Free symbolic software for linux

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.

Math::Symbolic::MiscAlgebra contains miscellaneous algebra routines like det().

SYNOPSIS

use Math::Symbolic qw/:all/;
use Math::Symbolic::MiscAlgebra qw/:all/; # not loaded by Math::Symbolic

@matrix = ([x*y, z*x, y*z],[x, z, z],[x, x, y]);
$det = det @matrix;

@vector = (x, y, z);
$solution = solve_linear(@matrix, @vector);

This module provides several subroutines related to algebra such as computing the determinant of quadratic matrices, solving linear equation systems and computation of Bell Polynomials.

Please note that the code herein may or may not be refactored into the OO-interface of the Math::Symbolic module in the future.

You may choose to have any of the following routines exported to the calling namespace. :all tag exports all of the following:

det
linear_solve
bell_polynomial

SyFi is a C++ library built on top of the symbolic math library GiNaC. The name SyFi stands for Symbolic Finite Elements.

The package provides polygonal domains, polynomial spaces, and degrees of freedom as symbolic expressions that are easily manipulated. This makes it easy to define finite elements.

Mathomatic is a highly portable, general purpose symbolic math program that can solve, simplify, combine, differentiate, integrate, and compare algebraic equations.
It can do standard, complex number, and polynomial arithmetic. Mathomatic is extremely easy to use and has pretty colored, easily readable display of equations.
Main features:
- Solve equations,
- Completely simplify equations,
- Do calculus transformations,
- Do sensitivity and finite series analysis,
- Do complex number and polynomial arithmetic,
- Generate efficient C or Java code,
- And more!
Enhancements:
- Minor code, documentation, and makefile improvements were made.

Sympy is a symbolic manipulation package, written in pure Python. Sympys aim is to become a full featured CAS in Python, while keeping the code as simple as possible in order to be comprehensible and easily extensible.
Currently, Sympy has only around 1600 lines of code (including comments), and its capabilities include basic arithmetics, basic simplification, series expansion, functions (exp, ln, sin, cos, tan, etc.), differentiation, integration (currently it can do only very simple integrals), basic substitution, arbitrary precision integers and rationals, standard (Python) floats, basic complex numbers, and symbolic limits.
Main features:
- basic arithmetics *,/,+,-
- basic simplification (like a*b*b + 2*b*a*b -> 3*a*b^2)
- expansion (like (a+b)^2 -> a^2 + 2*a*b + b^2)
- functions (exp, ln, sin, cos, tan, ...)
- complex numbers (like exp(I*x).evalc() -> cos(x)+I*sin(x))
- differentiation
- taylor series
- basic substitution (like x-> ln(x))
- arbitrary precision integers and rationals
- standard (python) floats
Then there are SymPy modules (1000 lines) for these tasks:
- limits (like limit(x*log(x), x, 0) -> 0)
- integration (currently it can only do very simple integrals)
- symbolic matrices

DirSync is a directory synchronizer. It takes two arguments: the source directory and the destination directory.
It recursively makes the two directories identical. DirSync can be used to make an incremental copy of large data. For example, if your file server is in the /data you can make a copy in /backup with the command dirsync /data /backup.
The first time, all data will be copied, but when you issue the command again, only the changed files are copied.
Enhancements:
- This release fixes a bug, compiles on Sun, and adds support for symbolic links.

B::Lint::StrictOO is a Perl module that apply strict to classes and methods.

SYNOPSIS

Validates that classes exist, that methods that are called on classes and objects, and variables arent used as method names.

$ perl -MB::Lint::StrictOO -MO=Lint,oo my_file.pl

sub Hickory::Dickory::dock;

Mouse->dockk; # Class Mouse doesnt exist
Hickory::Dickory->dock;
Hickory::Dickory->$_; # Symbolic method call
$obj->dockk; # Object cant do method
$obj->dock;
$obj->$_; # Symbolic method call