++ed by:
Steffen Müller


Math::Symbolic::Operator - Operators in symbolic calculations


  use Math::Symbolic::Operator;
  my $sum = Math::Symbolic::Operator->new('+', $term1, $term2);
  # or:
  my $division =
        type     => B_DIVISON,
        operands => [$term1, $term2],
  my $derivative =
        type     => U_P_DERIVATIVE,
        operands => [$term],


This module implements all Math::Symbolic::Operator objects. These objects are overloaded in stringification-context to call the to_string() method on the object. In numeric and boolean context, they evaluate to their numerical representation.

For a list of supported operators, please refer to the list found below, in the documentation for the new() constructor.

Math::Symbolic::Operator inherits from Math::Symbolic::Base.




Math::Symbolic::Operator contains several class data structures. Usually, you should not worry about dealing with any of them because they are mostly an implementation detail, but for the sake of completeness, here's the gist, but feel free to skip this section of the docs:

One of these is the %Op_Symbols hash that associates operator (and function) symbols with the corresponding constant as exported by Math::Symbolic or Math::Symbolic::ExportConstants. (For example, '+' => B_SUM which in turn is 0, if I recall correctly. But I didn't tell you that. Because you're supposed to use the supplied (inlined and hence fast) constants so I can change their internal order if I deem it necessary.)

The array @Op_Types associates operator indices (recall those nifty constants?) with anonymous hash datastructures that contain some info on the operator such as its arity, the rule used to derive it, its infix string, its prefix string, and information on how to actually apply it to numbers.


Constructor new

Expects a hash reference as first argument. That hash's contents will be treated as key-value pairs of object attributes. Important attributes are 'type' => OPERATORTYPE (use constants as exported by Math::Symbolic::ExportConstants!) and 'operands=>[op1,op2,...]'. Where the operands themselves may either be valid Math::Symbolic::* objects or strings that will be parsed as such.

Special case: if no hash reference was found, first argument is assumed to be the operator's symbol and the operator is assumed to be binary. The following 2 arguments will be treated as operands. This special case will ignore attempts to clone objects but if the operands are no valid Math::Symbolic::* objects, they will be sent through a Math::Symbolic::Parser to construct Math::Symbolic trees.

Returns a Math::Symbolic::Operator.

Supported operator symbols: (number of operands and their function in parens)

  +                  => sum (2)
  -                  => difference (2)
  *                  => product (2)
  /                  => division (2)
  log                => logarithm (2: base, function)
  ^                  => exponentiation (2: base, exponent)
  neg                => unary minus (1)
  partial_derivative => partial derivative (2: function, var)
  total_derivative   => total derivative (2: function, var)
  sin                => sine (1)
  cos                => cosine (1)
  tan                => tangent (1)
  cot                => cotangent (1)
  asin               => arc sine (1)
  acos               => arc cosine (1)
  atan               => arc tangent (1)
  atan2              => arc tangent of y/x (2: y, x)
  acot               => arc cotangent (1)
  sinh               => hyperbolic sine (1)
  cosh               => hyperbolic cosine (1)
  asinh              => hyperbolic area sine (1)
  acosh              => hyperbolic area cosine (1)

Method arity

Returns the operator's arity as an integer.

Method type

Optional integer argument that sets the operator's type. Returns the operator's type as an integer.

Method to_string

Returns a string representation of the operator and its operands. Optional argument: 'prefix' or 'infix'. Defaults to 'infix'.

Method term_type

Returns the type of the term. ( T_OPERATOR )

Method simplify

Term simpilification. First argument: Boolean indicating that the tree does not need to be cloned, but can be restructured instead. While this is faster, you might not be able to use the old tree any more.


  my $othertree = $tree->simplify();
  # can use $othertree and $tree now.

  my $yetanothertree = $tree->simplify(1);
  # must not use $tree any more because its internal
  # representation might have been destroyed.

If you want to optimize a routine and you're sure that you won't need the unsimplified tree any more, go ahead and use the first parameter. In all other cases, you should go the safe route.

Methods op1 and op2

Returns first/second operand of the operator if it exists or undef.

Method apply

Applies the operation to its operands' value() and returns the result as a constant (-object).

Without arguments, all variables in the tree are required to have a value. If any don't, the call to apply() returns undef.

To (temorarily, for this single method call) assign values to variables in the tree, you may provide key/value pairs of variable names and values. Instead of passing a list of key/value pairs, you may also pass a single hash reference containing the variable mappings.

You usually want to call the value() instead of this.

Method value



value() with one argument sets the object's value if you're dealing with Variables or Constants. In case of operators, a call with one argument will assume that the argument is a hash reference. (see next paragraph)

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 equivalent and valid syntax is to pass a single hash reference instead of a list.



Method signature

signature() returns a tree's signature.





Method explicit_signature


See also: signature().




List of contributors:

  Stray Toaster, mwk at users dot sourceforge dot net
  Oliver Ebenh�h




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