═══ 1. About  MathMate ═══

The program MathMate is a reliable assistant for fast numerical calculations, 
which is intended first of all for scientists and engineers, but can be used 
also as a simple calculator. MathMate calculates, integrates and sums up 
mathematical expressions and solves equations containing numbers, variables, 
arithmetical operations, elementary and special functions, mathematical and 
physical constants. The program has a number of advanced interface features 
including on-screen keypads, a history list, keeping a record of computations 
in a protocol, error tracking, extensive help and automatic export of results 
to the Clipboard for use by other applications. 

The main distinguishing feature of MathMate is a wide set of built-in special 
mathematical functions (24) which are calculated with the 8 bytes floating 
point maximum accuracy by effective fast algorithms. This draws MathMate 
potentialities close to those of the well - known mathematical handbooks like 
Handbook of Mathematical Functions by M.Abramowitz and I.A.Stegun or Tables of 
Higher Functions by E./Jahnke, F.Emde and F.Losch. 

MathMate runs under OS/2 on a computer with at least VGA display and 80386 CPU. 
A coprocessor is desirable but not required. Versions of OS/2 prior to 2.0 are 
not supported. 

To install MathMate insert the diskette into the floppy drive and type at the 
OS/2 prompt 

mminst <pathname> 

where <pathname> is the name of the path of your choice. The MathMate folder 
will appear on your desktop. 

MathMate is a product of SEnSE To see the developers' names choose Product 
information from the Help menu and click the mouse button on the logo when it 
is displayed. 

SEnSE is a registered name of Science & Engineering Software Exprerts Ltd. 

OS/2 is a registered trademark of the IBM Corporation. 

 For more information see: 

o Integration 

o Summation 

o Solving equations 

o Built-in Constants 

o Built-in Functions 


═══ 2. MathMate capabilities ═══

This section covers the following topics: 

o Built-in constants 

o Built-in functions 


═══ 2.1. Built-in constants ═══

There are several mathematical and physical (CGSE) constants which may be 
included in MathMate expressions referenced by names (in capital). 

The names of these constants are reserved and cannot be used as variable names. 

You may either type a constant from the keyboard or switch  MathMate numeric 
keypad to constants keypad and then click the desired button. The name of the 
constant will be inserted into the expression. 

The following constants are available in  MathMate expressions: 

Click on a button on the panel below to get information about specific constant 

A list of constants by name 

o у constant 

o e constant 

o Euler gamma constant 

o Light velocity 

o Electron charge 

o Avogadro number 

o Electron mass 

o Proton mass 

o Planck constant 

o Fine structure constant р 

o Rydberg constant 

o Boltzmann constant 

o Gravity constant 

o Bohr magneton 

o Earth gravity constant 


═══ 2.2. Built-in functions ═══

MathMate expressions may include plenty of elementary and special functions 
including nested calls like 

cos( n*arccos( x)) 

To insert a function name in the expression click the function button on the 
function panel or simply type in the function name into the expression input 
string from the keyboard. 

The function panel shows all the available MathMate functions. 


═══ 2.2.1. Built-in elementary functions ═══

Click a button on the panel below to get information about specific function 


═══ 2.2.1.1. Exponential function ═══

MathMate syntax:            exp(x) 
Domain:                     x any real 


═══ 2.2.1.2. Logarithm functions ═══

Natural  (base e ) 

Decimal (base 10) 

MathMate syntax:            ln(x), log (x) 
Domain:                     x > 0 


═══ 2.2.1.3. Absolute value (modulus) ═══

MathMate syntax:            abs(x) 
Domain:                     x any real 


═══ 2.2.1.4. Sign of the argument ═══

MathMate syntax:            sign(x) 
Domain:                     x any real 


═══ 2.2.1.5. Integer part ═══

MathMate syntax:            int(x) 
Domain:                     x any real 


═══ 2.2.1.6. Fractional part ═══

MathMate syntax:            frac(x) 
Domain:                     x any real 


═══ 2.2.1.7. Trigonometric functions ═══

Sine function 

Cosine function 

MathMate syntax:            sin(x), cos(x) 
Domain:                     x any real 

Tangent function 

MathMate syntax:            tan(x) 
Domain:                     x any real except  у(n+1/2),  n integer 

