of El_Cal, available from
Debonair Software, contains many more features;
they are listed in Volume 3 of the on-line help.
Our address also can be found there.
---- Page 2
>DISPLAY LINES, GREY BUTTONS
* Most Sub_Cal operations deal with display lines
(shown at the top). There are 4 display lines in
the subset version, only one visible at a time.
* Lines may be typed in or entered with the mouse.
Mouse entries will be always added at the end of
display line, regardless of the cursor position.
* Case is not significant and spaces are ignored.
* Switching between display lines is done by using
[] and [] at the top. Clicking on the line
number (between the arrows) jumps to Line 1.
NOTE: Screen buttons corresponding to features
available only in the full El_Cal are filled with
grey; clicking on them has no effect.
---- Page 3
>EDITING FUNCTIONS, DATA FORMATTING
* CLR - clear the current line.
* RST - clear all lines and variables.
* BSP - remove the last token from line.
* TAB sets number of fractional digits of variable
display, e.g. [TAB][6], and allows for floating
point format, e.g. [TAB][E][3]. Maximum accuracy
fitting into display width is set by using [.]
instead number of digits.
* TAB does not affect the accuracy of variables;
these are always stored with double precision
(about 16 decimal digits).
---- Page 4
>COMPUTING DISPLAYED EXPRESSIONS
* Click on the main display (or just press RETURN)
to compute the displayed line and store the re-
sult in the "destination variable" on the right.
* Clicking on [] and then on a variable from the
Variable Panel will nominate a new destination
variable and execute the line.
* To change destination variable without executing
the line: click on the destination variable but-
ton, and then on the variable to choose.
* Keyboard shortcut for the above: type the ex-
pression, then "=" and variable name, e.g. 2*3=Z
* "" left of display means, that the line was
computed; next mouse entry will start a new one.
---- Page 5
>VARIABLES AND NUMBERS
* Variables A..Z may be used to store results,
or as components of expressions.
* t is a special variable, used as a dummy in some
macros (e.g. integration, plotting). It cannot
be used for data storage.
* Constants: Ee (Euler's e = 2.71...) and Pi are
treated in expressions the same way as variables
* Numbers may use decimal exponent [E]: 1E6 or E6.
Zero before fraction is optional: .8 means 0.8 .
Some macros may modify displayed variable names.
The original names will be restored as soon as a
given variable is used in an expression or to sto-
re an expression result.
---- Page 6
>OPERATORS
* Arithmetic operators: [+], [-], [*], [/], [^]
(power) have generally accepted priorities.
* Implied multiplication: the "*" sign can be
omitted between two variables or between a value
and variable, e.g. 2A or 6.6PiXY. Implied multi-
plication has the same priority as "^" (highest)
* Operators of equal priority are executed from
left to right, except for "^" and implied mul-
tiplication, e.g. A^B^CD ð A^(B^(C*D)), and
2Pi^3A ð 2*(Pi^(3*A)).
* () may be nested to any depth; missing ones at
the beginning and at the end will be added, e.g.
5+2)*(8-3 is legal and gives 35.
---- Page 7
>FUNCTIONS - GENERAL
* Most of the functions accept a single argument.
If this argument is a variable, a value, or a
product using implied multiplication, then it
does not need to be enclosed in parentheses,
e.g. SIN A or LOG 2Pi, but COS(Pi/3).
* ATN2 accepts two arguments separated with a
comma, e.g. ATN2(R+.2,R-1.8).
* Function evaluation has the same priority as po-
wer and implied multiplication. This means, that
EXP A^2 ð EXP(A^2) but EXP 2*A ð (EXP 2)*A.
* [] switches between three Function Panels.
Only the Standard Function Panel is active in
the subset version.
---- Page 8
>STANDARD MATH FUNCTIONS
* SIN, COS, TAN, COT may be used with [ARC] and/or
[HYP] switches, e.g. [ARC][HYP][COT] gives ACOTH
* The [ARC] switch has to be re-entered for each
function, while [HYP] will stay on until reset.
