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OS/2 Help File
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1994-12-29
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ΓòÉΓòÉΓòÉ 1. About MathMate ΓòÉΓòÉΓòÉ
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
ΓòÉΓòÉΓòÉ 2. MathMate capabilities ΓòÉΓòÉΓòÉ
This section covers the following topics:
o Built-in constants
o Built-in functions
ΓòÉΓòÉΓòÉ 2.1. Built-in constants ΓòÉΓòÉΓòÉ
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
ΓòÉΓòÉΓòÉ 2.2. Built-in functions ΓòÉΓòÉΓòÉ
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.
ΓòÉΓòÉΓòÉ 2.2.1. Built-in elementary functions ΓòÉΓòÉΓòÉ
Click a button on the panel below to get information about specific function
ΓòÉΓòÉΓòÉ 2.2.1.1. Exponential function ΓòÉΓòÉΓòÉ
MathMate syntax: exp(x)
Domain: x any real
ΓòÉΓòÉΓòÉ 2.2.1.2. Logarithm functions ΓòÉΓòÉΓòÉ
Natural (base e )
Decimal (base 10)
MathMate syntax: ln(x), log (x)
Domain: x > 0
ΓòÉΓòÉΓòÉ 2.2.1.3. Absolute value (modulus) ΓòÉΓòÉΓòÉ
MathMate syntax: abs(x)
Domain: x any real
ΓòÉΓòÉΓòÉ 2.2.1.4. Sign of the argument ΓòÉΓòÉΓòÉ
MathMate syntax: sign(x)
Domain: x any real
ΓòÉΓòÉΓòÉ 2.2.1.5. Integer part ΓòÉΓòÉΓòÉ
MathMate syntax: int(x)
Domain: x any real
ΓòÉΓòÉΓòÉ 2.2.1.6. Fractional part ΓòÉΓòÉΓòÉ
MathMate syntax: frac(x)
Domain: x any real
ΓòÉΓòÉΓòÉ 2.2.1.7. Trigonometric functions ΓòÉΓòÉΓòÉ
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
ΓòÉΓòÉΓòÉ 2.2.1.8. Inverse trigonometric functions ΓòÉΓòÉΓòÉ
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
ΓòÉΓòÉΓòÉ 2.2.1.9. Hyperbolic functions ΓòÉΓòÉΓòÉ
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
ΓòÉΓòÉΓòÉ 2.2.1.10. Inverse hyperbolic functions ΓòÉΓòÉΓòÉ
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
ΓòÉΓòÉΓòÉ 2.2.1.11. Square root function ΓòÉΓòÉΓòÉ
MathMate syntax: sqrt(x)
Domain: x Є 0
ΓòÉΓòÉΓòÉ 2.2.2. Built-in special functions ΓòÉΓòÉΓòÉ
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)
ΓòÉΓòÉΓòÉ 2.2.2.3. Digamma function (Euler psi - function) ΓòÉΓòÉΓòÉ
MathMate syntax: Psi(x)
Domain: x any real except 0, -1, -2, ...