Cotangent function 

MathMate syntax:            cot(x) 
Domain:                     x any real except уn,  n integer 


═══ 2.2.1.8. Inverse trigonometric functions ═══

Arcsine function 

Arccosine function 

MathMate syntax:            asin(x), acos(x) 
Domain:                     -1 є x є 1 

Arctangent function 

Arccotangent function 

MathMate syntax:            atan(x), acot(x) 
Domain:                     x any real 


═══ 2.2.1.9. Hyperbolic functions ═══

Hyperbolic sine 

Hyperbolic cosine 

Hyperbolic tangent 

MathMate syntax:            sinh(x), cosh(x), tanh(x) 
Domain:                     x any real 

Hyperbolic cotangent 

MathMate syntax:            coth(x) 
Domain:                     x any nonzero real 


═══ 2.2.1.10. Inverse hyperbolic functions ═══

Hyperbolic arcsine 

MathMate syntax:            asinh(x) 
Domain:                     x any real 

Hyperbolic arccosine 

MathMate syntax:            acosh 
Domain:                     x є 1 

Hyperbolic arctangent 

MathMate syntax:            atanh(x) 
Domain:                     -1 < x < 1 

Hyperbolic arccotangent 

MathMate syntax:            acoth(x) 
Domain:                     x < -1 or x > 1 


═══ 2.2.1.11. Square root function ═══

MathMate syntax:            sqrt(x) 
Domain:                     x Є 0 


═══ 2.2.2. Built-in special functions ═══

Click a button on the panel below to get information about specific function 


═══ 2.2.2.1. т function ═══

for x>0; for negative noninteger x the definition is extended according to the 
formula 

MathMate syntax:            Gam(x) 
Domain:                     x any real except 0, -1, -2, ... 

See also: 

o Incomplete т function 

o Digamma (psi - function) 


═══ 2.2.2.2. Incomplete т function ═══

MathMate syntax:            IGam(a,x) 
Domain:                     a any real except 0, -1, -2, ... ; x real 

See also: 

o т function 

o Digamma (psi - function) 


═══ 2.2.2.3. Digamma function (Euler psi - function) ═══

MathMate syntax:            Psi(x) 
Domain:                     x any real except 0, -1, -2, ... 

See also: 

o т function 

o Incomplete т function 


═══ 2.2.2.4. Error function ═══

MathMate syntax:            Erf(x) 
Domain:                     x any real 

See also: 

o Fresnel integrals 


═══ 2.2.2.5. Sine and Cosine Fresnel integrals ═══

MathMate syntax:            Fs(x), Fc(x) 
Domain:                     x any real 

See also: 

o Error function 

o Integral sines 

o Integral cosines 


═══ 2.2.2.6. Integral sines ═══

Integral sine 

Integral hyperbolic sine 

MathMate syntax:            Si(x), Shi(x) 
Domain:                     x any real 


═══ 2.2.2.7. Integral cosines ═══

Integral cosine 

Integral hyperbolic cosine 

 where  is the Euler constant 

MathMate syntax:            Ci(x), Chi(x) 
Domain:                     x > 0 


═══ 2.2.2.8. Integral exponential ═══

MathMate syntax:            Ei(x) 
Domain:                     x any nonzero real 

See also: 

o Fresnel integrals 


═══ 2.2.2.9. Complete elliptic integrals  K(x), E(x) ═══

 x - modulus square 

MathMate syntax:            EllK(x), EllE(x) 
Domain:                     0 є x є 1 

Note:  Sometimes another definition is used where the argument is modulus (not 
its square, i.e. t¤=x). To obtain the elliptic integral of the argument t 
calculate EllE (sqrt (t)), EllK (sqrt (t)). 

See also: 

o Incomplete elliptic integrals 


═══ 2.2.2.10. Incomplete elliptic integrals ═══

 э - amplitude, x - modulus square 

MathMate syntax:            IEllF(phi,x), IEllE(phi,x) 
Domain:                     phi any real, 0 є x є 1 

Note:  Sometimes another definition is used where the argument is modulus (not 
its square, i.e. t¤=x). To obtain the elliptic integral of this argument 
calculate IEllE(phi,sqrt(t)), IEllF(phi, sqrt(t)). 

