*******************************************************************************

Mathomatic Version 15.7.3 Command Summary
-----------------------------------------
approximate - Approximate all numerical values in equation spaces.
Usage: approximate [equation-number-ranges]
Related command: calculate

calculate - Temporarily plug in values for variables and approximate.
Usage: calculate ["factor"] [equation-number-range] [variable iterations]
This command may be preceded with "repeat".

clear - Delete expressions stored in memory so equation spaces can be reused.
Usage: clear [equation-number-ranges]
Tip: Use "clear all" to quickly restart Mathomatic.

code - Output C, Java, or Python code for the specified equations.
Usage: code ["c" or "java" or "python" or "integer"] [equation-number-ranges]
Related commands: simplify, optimize, and variables

compare - Compare two equation spaces for mathematical equivalence.
Usage: compare ["symbolic" "approx"] equation-number ["with" equation-number]
This command may be preceded with "repeat".

copy - Duplicate the contents of the specified equation spaces.
Usage: copy [equation-number-ranges]

derivative - Symbolically differentiate and simplify, order times.
Usage: derivative ["nosimplify"] variable or "all" [order]
Alternate name for this command: differentiate

display - Display equation spaces in pretty, 2D multi-line fraction format.
Usage: display ["factor" "mixed"] [equation-number-ranges]

divide - Divide 2 numbers or polynomials. Give detailed result and GCD.
Usage: divide [base-variable] [dividend divisor]
This command may be preceded with "repeat".

echo - Output a line of text, followed by a newline.
Usage: echo [text]
This command may be preceded with "repeat".

edit - Edit all equation spaces or an input file, then read them in.
Usage: edit [file-name]
Editor name in EDITOR environment variable.

eliminate - Substitute the specified variables with solved equations.
Usage: eliminate variables or "all" ["using" equation-number]
This command may be preceded with "repeat".

extrema - Show where the slope of the current equation equals zero.
Usage: extrema [variable] [order]
Helps with finding the minimums and maximums.

factor - Factor variables in equation spaces or factorize given integers.
Usage: factor ["number" [integers]] or ["power"] [equation-number-range] [variables]
Alternate name for this command: collect

for - Evaluate and display the current expression for each value of variable.
Usage: for variable start end [step-size]
Same syntax as the sum and product commands.

fraction - Convert expression to a single simple algebraic fraction.
Usage: fraction ["numerator" "denominator"] [equation-number-range]
This command may be preceded with "repeat".

help - Short, built-in help and reference.
Usage: help [topics or command-names]
Alternate name for this command: ?

imaginary - Copy the imaginary part of the current expression.
Usage: imaginary [variable]
Related command: real

integrate - Symbolically integrate polynomials order times, then simplify.
Usage: integrate ["constant" or "definite"] variable [order]
Alternate name for this command: integral

laplace - Compute the Laplace or inverse Laplace transform of polynomials.
Usage: laplace ["inverse"] variable
This command only works with polynomials.

limit - Take the limit as variable goes to expression.
Usage: limit variable expression
This limit command is experimental.

list - Display equation spaces in single-line (one-dimensional) format.
Usage: list ["export" or "maxima" or "gnuplot" or "hex"] [equation-number-ranges]
Options to export expressions to other math programs.

nintegrate - Do numerical definite integration using Simpson's rule.
Usage: nintegrate ["trapezoid"] variable [partitions [lower-bound upper-bound]]
This command cannot integrate over singularities.

optimize - Split up equations into smaller, more efficient equations.
Usage: optimize [equation-number-range]

pause - Display a line of text and wait for user to press the Enter key.
Usage: pause [text]

plot - Automatically plot expressions in 2D or 3D with gnuplot.
Usage: plot [equation-number-ranges] [xyz-ranges] [expressions,]
Plots variable x; if expression contains y, do a 3D surface plot.

product - Compute the product as variable goes from start to end.
Usage: product variable start end [step-size]
Related command: sum

push - Push equation spaces or text into readline history for editing.
Usage: push [equation-number-ranges or text-to-push]
Available only if readline is enabled.

quit - Terminate this program without saving.
Usage: quit [exit-value]
Alternate name for this command: exit

read - Read in a text file as if it was typed in.
Usage: read file-name
This command may be preceded with "repeat".