See also:
o т function
o Incomplete т function
ΓòÉΓòÉΓòÉ 2.2.2.4. Error function ΓòÉΓòÉΓòÉ
MathMate syntax: Erf(x)
Domain: x any real
See also:
o Fresnel integrals
ΓòÉΓòÉΓòÉ 2.2.2.5. Sine and Cosine Fresnel integrals ΓòÉΓòÉΓòÉ
MathMate syntax: Fs(x), Fc(x)
Domain: x any real
See also:
o Error function
o Integral sines
o Integral cosines
ΓòÉΓòÉΓòÉ 2.2.2.6. Integral sines ΓòÉΓòÉΓòÉ
Integral sine
Integral hyperbolic sine
MathMate syntax: Si(x), Shi(x)
Domain: x any real
ΓòÉΓòÉΓòÉ 2.2.2.7. Integral cosines ΓòÉΓòÉΓòÉ
Integral cosine
Integral hyperbolic cosine
where is the Euler constant
MathMate syntax: Ci(x), Chi(x)
Domain: x > 0
ΓòÉΓòÉΓòÉ 2.2.2.8. Integral exponential ΓòÉΓòÉΓòÉ
MathMate syntax: Ei(x)
Domain: x any nonzero real
See also:
o Fresnel integrals
ΓòÉΓòÉΓòÉ 2.2.2.9. Complete elliptic integrals K(x), E(x) ΓòÉΓòÉΓòÉ
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
ΓòÉΓòÉΓòÉ 2.2.2.10. Incomplete elliptic integrals ΓòÉΓòÉΓòÉ
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
ΓòÉΓòÉΓòÉ 2.2.2.11. Bessel functions J(n,z) and Y(n,z) ΓòÉΓòÉΓòÉ
Bessel (cylindric) functions J(n,z) and Y(n,z)may be defined as solutions of
the equation
ΓòÉΓòÉΓòÉ 2.2.2.12. Bessel function J(n,z) ΓòÉΓòÉΓòÉ
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
ΓòÉΓòÉΓòÉ 2.2.2.13. Bessel function Y(n,z) ΓòÉΓòÉΓòÉ
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
ΓòÉΓòÉΓòÉ 2.2.2.14. (Modified) Bessel functions I(n,z) and K(n,z) ΓòÉΓòÉΓòÉ
The modified Bessel functions I(n,z) and K(n,z) may be defined as solutions of
the equation
ΓòÉΓòÉΓòÉ 2.2.2.15. Bessel function I(n,z) ΓòÉΓòÉΓòÉ
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
ΓòÉΓòÉΓòÉ 2.2.2.16. Bessel function K(n,z) (McDonald's function) ΓòÉΓòÉΓòÉ
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
ΓòÉΓòÉΓòÉ 2.2.2.17. Legendre functions P(m,n,x) ΓòÉΓòÉΓòÉ
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
ΓòÉΓòÉΓòÉ 2.2.2.19. Sn, Cn, Dn Jacobi functions ΓòÉΓòÉΓòÉ
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
ΓòÉΓòÉΓòÉ 3. Calculation modes ΓòÉΓòÉΓòÉ
This section covers the following topics:
o Evaluating expressions
o Integrating expressions
o Summing up series
o Solving equations
ΓòÉΓòÉΓòÉ 3.1. Evaluating expressions ΓòÉΓòÉΓòÉ
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.
ΓòÉΓòÉΓòÉ 3.2. Integrating expressions ΓòÉΓòÉΓòÉ
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
ΓòÉΓòÉΓòÉ 3.2.1. Integration sample ΓòÉΓòÉΓòÉ
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
ΓòÉΓòÉΓòÉ 3.3. Summing up series ΓòÉΓòÉΓòÉ
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
ΓòÉΓòÉΓòÉ 3.3.1. Summation sample ΓòÉΓòÉΓòÉ
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
ΓòÉΓòÉΓòÉ 3.4. Solving equations ΓòÉΓòÉΓòÉ
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
ΓòÉΓòÉΓòÉ 3.4.1. Solution sample ΓòÉΓòÉΓòÉ
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
ΓòÉΓòÉΓòÉ 4. Operation ΓòÉΓòÉΓòÉ
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
ΓòÉΓòÉΓòÉ 4.1. Entering expressions ΓòÉΓòÉΓòÉ
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
ΓòÉΓòÉΓòÉ 4.2. Syntax errors in expressions ΓòÉΓòÉΓòÉ
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
ΓòÉΓòÉΓòÉ 4.3. Initialization ΓòÉΓòÉΓòÉ
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.
ΓòÉΓòÉΓòÉ 4.4. Settings ΓòÉΓòÉΓòÉ
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.
ΓòÉΓòÉΓòÉ 4.5. History ΓòÉΓòÉΓòÉ
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.
ΓòÉΓòÉΓòÉ 4.6. MathMate Protocol ΓòÉΓòÉΓòÉ
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
ΓòÉΓòÉΓòÉ 4.7. Protocol file errors ΓòÉΓòÉΓòÉ
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.
ΓòÉΓòÉΓòÉ 4.8. Run-time floating point errors ΓòÉΓòÉΓòÉ
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)
ΓòÉΓòÉΓòÉ 5. How to... ΓòÉΓòÉΓòÉ
...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
ΓòÉΓòÉΓòÉ 5.1. ...install MathMate ΓòÉΓòÉΓòÉ
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.