See also: 

o Complete elliptic integrals 


═══ 2.2.2.11. Bessel functions J(n,z) and Y(n,z) ═══

Bessel (cylindric) functions J(n,z) and Y(n,z)may be defined as solutions of 
the equation 


═══ 2.2.2.12. Bessel function J(n,z) ═══

 is the solution of the Bessel equation which is zero at z=0 (for n>0, J(0, 
0)=1 ) and has the following behavior at positive infinity: 

It admits the following integral representation: 

n-index, z-argument 

MathMate syntax:            J(n,z) 
Domain:                     n an integer, z any real number 


═══ 2.2.2.13. Bessel function Y(n,z) ═══

 is the solution of the Bessel equation which is singular at z=0 and has the 
following behavior at positive infinity: 

It admits the following integral representation: 

 n-index, z-argument 

MathMate syntax:            Y(n,z) 
Domain:                     n an integer, z positive real 


═══ 2.2.2.14. (Modified) Bessel functions I(n,z) and K(n,z) ═══

The modified Bessel functions I(n,z) and K(n,z) may be defined as solutions of 
the equation 


═══ 2.2.2.15. Bessel function I(n,z) ═══

 is the solution of the modified Bessel equation which is zero at z=0 (for n>0, 
I(0, 0) = 1 ) and has the following behavior at positive infinity: 

It admits the following integral representation: 

n-index, z-argument 

MathMate syntax:            I(n,z) 
Domain:                     n an integer, z any real number 


═══ 2.2.2.16. Bessel function K(n,z) (McDonald's function) ═══

is the solution of the modified Bessel equation which is singular at z=0 and 
has the following behavior at positive infinity: 

It admits the following integral representation: 

n-index, z-argument 

MathMate syntax:            K(n,z) 
Domain:                     n an integer, z positive real 

Note:  If the index is given as a non-integer number MathMate rounds it towards 
negative infinity. 

See also: 

o Spherical (Legendre) functions 


═══ 2.2.2.17. Legendre functions P(m,n,x) ═══

Legendre functions may be defined as solutions of the equation 

When m = 0 one non-degenerate solution is the Legendre polynomial: 

When m > 0 the solution is given by the formula: 

MathMate syntax:            Leg(n,m,x) 
Domain:                     m, n non-negative integers, m< n, |x|< 1 

See also: 

o Cylindric (Bessel) functions 


═══ 2.2.2.18. Degenerate hypergeometric function ш(a,b,z) ═══

is the solution of the equation 

which has the following series representation: 

MathMate syntax:            Phi(a,b,z) 
Domain:                     a,b,z real, b cannot be a negative integer 

See also: 

o Error function 

o Incomplete т function 


═══ 2.2.2.19. Sn, Cn, Dn Jacobi functions ═══

Let u be defined by the implicit formula 

Then Jacobi elliptic functions are defined as 

u - argument, x - modulus square 

The following four equations also define the functions uniquely: 

MathMate syntax:            Sn(x,u), Cn(x,u), Dn(x,u) 
Domain:                     0 є x є 1, u any real 

See also: 

o Incomplete elliptic integrals 


═══ 3. Calculation modes ═══

This section covers the following topics: 

o Evaluating expressions 

o Integrating expressions 

o Summing up series 

o Solving equations 


═══ 3.1. Evaluating expressions ═══

This is the simplest operation MathMate performs. Evaluation (calculator) mode 
may be turned on by clicking the Modes icon or choosing Evaluation in the Modes 
menu. When the calculator mode is on the evaluation icon is displayed to the 
left of the expression. 

In the calculator mode you may use MathMate as a simple calculator to evaluate 
expressions in the following way 

 1. Switch the calculator mode on 

 2. Input an expression, e.g. 2*2 

    If the expression contains variables, e.g. 2*x/y, you may compute the value 
    of the expression under various choices of variable values. In this case 
    you have to 

 3. Initialize all the parameters in the corresponding listbox 

 4. Click Do it! or press Enter 

    The result is displayed immediately in a special window. The status line 
    reports of errors if any. 

To evaluate the same expression again, just modify any desired parameters and 
press Do it! or Enter. 


═══ 3.2. Integrating expressions ═══

To integrate an expression switch MathMate to integration mode by clicking the 
modes icon until you see the integration sign or choosing Integration in the 
Modes menu. The modes icon is situated to the left of the expression input 
line. Below and above the integration sign there are entry fields for 
integration limits. 