* ATN2(Y,X) computes arctan(y/x) in (0,2Pi)
* The Rad/Deg switch sets the angular mode valid
at the computing (not entry!) time.
* LOG and EXP - with base e, 10 or 2 will give LN,
LOG or LG2 and EXP, TEN and TWO (base to...).
Choosing the base will change appropriately the
[LOG] and [EXP] buttons.
* ABS, RCP - absolute value and reciprocal (1/x).
* INT, FRA - integer and fractional part.
---- Page 9
>MACROS: ZERO, INTEGRAL, dF/dt
Macros are applied to currently displayed ex-
pression treated as F(t). The result (if any) will
be stored in the current destination variable.
* ZERO - find a (single) zero of F(t) within a gi-
ven interval (bisection method is used)
* INTEGRAL - compute integral of F(t) over a given
interval (Romberg algorithm)
* dF/dt - compute dF(t)/dt at given t value (quad-
ratic approximation with given finite step)
* The program will ask for any parameters needed
(as e.g. interval limits and accuracy in ZERO).
---- Page 10
>FUNCTION PLOTTING
* [PLOTS] switches to the Plotting Panel, from
where any set of lines can be plotted together.
* From the Plotting Panel, [PLOT] plots the selec-
ted lines as functions of the dummy variable t.
(Other variables can be used as constants).
* The program will ask for the horizontal and ver-
tical plot limits. [Find] computes the latter
for given horizontal range. (Narrow spikes may
run out of frame).
* Points for which function could not be computed
will be just ignored.
* Pressing any key will suspend the plotting.
* Click in the plot area for coordinate readout.
----Page 11
>POLYNOMIAL ROOTS
* [ROOTS] will bring us into the Root Panel. From
here linear, quadratic and cubic equations can
be solved (real roots only!), as chosen with the
degree selector.
* [COMP] solves the equation with parameters sto-
red beforehand in A, B, C and D, depending on
the degree.
* Depending on the status of these variables, some
choices of polynome degree can be disabled.
* Results are displayed in the Variable Panel.
----Page 12
>EL_CAL: DO YOU NEED THE FULL VERSION?
Depending on your need for numerical and statis-
tical functions, you may decide to purchase the
full version of El_Cal, already available from the
Debonair Software.
El_Cal, of course, comes with a user manual (60
pages) and one update at no extra cost.
>
In addition to all features of Sub_Cal, El_Cal
contains very significant extensions. To help you
decide, whether it is worth spending your money,
a brief listing of these features follows in the
next two pages.
----Page 13
>EL_CAL: EXTRA FEATURES (I)
* 44 statistical distribution functions (differen-
tial, cumulative and inverse cumulative) for 8
most common probability distributions: Gaussian
(Normal), Chi-Square, Student (t), Snedecor (F),
Binomial, Poisson, Gamma and Beta;
* Euler functions Gamma, Log Gamma and Beta;
* Factorial and combinations (Newton symbol);
* Statistical buffers for data entered from the
keyboard or a disk file (ASCII format);
* Histograms and scatter plots of buffered data;
* Mean, standard deviation, linear regression and
correlation;
* Polynomial least squares (up to the 6th degree);
----Page 14
>EL_CAL: EXTRA FEATURES (II)
* Minimization and maximization of functions (up
to nine arguments);
* Fitting data points with any function (up to
nine optimized parameters) - least squares or
least absolute difference minimization;
* Fitting data with any distribution (as above) -
binned chi-square or maximum likelihood method;
* Up to 12 user-defined functions;
* Switching between 20 display lines;
* Echo to the printer or to a disk file;
* Load/Save of the formulas and data from/to disk;
* Access to the menu bar;
----Page 15
>DEBONAIR SOFTWARE
>
The full version of EL_CAL can be ordered from
Debonair Software
P.O.Box 521166
Salt Lake City, UT 84152-1166
>
The price of $44 (check or money order, please)
includes shipping and one update.
>
Technical queries, remarks, etc. can be also for-
warded directly to the Author:
CompuServe: 70611, 2552
GEnie: J.WROTNIAK
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