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Quick Start Guide Auto-calculation
Quick Start Guide
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Auto-calculation
Symbolic Algebraic
Having AnalyticMath perform symbolic calculations is very simple and straightforward
providing one remembers that they must be performed one at a time.
The program can currently perform the following symbolic (algebraic) calculations:
To perform one of the above symbolic algebraic calculations simply
select (with the mouse) the expression for which a symbolic calculation is desired
to be performed and press the <List Auto-calculation(s)> button at the top left of
the program window (one can also access this command by right clicking within the selected
region in order to bring up the pop-up menu). The program will list the operations
that it is able to perform in the list-box to the right
of the above-mentioned button. One need only click on the desired calculation in the
list in order to start the calculation. If the program is not able
to perform any type of calculation on the selected expression, then the list will
display 'Not a Valid Selection for Calculation'.
Before doing a calculation, it is important to note that there are two modes of
calculation available: 'Replace Mode' and 'Equals Mode'. The mode
can be changed at any time using the two buttons at the bottom right of the program
window (on the status bar) or by selecting one of these modes in the 'Preferences'
menu. 'Replace Mode' simply replaces the expression on which a calculation is
performed with the answer to that calculation, whereas, 'Equals Mode' places an
equal sign and then the answer to the calculation to the right of the expression
on which a calculation is performed.
The difference between these two modes can best be understood using the following
simple example calculation:
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(a + b)2 -->
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a2 + 2ab + b2
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Replace Mode
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(a + b)2 -->
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(a + b)2 = a2 + 2ab + b2
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Equals Mode
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Expansion of a Simple Binomial Square
(Note that the program is capable of expanding multinomial (i.e. multi-term)
expressions taken to any positive integral power.)
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(1) Type an expression into the editor.
The keypad to the right of the edit window is used to add the exponent
(i.e. the square) in this example. The keypad is used, in general, to add mathematical
symbols and structures to mathematical expressions.
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(2) Select a calculable expression with the mouse.
Be sure to select only the expression for
which a calculation is desired, remembering that the program can do only
one symbolic calculation at a time. Notice, in this example, that we have selected only the
(a + b)2 expression in order to expand the square and have not
included the 'A' sitting to its left. If the 'A' had been included,
the program would have returned 'Not a Valid Selection for Calculation'
when the <List Auto-calculation(s)> button was pressed.
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(3) Perform the Calculation:
(i) Press the
<List Auto-calculation(s)> button.
(ii) Click on:
'Expand the Square (click here)'
in the list box.
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(4a) Solution:
This is the solution that would be displayed in 'Replace Mode'.
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(4b) Solution:
This is the solution that would be displayed in 'Equals Mode'.
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Multiplication of Two Expressions Within Brackets
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Multiplication of two expressions within brackets.
One performs a similar series of steps to multiply expressions to those are performed when
expanding multinomials (see the above example of a binomial expansion).
Use the mouse to select the bracketed expressions that are to be multiplied. Then:
(i) Press the <List Auto-calculation(s)> button.
(ii) Click on:
'Multiply the Two Brackets (click here)'
in the list box.
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Note: When multiplying a single term
through another bracket, be sure that such a term is enclosed within brackets;
for example, (a)(a+b+...).
(This program will not multiply an expression such as a(b+c) because the 'a' in
this expression is not enclosed within brackets.)
Symbolic Algebra - The Program's Present Capabilities
In the list below, an arrow '-->' going to the right means that the program can currently
expand/simplify the stated expression in one direction only, from the state of the expression on the left
to that on the right. If a double arrow is present '<-->', it means that the program is capable of
expanding/simplifying the expression in both directions (there is actually none of these at present).
For reasons of generality, the equations below contain just simple letters (a, b, c...) or
letters with subscripts
(a1, a2, b1, b2,...); however,
these are meant to be representative of any type of general expression that
could be properly entered in their place.
Functions Presently Recognized By this Program
| sin(x) | cos(x) | tan(x) |
| csc(x) | sec(x) | cot(x) |
| arcsin(x) | arccos(x) | arctan(x) |
| arccsc(x) | arcsec(x) | arccot(x) |
| sinh(x) | cosh(x) | tanh(x) |
| csch(x) | sech(x) | coth(x) |
| arcsinh(x) | arccosh(x) | arctanh(x) |
| arccsch(x) | arcsech(x) | arccoth(x) |
| ln(x), base e | log(x), base 10 | logb(x), base b {bER| b>0 and b!=1} | .
| ex | 10x | bx, where {bER| inf < b < inf}, 00 is indeterminate |
Note that the inverse trigonometric and hyperbolic functions can be written (using sine as an example)
as either: arcsin(x) or sin-1(x), where the '-1' in the second form can be
inserted using either the <Superscript> or <Exponent> primary key-pad button (the
latter form is technically incorrect; it will, however, be interpreted correctly by the program -
to signify the reciprocal of sin(x) using an exponent, type: (sin(x))-1 ).
Present Editor Capabilities of Note
(At present, the mathematics editor is a one-line editor only.)
- All user-entered characters making up mathematical expressions are sized and
positioned automatically.
- The editor was written to be extremely flexible with respect
to mathematical syntax so that mathematical expressions can be entered just as they
would be written on paper. For example, any of the following is perfectly acceptable
for representing the product of 'A' and 'sin(x)': Asin(x) (this is likely the
most common syntax),
A*sin(x) (where the asterisk could be any one of the 3 symbols
available for scalar multiplication), (A)sin(x), (A)(sin(x)) etc.
In fact, the product can be written in an infinite number of ways and as long as it
is mathematically correct, the program will accept it - as an extreme example,
the following would also be acceptable: [((A))][[(([sin(x)]))]].
- Mathematical structures (exponents, fractions, square roots etc.) can be nested
(one inside the other) with no practical limit, thus allowing the creation of
complex mathematical expressions.
- All the mathematical functions have undo/redo capability.
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The movement of the caret (via the arrow keys or mouse) allows
for maximum flexibility when navigating around and through mathematical
structures. The below example demonstrates the movement of the caret
through a simple variable taken to an exponent on a series of
right arrow presses:
|ex --> e|x --> e|x --> ex| --> ex|
Note that the caret takes on the character of every possible position during the right
traversal of this expression. This allows mathematical expressions to be quickly and easily
edited.
- The program will not allow invalid selections to be made, and thus will
automatically complete selections that it determines to be incorrect.
For example, a selection cannot be halted somewhere in the middle of a
fraction if such a selection was started outside of that fraction - the program
will automatically complete the selection in order to incorporate the entire fraction.
On the other hand, full or partial selections of either the numerator or denominator are
permitted as long as such selections are started within those areas. This type of
functionalism is applied to all the mathematical structures that this program is capable
of creating (exponents, subscripts, superscripts, square roots, fractions, etc.).
Present Editor Limitations
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The fact that the editor is a one-line editor only is a definite
limitation. This is being worked on in hopes that in future versions
this restriction will be lifted.
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Only round and square brackets are automatically sized by the program. The
algorithms to size braces such as '{' and '}' have not been completed nor have the algorithms
for sizing absolute value symbols.
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