In the integration mode you may calculate (one-dimensional) integrals of 
expressions with respect to a given integration variable. Other variables of 
the expression are considered parameters. The choice of the integration 
variable and initialization of parameters are performed during the 
initialization dialog. 

To integrate an expression: 

 1. Switch the integration mode on. 
 2. Enter an expression, e.g. exp(x) 
 3. Enter the integration limits 
 4. If the expression contains several identifiers point out which one is to be 
    taken as the integration variable and input the values of the other 
    parameters 
 5. Click Do it! or press Enter 

If MathMate detects only one variable in the expression the latter is taken as 
integration variable by default. You may integrate the same expression again 
after modifying integration variable name, integration limits and parameter 
values. 

The desired and actual computation accuracy 

Numerical integral computation is certainly not an exact procedure and the 
result may be obtained with more or less accuracy. The desired relative error 
of integration is defined by the Precision option. However the actual error of 
the result may be sometimes different from the given one. 

When MathMate displays the result of the integration it also shows the 
estimated absolute computation errror in the Result window. 

Sometimes the MathMate integration algorithm is unable to reach the given 
accuracy. It can happen if the function contains fast oscillations or a 
singularity near some point X. In these cases MathMate interrupts calculation 
and displays the message 

Precision not reached, may be singularity near X 

When you see such a message first try to analyze if there is a non-integrable 
singularity point in the neighbourhood or try to decrease the accuracy using 
significant digits option (increasing significant digits is NEVER recommended 
in case you get the message about a singularity point) 

See also 

o Integration sample 


═══ 3.2.1. Integration sample ═══

Calculation of the modified Bessel function K(n, x) with a non-integer index n 
by its integral representation. 

 1. Type in the expression input line: 

    exp(-x*cosh(t)) * cosh(nu*t) 

 2. Switch the Integration mode on 

 3. In the corresponding entry fields enter 

   0 for the lower limit 

   5 for the upper limit 

 4. Initialize the parameters as follows 

   t - mark as variable 

   x = 2 

   nu = 1.5 

 5. Click the Do it! button. 

You obtain immediately: 

Result = 0.179907
Estimated error = 2.69103e-08

To verify this result, let us use the exact formula for the modified Bessel 
function of half-integer index. Input the following expression: 

sqrt(PI/(2*x)) * exp(-x) * (1+1/x), 

switch to the calculator mode and input the value of x: 

x = 2 

Then click the Do it! button. 

You will obtain the same result: 

Result = 0.179907 


═══ 3.3. Summing up series ═══

To calculate a partial sum of a series, switch MathMate into Summation mode. 
Then the entry fields for the summation limit appear. 

Using this operation you are able to calculate partial sums of series with the 
given term when the summation variable takes values in the given limits. On 
every step the summation variable is incremented by 1 and the value of the 
expression is added to the result if the summation variable does not exceed the 
upper summation limit. Summation variable and limits may take non-integer 
values. 

To calculate a sum: 

 1. Switch the Summation mode on 

 2. Input an expression, e.g. 1/x 

 3. Input the summation limits 

 4. If the expression contains several identifiers point out which one is to be 
    assumed the summation variable 

    If MathMate detects only one variable in the expression the latter is taken 
    as summation variable by default. 

 5. Initialize the other parameters 

 6. Click Do it! or press Enter 

See also 

o Summation sample 


═══ 3.3.1. Summation sample ═══

Calculation of the modified Bessel function I(n, x) with a non-integer index n 
by its series representation. 

 1. Type in the expression input line: 

    (x/2)^(2*m + nu) / ( Gam(m+1) * Gam(m+nu+1) ) 

 2. Switch to Summation mode 

 3. In the corresponding entry fields enter 

    0 for the lower limit 

   10 for the upper limit 

 4. Initialize the parameters as follows 

   m - mark as variable 

   x = 2 

   nu = 1.5 

 5. Click the Do it!. button. 

You obtain immediately: 

Result = 1.09947 

To verify this result, let us use the exact formula for the modified Bessel 
function of the half-integer index. Input the following expression: 

sqrt(2*x/PI) * ( -sinh(x)/x^2 + cosh(x)/x ), 

then switch to calculator mode, input the value of x: 

x = 2 

and click the Do it! button. 

