A short guide to the application
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Expressions: the parser of the applet understands expressions
in the usual mathematical notations (more or less).
- operators: +, -, *, /, ^ - add, subtract, multiply, divide, power
- operands: real numbers in decimal notation and x for the variable
- predefined functions: abs, sqrt, sin, cos, asin, acos, sinh, cosh, ln, lg, tor with obvious meanings,
except tor which stands for to_radians, converting a value in degrees into
radians
- mathematical constants: p - the ratio of a circle's circumference to its diameter - approx. 3.141592,
and e - Euler's number (Napier's constant), approximately 2.718281828.
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Available commands:
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[ev ]{expression [argument]} - evaluates an expression (for an
argument, eventually).
e.g.2*p and 2*p*x 1 is evaluated to 6.28.
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eva {argument} - evaluate the current function for an
argument
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f {expression} - declare a new function. The newly declared
function (if the expression is deemed correct) becomes the currently
selected one.
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p {space separated coefficients} - declare a new polynomial function.
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sel {n} - select the nth function (commands like eva
and seq use the selected/current function)
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seq [xl xr] - solve the selected/current equation. If xl
and xr are specified, a root is searched in the interval [xl,xr].
If the current function is a polynomial, and no start intervals are specified,
all roots are determined using Bairstow's method.
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rs[can] [xl xr] - scan for intervals which may contain roots.
If the optional argument is specified, intervals are searched for
in [xl, xr], otherwise the default interval [-20,20] is scanned
for roots.
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dv1 {x0} - compute the first derivative of the selected function in x0
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dv2 {x0} - compute the second derivative of the selected function in x0
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int {xl xr} - compute the finite integral of the selected function for [xl,xr]
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ls - list the declared functions. The currently selected one is marked with <->
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mat a11,a12,...,ann - declare a matrix
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lsm - list the currently selected matrix
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lsma - list all declared matrices
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selm n - select the nth matrix
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det [n] - compute the determinant of the current (or n-th) matrix
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? | help - display summary help
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Using the keyboard:
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The Enter key can be used to start processing the command
entered in the commandline(the yellow field). The same effect
can be obtained using the Process button.
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The Escape key can be used to clear the commandline.
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The Up and Down keys can be used to parse through the latest
entries in the commandline.
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Known limitations:
- The application stores only the latest 10 declared functions
and the latest 5 declared matrices. But, it also stores the last
15 expressions entered (you can access these using the Up and Down keys).
- For many equations, just using the command seq, without
specifying the start interval, the command will not work (no solutions
will be found). In such cases, specifying a small start interval will
be of help. For this, one should use the command rscan (or the
equivalent rs) to get the list of intervals which may contain
roots.
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When solving a polynomial equation using Bairstow's method,
in some cases, the found roots may be inaccurate (very!).
This is because of a poor implementation of the method (my bad).
In the case of real solutions (roots), you may check them using
the command eva(for a solution, the result should be approx. 0).
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Examples
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