ΓòÉΓòÉΓòÉ 5.2. ...start MathMate ΓòÉΓòÉΓòÉ
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.
ΓòÉΓòÉΓòÉ 5.3. ...get help ΓòÉΓòÉΓòÉ
Press F1 or choose the Help menu item.
ΓòÉΓòÉΓòÉ 5.4. ...set a calculation mode ΓòÉΓòÉΓòÉ
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).
ΓòÉΓòÉΓòÉ 5.5. ...enter expressions ΓòÉΓòÉΓòÉ
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.
ΓòÉΓòÉΓòÉ 5.6. ...use the function panel ΓòÉΓòÉΓòÉ
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.
ΓòÉΓòÉΓòÉ 5.7. ...use the MathMate keypad ΓòÉΓòÉΓòÉ
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.
ΓòÉΓòÉΓòÉ 5.8. ...enter limits ΓòÉΓòÉΓòÉ
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.
ΓòÉΓòÉΓòÉ 5.9. ...initialize parameters ΓòÉΓòÉΓòÉ
Double-click on the corresponding line in the parameter list and enter the
value from the keyboard or using the keypad.
ΓòÉΓòÉΓòÉ 5.10. ...set precision ΓòÉΓòÉΓòÉ
Choose Precision from the Settings menu and use the slider to set the number of
decimal digits in the calculations.
ΓòÉΓòÉΓòÉ 5.11. ...retrieve expressions from the history list ΓòÉΓòÉΓòÉ
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.
ΓòÉΓòÉΓòÉ 5.12. ...start calculations ΓòÉΓòÉΓòÉ
If all the parameters are initialized, click on the Do it! button or press
Enter.
ΓòÉΓòÉΓòÉ 5.13. ...terminate calculations ΓòÉΓòÉΓòÉ
Click on the Stop button or press Esc.
ΓòÉΓòÉΓòÉ 5.14. ...view results ΓòÉΓòÉΓòÉ
Results are displayed in the Result window after the calculation is finished.
ΓòÉΓòÉΓòÉ 5.15. ...view protocol ΓòÉΓòÉΓòÉ
Click the mouse on the Result window or choose View protocol from the File
menu.
ΓòÉΓòÉΓòÉ 5.16. ...open protocol ΓòÉΓòÉΓòÉ
Choose Open protocol from the File menu.
ΓòÉΓòÉΓòÉ 5.17. ...save protocol ΓòÉΓòÉΓòÉ
Choose Save protocol from the File menu.
ΓòÉΓòÉΓòÉ 5.18. ...hide protocol ΓòÉΓòÉΓòÉ
Choose the Hide menu item in the Protocol window.
ΓòÉΓòÉΓòÉ 5.19. ...import expressions from the protocol ΓòÉΓòÉΓòÉ
Highlight text in the protocol area and choose Send menu item from the Protocol
window.
ΓòÉΓòÉΓòÉ 5.20. ...display product information ΓòÉΓòÉΓòÉ
Choose Product information from the Help menu.
ΓòÉΓòÉΓòÉ 5.21. ...exit MathMate ΓòÉΓòÉΓòÉ
Choose Exit in the menu.