You will obtain the same result: 

Result = 1.09947 


═══ 3.4. Solving equations ═══

Using the MathMate Equation mode you can find root of the equation 

                                  EXPRESSION=0

To solve an equation switch MathMate  into Equation mode. When you are in the 
Equation mode the equation icon appears to the left of the expression input 
line. 

In the equation mode you may solve the equation relative to only one of the 
parameters which is considered to be unknown. The other parameters should be 
initialized by the user. 

To solve an equation: 

 1. Switch the Equation mode on 

 2. Input an expression, e.g. x^2-5*x+6 

 3. In the corresponding entry fields enter the limits of the interval where 
    the root is to be sought 

 4. If the expression contaions several identifiers mark one as variable and 
    initialize the other parameters. 

 5. Click Do it! or press Enter 

If MathMate detects only one identifier in the expression the latter is 
considered to be variable by default. You may solve the equation with the same 
expression again by marking another identifier name as unknown, or changing the 
interval. 

If the given interval contains several roots the least of them is found. 

Computation accuracy 

The value of the root is approximate, the relative error in the result is 
defined by the Precision option. However the function value at the given point 
might be rather huge sometimes. 

When MathMate displays the solution (root) it also shows the expression value 
at the root point in the Result window. 

Sometimes the MathMate solution algorithm is unable to reach the given 
accuracy. It can happen if the  function contains singularity near some point 
X.  Also, the given interval may contain no solution at all. Then MathMate 
interrupts calculation and displays the message 

Precision not reached, root not found 

If this happens check whether the search interval is set correctly: it probably 
contains no solution at all. 

See also 

o Solution sample 


═══ 3.4.1. Solution sample ═══

Calculation of the value of Bessel function's zeros 

 1. Type in the expression input line: 

    Y(0,x) 

 2. Switch to Equation mode 

 3. In the corresponding entry field enter 

   12 for the lower limit 

   15 for the upper limit 

 4. Click the Do it! button 

You obtain: 

Result = 13.3610974738728
Function value = -7.70198e-16


═══ 4. Operation ═══

This section covers the following topics: 

o Entering expressions 

o Errors in expressions 

o Initialization 

o Settings 

o History 

o Mathmate protocol 

o Protocol file errors 

o Run-time floating point errors 


═══ 4.1. Entering expressions ═══

MathMate uses a sort of command line (expression input line) for its 
performance. This line cannot contain more than 100 symbols. 

In the expression input line you can enter and edit mathematical expressions. 
Quick samples: 

2*2 

sqrt(PI) 

sin(x^2*t)+z^2+exp(-x) 

You can enter an expression either by typing it directly on the keyboard or 
clicking buttons with the mouse.  With the keyboard you just type in an 
expression, an alternative way is using MathMate keypad and function panels. 
When you click keypad buttons the corresponding symbols are typed. To insert a 
function name click the corresponding button on the function panel (the 
function panel shows the names of elementary functions, it can be switched to 
show the names of the built-in special functions). When you click a button in 
the function panel the corresponding name appears immediately in the expression 
input line. 

MathMate keypad provides complete functionality without the keyboard. It has 
numbers, symbols of mathematical operations, punctuation signs, backspace and 
clear simulation, letters usually used for parameter names, such as x, y, z, t 
If you want to enter other letters use the keyboard. 

Recent expressions are stored in the history list and may be reentered by 
highlighting the corresponding line after opening the history list box. 

MathMate protocol also gives a possibility to insert text into the expression 
input line. Highlight the text you want to insert and click the Send button. 
The highlighted text is then sent to the input line. 

Expressions may contain: 

o decimal numbers (not more than 21): 

   - integers, 

   - numbers with decimal point and in the exponential form (e.g., 5, 3.14, 
     1.2e3, 1.2e+3, 1.2e-3 etc.). Note that the uppercase  E means the built-in 
     mathematic constant e 

o round brackets ( ) 

o arithmetical signs + - * / and the power sign ^ 

o parameter identifiers (not more than 10) up to 6 symbols (letters or digits) 
  long.  The first symbol  must be a letter (e.g., x, y1, Delta etc.) 

o names of built-in  functions with  arguments separated by commas (e.g., 
  J(n,x)); 

o names of built-in constants. 