real - Copy the real part of the current expression.
Usage: real [variable]
Related command: imaginary

replace - Substitute variables in the current equation with expressions.
Usage: replace [variables ["with" expression]]

roots - Display all the roots of a complex number.
Usage: roots root real-part imaginary-part
This command may be preceded with "repeat".

save - Save all equation spaces in a text file.
Usage: save file-name
Related command: read

set - Display, set, or save current session options.
Usage: set [["no"] option [value]] ...
"set" by itself will show all current option settings.

simplify - Completely simplify expressions.
Usage: simplify ["sign" "symbolic" "quick[est]" "fraction"] [equation-number-ranges]
This command may be preceded with "repeat".

solve - Solve the specified equations for a variable or for zero.
Usage: solve ["verify"] [equation-number-range] ["for"] variable or "0"
The verify option checks all displayed solutions.

sum - Compute the summation as variable goes from start to end.
Usage: sum variable start end [step-size]
Related command: product

tally - Prompt for and add entries, showing running total.
Usage: tally ["average"]

taylor - Compute the Taylor series expansion of the current expression.
Usage: taylor ["nosimplify"] variable order point

unfactor - Algebraically expand (multiply out) expressions.
Usage: unfactor ["count" "fraction" "quick" "power"] [equation-number-range]
Alternate name for this command: expand

variables - Show all variable names used within the specified expressions.
Usage: variables ["c" or "java" or "integer" or "count"] [equation-number-ranges]
Related command: code

version - Display Mathomatic version, compiler, and license information.
Usage: version 

End of command list.  Total of 43 different commands.

*******************************************************************************

At the Mathomatic main prompt, you may enter:

  * a numerical expression, which is instantly evaluated and displayed with
    the calculate command (autocalc) (see "help constants"),
  * an algebraic expression or equation, which is stored and made the current
    equation (see "help expressions"),
  * a variable to solve the current equation for (autosolve),
  * an equation number to select as the current equation (autoselect),
  * a slash (/) or pound sign (#) followed by a variable name to search all
    equations spaces forward or backward for,
  * a Mathomatic command (see "help all"),
  * a question mark (?) for quick, short help (same as the help command),
  * a semicolon (;) followed by a comment (everything on a line after a
    semicolon is ignored),
  * or an exclamation point (!) followed by a shell or system command. "!" by
    itself invokes the default shell.

If a colon (:) starts the line, preceding any of the above input to the main
prompt, it will always return with successful status, preventing any current
read command operations from aborting.

*******************************************************************************

To enter an expression or equation, simply type it in at the prompt.
Operators have precedence decreasing as indicated:

    ! factorial (same as gamma(x+1) function; highest precedence)
    ** or ^ power (exponentiation; high precedence)
    * multiply      / divide        % modulus       // integral divide
    + add           - subtract or negate
    = equate (lowest precedence)

Multiple operators of the same precedence level are grouped left to right.
Parentheses are used to override operator precedence and group things together.
Valid parentheses characters are () and {}.

Variables consist of any combination of letters, digits, and underscores (_),
and "set special_variable_characters".  Variables never start with a digit.
Predefined variables follow:

    sign, sign1, sign2, ... - may only be +1 or -1
    integer, integer1, ... - may be any integer value

Absolute value notation "|x|" and dual polarity "+/-x" are understood.
Type "help constants" for help with entering Mathomatic constants.

*******************************************************************************

Constants are displayed as decimal, double precision floating point values
with about 14 digits accuracy.  They can be entered in standard, scientific,
or hexadecimal notation.  Any constant can be entered in hexadecimal (base 16)
by prepending "0x" to it.  Excepting named constants, constants always start
with a decimal digit (0..9) or a period.

Named constants follow:

    e or e# - the universal constant e (2.7182818284...)
    pi or pi# - the universal constant pi (3.1415926535...)
    i or i# - the imaginary unit (square root of -1)
The above constants may also be used anywhere variables are required.
    inf - floating point infinity constant
    nan - invalid floating point result

The largest valid constant is +/-1.797693e+308 (slightly less than 2^1024).
The smallest valid constant is +/-2.225074e-308 or 0.


For more information visit www.mathomatic.org