Free math software software for linux

MathWar project is a flashcard math game for kids.

MathWar is a flashcard math game in which the child plays against the computer to solve simple addition, subtraction, and multiplication problems before the computer player answers.

MathWar is aimed at kids who are just learning their math facts, and can easily be tailored to fit different skill levels.

MathTables is a program that helps parents teach their children how to use the four basic math operations, multiplication, substraction, addition and division.

With MathTables parents can print sheets full of math operations for their children to answer. They can also print corresponding sheets with the solutions so that either them, or the children themselves, can work on the corrections.

This program arose from the actual need to print math tables almost daily for my children, as requested by their school.

MathTables is written in Python using the PyGTK toolkit.

Math::MagicSquare is a Magic Square Checker and Designer.

SYNOPSIS

use Math::MagicSquare;

$a= Math::MagicSquare -> new ([num,...,num],
...,
[num,...,num]);
$a->print("string");
$a->printhtml();
$a->printimage();
$a->check();
$a->rotation();
$a->reflection();

The following methods are available:

new

Constructor arguments are a list of references to arrays of the same length.

$a = Math::MagicSquare -> new ([num,...,num],
...,
[num,...,num]);

check

This function can return 4 value

0: the Square is not Magic
1: the Square is a Semimagic Square (the sum of the rows and the columns is equal)
2: the Square is a Magic Square (the sum of the rows, the columns and the diagonals is equal)
3: the Square ia Panmagic Square (the sum of the rows, the columns, the diagonals and the broken diagonals is equal)

print

Prints the Square on STDOUT. If the method has additional parameters, these are printed before the Magic Square is printed.

printhtml

Prints the Square on STDOUT in an HTML format (exactly a inside a TABLE)

printimage

Prints the Square on STDOUT in png format.

rotation

Rotates the Magic Square of 90 degree clockwise

reflection

Reflect the Magic Square

Math Objects is a math template library written in C++ using generic programming techniques. In order to use the "Math Objects" library, the user only has to include the header files he needs (e.g. Matrix.h, Polynomial.h etc.).
In order to compile the library the user needs an ISO/IEC 14882:1998 standard compliant C++ compiler (e.g. one that supports partial template specializations).
The math library has math objects like matrices, polynomials, rational functions, extended precision numbers, complex numbers etc. that can be handled in a similar way like basic numerical types (e.g. integers or floating point numbers).
One can access properties of a mathematical type through a (partial) specialization of a traits class for that type (AlgebraicTraits). Having the traits classes to expose properties of mathematical objects, one can define for example matrices of polynomials having extended precision complex coefficients and apply to them basic linear algebra algorithms using normal C++ syntax.
This library also implements two functions using two deterministic algorithms that compute the Smith form for polynomial matrices, and the Smith-McMillan form of a transfer functions matrix also keeping track of the transformation matrices.
These algorithms can be used to describe a MIMO (multi input-multi output) system by means of its zeros and poles and also give the MFD (matrix fraction description) of the system.
Enhancements:
- Recoded the LongInt class aiming for better runtime efficiency.

Math::XOR is a package to handle XOR encryption of string buffers.

SYNOPSIS

use XOR;
print xor_buf("hello", "world"), "n";

The XOR module allows you to quickly XOR two strings together. This is the only method of encryption that (assuming the randomness of the pattern used as an encryption key) truly cannot be broken. It also has interesting, very direct mathematical properties which can be fun to play with:

XOR string 1 and string 2, you get string 3 XOR string 1 and string 3, you get string 2 XOR string 2 and string 3, you get string 1

FUNCTIONS

xor_buf($string1, $string2)

This function will return a scalar, which is the result of XORing the two strings passed to it together. The strings may contain binary data.

If $string2 is not at least as many characters long as $string1, xor_buf() will print an error and return undef. Only as many characters as there are in $string1 will be returned; excess characters in $string2 will be ignored. For this reason, when encrypting data it is good to think of $string1 as your "data" and $string2 as your "key".

Math::BaseArith is a Perl extension for mixed-base number representation (like APL encode/decode).

SYNOPSIS

use Math::BaseArith;
encode( value, base_list );
decode( representation_list, base_list );

The inspiration for this module is a pair of functions in the APL programming language called encode (a.k.a. "representation") and decode (a.k.a. base-value). Their principal use is to convert numbers from one number base to another. Mixed number bases are permitted.

In this perl implementation, the representation of a number in a particular number base consists of a list whose elements are the digit values in that base. For example, the decimal number 31 would be expressed in binary as a list of five ones with any number of leading zeros: [0, 0, 0, 1, 1, 1, 1, 1]. The same number expressed as three hexadecimal (base 16) digits would be [0, 1, 15], while in base 10 it would be [0, 3, 1]. Fifty-one inches would be expressed in yards, feet, inches as [1, 1, 3], an example of a mixed number base.