ΓòÉΓòÉΓòÉ <hidden> ΓòÉΓòÉΓòÉ
у constant
PI = 3.1415926535898
ΓòÉΓòÉΓòÉ <hidden> ΓòÉΓòÉΓòÉ
e constant
E = 2.7182818284590
ΓòÉΓòÉΓòÉ <hidden> ΓòÉΓòÉΓòÉ
Euler constant
GE = 0.5772156649015
ΓòÉΓòÉΓòÉ <hidden> ΓòÉΓòÉΓòÉ
Light velocity
CL = 2.997925e+10
ΓòÉΓòÉΓòÉ <hidden> ΓòÉΓòÉΓòÉ
Electron charge
EC = 4.80325e-10
ΓòÉΓòÉΓòÉ <hidden> ΓòÉΓòÉΓòÉ
Avogadro number
AN = 6.022169e+23
ΓòÉΓòÉΓòÉ <hidden> ΓòÉΓòÉΓòÉ
Electron mass
EM = 9.109558e-28
ΓòÉΓòÉΓòÉ <hidden> ΓòÉΓòÉΓòÉ
Proton mass
PM = 1.672614e-24
ΓòÉΓòÉΓòÉ <hidden> ΓòÉΓòÉΓòÉ
Planck constant
hp = 1.0545910e-27
ΓòÉΓòÉΓòÉ <hidden> ΓòÉΓòÉΓòÉ
Fine structure constant р
AL = 7.297351e-3
ΓòÉΓòÉΓòÉ <hidden> ΓòÉΓòÉΓòÉ
Rydberg constant
RY = 1.09737312e+5
ΓòÉΓòÉΓòÉ <hidden> ΓòÉΓòÉΓòÉ
Boltzmann constant
KB = 1.380622e-16
ΓòÉΓòÉΓòÉ <hidden> ΓòÉΓòÉΓòÉ
Gravity constant
GC = 6.6732e-8
ΓòÉΓòÉΓòÉ <hidden> ΓòÉΓòÉΓòÉ
Bohr magneton
MU = 9.274096e-21
ΓòÉΓòÉΓòÉ <hidden> ΓòÉΓòÉΓòÉ
Earth gravity constant
EG = 980.665
ΓòÉΓòÉΓòÉ <hidden> ΓòÉΓòÉΓòÉ
Too many operations
Explanation:
The number of operations exceeds 50. MathMate cannot process such a long input
string. Break it into parts.
ΓòÉΓòÉΓòÉ <hidden> ΓòÉΓòÉΓòÉ
Too many constants
Explanation:
The number of constants exceeds 21.
ΓòÉΓòÉΓòÉ <hidden> ΓòÉΓòÉΓòÉ
Too many identifiers
Explanation:
The number of identifiers exceeds 10.
ΓòÉΓòÉΓòÉ <hidden> ΓòÉΓòÉΓòÉ
Identifier expected
Explanation:
Illegal sequence of symbols
ΓòÉΓòÉΓòÉ <hidden> ΓòÉΓòÉΓòÉ
Expression expected
Explanation:
Illegal sequence of symbols
ΓòÉΓòÉΓòÉ <hidden> ΓòÉΓòÉΓòÉ
Operator expected
Explanation:
Illegal sequence of symbols
ΓòÉΓòÉΓòÉ <hidden> ΓòÉΓòÉΓòÉ
Too many ')'
Explanation:
Mismatch of numbers of the opening and closing brackets.
ΓòÉΓòÉΓòÉ <hidden> ΓòÉΓòÉΓòÉ
Syntax error
Explanation:
General syntax error.
ΓòÉΓòÉΓòÉ <hidden> ΓòÉΓòÉΓòÉ
Too few ')'
Explanation:
Mismatch of numbers of the opening and closing brackets.
ΓòÉΓòÉΓòÉ <hidden> ΓòÉΓòÉΓòÉ
Too many arguments
Explanation:
Wrong number of function arguments
ΓòÉΓòÉΓòÉ <hidden> ΓòÉΓòÉΓòÉ
Too few arguments
Explanation:
Wrong number of function arguments
ΓòÉΓòÉΓòÉ <hidden> ΓòÉΓòÉΓòÉ
Illegal identifier
Explanation:
The first symbol of a variable name is not a letter.
ΓòÉΓòÉΓòÉ <hidden> ΓòÉΓòÉΓòÉ
Too long identifier
Explanation:
The length of identifier exceeds 6 symbols.
ΓòÉΓòÉΓòÉ <hidden> ΓòÉΓòÉΓòÉ
Must be function
Explanation:
The variable name coincides with that of a built-in function.
ΓòÉΓòÉΓòÉ <hidden> ΓòÉΓòÉΓòÉ
Unknown function
Explanation:
The function is not a built-in one.
ΓòÉΓòÉΓòÉ <hidden> ΓòÉΓòÉΓòÉ
Unknown symbol
Explanation:
Illegal symbol in expression
(.txt)
(.txt)