Blank spaces in the expression are ignored.  Lowercase and uppercase letters 
are interpreted as different symbols. 

See also 

o Errors in expressions 

o MathMate settings 

o Built-in constants 

o Built-in functions 


═══ 4.2. Syntax errors in expressions ═══

Before calculation, MathMate analyzes the expression. If any syntax error is 
found, MathMate displays the corresponding error message (see below) in a 
message box, hilights the error location in the expression input line and 
places the caret there. 

The following syntax error messages can be displayed: 

o Too many operations 

o Too many constants 

o Too many identifiers 

o Identifier expected 

o Expression expected 

o Operator expected 

o Too many ')' 

o Syntax error 

o Too few ')' 

o Too many arguments 

o Too few arguments 

o Illegal identifier 

o Too long identifier 

o Must be function 

o Unknown function 

o Unknown symbol 


═══ 4.3. Initialization ═══

MathMate analyzes the expression entry field and places all the identifiers 
into the parameter list. Prior to calculations these parameters must be 
initialized. In the calculator mode all the parameters must be assigned some 
values. In the other modes one of the parameters may be variable (integration 
variable, etc.). If none of the parameters is marked as variable and one of 
them has not been assigned any value, it is considered variable automatically. 
If there is one parameter already marked as variable and another parameter is 
being also marked variable, the first one must be assigned some value. 

To initialize (assign a value to) a parameter, double-click on the correponding 
line in the parameter list. Then the initialization panel appears in the place 
of the list. To mark a parameter as variable, check the corresponding radio 
button. To unmark it check another button. If a parameter is not marked 
variable, enter the value to assign to it and click Ok. 

MathMate stores the names of all identifiers previously initialized within the 
current session. Thus if one uses an identifier in another expression, it 
appears in the parameter list with the value it has been assigned before. This 
value can be changed if necessary. 


═══ 4.4. Settings ═══

There are currently only two option available: Change precision and Show hints. 

Precision is given in decimal digits. The default value is 6. Before you decide 
to alter this value please read the sections concerning calculation modes. The 
value can be changed with the help of the slider after one chooses this option 
in the menu. The range is from 1 to 15. This parameter is stored in the 
mathmate.ini file. If this file is not found at program startup, default value 
is assumed. 

It might be helpful to let MathMate show hints before the user gains experience 
in operating the program. The user may want to disable this option. This can be 
done by unchecking the corresponding menu item. This parameter is also stored 
in mathmate.ini. If this file is not found at program startup, the default 
value for this option is ON. 


═══ 4.5. History ═══

The already processed expressions are stored in the history list. The history 
list is the drop-down list attached to the expression entry field. To reenter 
an expression find it in the history list and click on the corresponding line 
of the list. The expression appears then in the input line. 


═══ 4.6. MathMate Protocol ═══

MathMate keeps track of all calculations in a protocol. 

To view the protocol click the left mouse button over the Result window. 
Alternatively choose View protocol in the File menu. The Protocol Viewer is 
then activated. Use scrolling to view the desired place. 

The Protocol Viewer menu is easy to operate. Choose Help to view this help. 
Choose Hide to cancel protocol view. Highlight text in the protocol and choose 
Send to insert this text into the expression entry field. 

The main MathMate window contains the File menu to manipulate the protocol 
files. Protocol files have extension .pro. To open a new protocol file choose 
Open, to save the current protocol choose Save 

Each protocol entry has the following layout: 

operation name
Expression:expression
Precision:precision
[Lower limit:lower limit]
[Upper limit:upper limit]
[Operation variable:operation variable]
[Parameters:]
[parameter_1 = value_1]
[...]
[parameter_n = value_n]
--
Result:result
[Estimated error:estimated error]
[Function value:function value]
[error message]

One can transfer text from the protocol to the input fields of Mathmate using 
Send and to any other application using Clipboard. 

When quitting MathMate the user is asked whether the protocol is to be saved. 

See also 

o Protocol file errors 


═══ 4.7. Protocol file errors ═══

The following errors may occur during protocol file operations: 

Message                                 Explanation 
Cannot open file filename               File filename does not exist. 
Cannot create file filename             Illegal file name filename 
Cannot overwrite file filename          File filename is read-only. 
Cannot write file filename to disk      Not enough disk space. Erase other 
                                        files to free extra disk space. 