In the following description of encode and decode, Q will mean an abstract value or quantity, R will be its representation and B will define the number base. Q will be a perl scalar; R and B are perl lists. The values in R correspond to the radix values in B.

In the examples below, assume the output of print has been altered by setting $, = and that => is your shell prompt.

Math::MatrixReal is a nifty perl module for doing just about anything you could want with an NxN matrix, or vector of real numbers.
Main features:
- operator overloading, $a * $b multiplies 2 matrices, $a / $b is shorthand for $a * $b ** -1
- create matrices from strings or array references
- inverse
- determinant
- transpose (overloaded to ~)
- normalization
- diagonalization ( symmetric only )
- eigenvalues, eigenvectors ( symmetric only )
- boolean checks for: symmetric,orthogonal,diagonal,tridiagonal,triangular,
- gramian,binary,idempotent,periodic
- norms: p-norms, frobenius norm, 1-norm, 2-norm
- cofactor matrix
- minor matrix
- rank (order)
- Analytic solution of Ax=b with LR decomposition
- 3d vector product
- 3 iterative algorithms to solve Ax=b
- Single Step Method
- Global Step Method
- Relaxation Method
- export matrix to Matlab, Scilab, Yacas or LaTeX

Math::Symbolic::Base is a case class for symbols in symbolic calculations.

SYNOPSIS

use Math::Symbolic::Base;

This is a base class for all Math::Symbolic::* terms such as Math::Symbolic::Operator, Math::Symbolic::Variable and Math::Symbolic::Constant objects.

METHODS

Method to_string

Default method for stringification just returns the objects value.

Method value

value() evaluates the Math::Symbolic tree to its numeric representation.

value() without arguments requires that every variable in the tree contains a defined value attribute. Please note that this refers to every variable object, not just every named variable.

value() with one argument sets the objects value (in case of a variable or constant).

value() with named arguments (key/value pairs) associates variables in the tree with the value-arguments if the corresponging key matches the variable name. (Can one say this any more complicated?) Since version 0.132, an alternative syntax is to pass a single hash reference.

Example: $tree->value(x => 1, y => 2, z => 3, t => 0) assigns the value 1 to any occurrances of variables of the name "x", aso.

If a variable in the tree has no value set (and no argument of value sets it temporarily), the call to value() returns undef.

Method signature

signature() returns a trees signature.

In the context of Math::Symbolic, signatures are the list of variables any given tree depends on. That means the tree "v*t+x" depends on the variables v, t, and x. Thus, applying signature() on the tree that would be parsed from above example yields the sorted list (t, v, x).

Constants do not depend on any variables and therefore return the empty list. Obviously, operators dependencies vary.

Math::Symbolic::Variable objects, however, may have a slightly more involved signature. By convention, Math::Symbolic variables depend on themselves. That means their signature contains their own name. But they can also depend on various other variables because variables themselves can be viewed as placeholders for more compicated terms. For example in mechanics, the acceleration of a particle depends on its mass and the sum of all forces acting on it. So the variable acceleration would have the signature (acceleration, force1, force2,..., mass, time).

If youre just looking for a list of the names of all variables in the tree, you should use the explicit_signature() method instead.

Method explicit_signature

explicit_signature() returns a lexicographically sorted list of variable names in the tree.

See also: signature().

Method set_signature

set_signature expects any number of variable identifiers as arguments. It sets a variables signature to this list of identifiers.

Method implement

implement() works in-place!

Takes key/value pairs as arguments. The keys are to be variable names and the values must be valid Math::Symbolic trees. All occurrances of the variables will be replaced with their implementation.

Method replace

First argument must be a valid Math::Symbolic tree.

replace() modifies the object it is called on in-place in that it replaces it with its first argument. Doing that, it retains the original object reference. This destroys the object it is called on.

However, this also means that you can create recursive trees of objects if the new tree is to contain the old tree. So make sure you clone the old tree using the new() method before using it in the replacement tree or you will end up with a program that eats your memory fast.

fill_in_vars

This method returns a modified copy of the tree it was called on.

It walks the tree and replaces all variables whose value attribute is defined (either done at the time of object creation or using set_value()) with the corresponding constant objects. Variables whose value is not defined are unaffected. Take, for example, the following code:

$tree = parse_from_string(a*b+a*c);
$tree->set_value(a => 4, c => 10); # value of b still not defined.
print $tree->fill_in_vars();
# prints "(4 * b) + (4 * 10)"

Method simplify

Minimum method for term simpilification just clones.

Method descending_operands

When called on an operator, descending_operands tries hard to determine which operands to descend into. (Which usually means all operands.) A list of these is returned.

When called on a constant or a variable, it returns the empty list.

Of course, some routines may have to descend into different branches of the Math::Symbolic tree, but this routine returns the default operands.

The first argument to this method may control its behaviour. If it is any of the following key-words, behaviour is modified accordingly:

default -- obvious. Use default heuristics.

These are all supersets of default:
all -- returns ALL operands. Use with caution.
all_vars -- returns all operands that may contain vars.