═══ 4.8. Run-time floating point errors ═══

To prevent abnormal termination MathMate intercepts the following run-time 
errors: 

o floating point math package errors; 

o math library elementary function errors; 

o built-in special functions domain errors 

If any such error occurs MathMate interrupts calculations and displays the 
corresponding message. 

List of run-time error messages 

Message                                 Explanation 
Overflow                                Too large value 

Example 

1e200*1e200 

Message                                 Explanation 
Underflow                               Too small value 

Example 

1e-200*1e-200 

Message                                 Explanation 
Division by zero                        Division by zero 

Example 

1/0 

Message                                 Explanation 
Overflow in func                        Too large value of C math library 
                                        function func 

Example 

exp(1000) 

Message                                 Explanation 
Underflow in func                       Too small value of C math library 
                                        function func 

Example 

exp(-1000) 

Message                                 Explanation 
Domain error in func                    Intolerable argument of C math library 
                                        function func 

Example 

ln(-1) 

Message                                 Explanation 
Significant digits loss in func         Loss of significant digits in C math 
                                        library function func 

Example 

sin(1e+50) 

Message                                 Explanation 
Bad argument = x in func                Intolerable argument x in the built-in 
                                        Mathmate function func 

Example 

Y(0, -1) 

Message                                 Explanation 
Bad index n = x in func                 Intolerable argument x in the built-in 
                                        Mathmate function func 

Example 

Leg(-1, 1, 0.5) 

Message                                 Explanation 
Bad module = x in func                  Intolerable argument x in the built-in 
                                        Mathmate function func 

Example 

Sn(-2, 2) 


═══ 5. How to... ═══

...install MathMate 
...start MathMate 
...get help 
...set a calculation mode 
...enter expressions 
...use the function panel 
...use the MathMate keypad 
...enter limits 
...initialize parameters 
...set precision 
...retrieve expressions from the history list 
...start calculations 
...terminate calculations 
...view results 
...view protocol 
...open protocol 
...save protocol 
...hide protocol 
...import expressions from the protocol 
...display product information 
...exit MathMate 


═══ 5.1. ...install MathMate ═══

Insert the diskette with the program files into the floppy drive switch to that 
drive and type at the OS/2 prompt 

mminst <pathname> 

where <pathname> is the name of the path of your choice. The MathMate folder 
will appear on your desktop. 

If you are using OS/2 version 3.0 it is recommended to place MathMate icon on 
the Launch Pad. 


═══ 5.2. ...start MathMate ═══

Double-click on the MathMate icon or switch to the directory where mathmate 
files were installed and type 

mathmate 

at the OS/2 command prompt. 


═══ 5.3. ...get help ═══

Press F1 or choose the Help menu item. 


═══ 5.4. ...set a calculation mode ═══

There are 3 ways: 

o Choose the corresponding menu item. 
o Choose the corresponding icon in the value set. 
o Click on the mode icon (to the left of the expression input line). 


═══ 5.5. ...enter expressions ═══

Make sure the cursor is in the expression entry field (use TAB or mouse to 
switch). Type the expression on the keyboard or enter it by clicking the mouse 
on the keypad and function panel buttons. 


═══ 5.6. ...use the function panel ═══

Click the mouse on a button in the panel to insert the function's name into the 
expression. Switch the panel layout by choosing Elementary or Special in the 
corresponding value set. 


═══ 5.7. ...use the MathMate keypad ═══

Click the mouse on a button in the keypad to insert the symbol into the 
expression. Switch the panel layout by choosing Numbers or Constants in the 
corresponding value set. 


═══ 5.8. ...enter limits ═══

Make sure the cursor is in the corresponding entry field (use TAB or mouse to 
switch). Type the value on the keyboard or enter it by clicking the mouse on 
the keypad buttons. 


═══ 5.9. ...initialize parameters ═══

Double-click on the corresponding line in the parameter list and enter the 
value from the keyboard or using the keypad. 


═══ 5.10. ...set precision ═══

Choose Precision from the Settings menu and use the slider to set the number of 
decimal digits in the calculations. 


═══ 5.11. ...retrieve expressions from the history list ═══

Activate the drop down list attached to the expression input line and choose 
one to place in the expression entry field. Use the mouse or press Enter to 
choose. 


═══ 5.12. ...start calculations ═══

If all the parameters are initialized, click on the Do it! button or press 
Enter. 


═══ 5.13. ...terminate calculations ═══

Click on the Stop button or press Esc. 


═══ 5.14. ...view results ═══

Results are displayed in the Result window after the calculation is finished. 


═══ 5.15. ...view protocol ═══

Click the mouse on the Result window or choose View protocol from the File 
menu. 


═══ 5.16. ...open protocol ═══

Choose Open protocol from the File menu. 


═══ 5.17. ...save protocol ═══

Choose Save protocol from the File menu. 


═══ 5.18. ...hide protocol ═══

Choose the Hide menu item in the Protocol window. 


═══ 5.19. ...import expressions from the protocol ═══

Highlight text in the protocol area and choose Send menu item from the Protocol 
window. 


═══ 5.20. ...display product information ═══

Choose Product information from the Help menu. 


═══ 5.21. ...exit MathMate ═══

Choose Exit in the menu. 


═══ <hidden>  ═══

у constant 

PI = 3.1415926535898 


═══ <hidden>  ═══

e constant 

E  = 2.7182818284590 


═══ <hidden>  ═══

Euler  constant 

GE = 0.5772156649015 


═══ <hidden>  ═══

Light velocity 

CL   = 2.997925e+10 


═══ <hidden>  ═══

Electron charge 

EC   = 4.80325e-10 


═══ <hidden>  ═══

Avogadro number 

AN   = 6.022169e+23 


═══ <hidden>  ═══

Electron mass 

EM   = 9.109558e-28 


═══ <hidden>  ═══

Proton mass 

PM   = 1.672614e-24 


═══ <hidden>  ═══

Planck constant 

hp   = 1.0545910e-27 


═══ <hidden>  ═══

Fine structure constant р 

AL = 7.297351e-3 


═══ <hidden>  ═══

Rydberg constant 

RY   = 1.09737312e+5 


═══ <hidden>  ═══

Boltzmann constant 

KB   = 1.380622e-16 


═══ <hidden>  ═══

Gravity constant 

GC   = 6.6732e-8 


═══ <hidden>  ═══

Bohr magneton 

MU   = 9.274096e-21 


═══ <hidden>  ═══

Earth gravity constant 

EG   = 980.665 


═══ <hidden>  ═══

Too many operations 

Explanation: 

The number of operations exceeds 50. MathMate cannot process such a long input 
string. Break it into parts. 


═══ <hidden>  ═══

Too many constants 

Explanation: 

The number of constants exceeds 21. 


═══ <hidden>  ═══

Too many identifiers 

Explanation: 

The number of identifiers exceeds 10. 


═══ <hidden>  ═══

Identifier expected 

Explanation: 

Illegal sequence of symbols 


═══ <hidden>  ═══

Expression expected 

Explanation: 

Illegal sequence of symbols 


═══ <hidden>  ═══

Operator expected 

Explanation: 

Illegal sequence of symbols 


═══ <hidden>  ═══

Too many ')' 

Explanation: 

Mismatch of numbers of the opening and closing brackets. 


═══ <hidden>  ═══

Syntax error 

Explanation: 

General syntax error. 


═══ <hidden>  ═══

Too few ')' 

Explanation: 

Mismatch of numbers of the opening and closing brackets. 


═══ <hidden>  ═══

Too many arguments 

Explanation: 

Wrong number of  function arguments 


═══ <hidden>  ═══

Too few arguments 

Explanation: 

Wrong number of function arguments 


═══ <hidden>  ═══

Illegal identifier 

Explanation: 

The first symbol of a variable name is not a letter. 


═══ <hidden>  ═══

Too long identifier 

Explanation: 

The length of identifier exceeds 6 symbols. 


═══ <hidden>  ═══

Must be function 

Explanation: 

The variable name coincides with that of a built-in function. 


═══ <hidden>  ═══

Unknown function 

Explanation: 

The function is not a built-in one. 


═══ <hidden>  ═══

Unknown symbol 

Explanation: 

Illegal symbol in expression