Math::Sequence - Perl extension dealing with mathematic sequences


  use Math::Sequence;
  my $x_n = Math::Sequence->new('x^2 - 1', 2);
  print $x_n->next(), "\n" foreach 0..9;
  # prints 2, 3, 8, 63...
  print $x_n->at_index(5);
  # prints 15745023

  $x_n->cached(0); # don't cache the results (slow!)
  $x_n->cached(1); # cache the results (default)


Math::Sequence defines a class for simple mathematic sequences with a recursive definition such as x_(n+1) = 1 / (x_n + 1). Creation of a Math::Sequence object is described below in the paragraph about the constructor.

Math::Sequence uses Math::Symbolic to parse and modify the recursive sequence definitions. That means you specify the sequence as a string which is parsed by Math::Symbolic. Alternatively, you can pass the constructor a Math::Symbolic tree directly.

Because Math::Sequence uses Math::Symbolic for its implementation, all results will be Math::Symbolic objects which may contain other variables than the sequence variable itself.

Each Math::Sequence object is an iterator to iterate over the elements of the sequence starting at the first element (which was specified by the starting element, the second argument to the new() constructor). It offers facilities to cache all calculated elements and access any element directly, though unless the element has been cached in a previous calculation, this is just a shortcut for repeated use of the iterator.

Every element in the sequence may only access its predecessor, not the elements before that.


  use strict;
  use warnings;
  use Math::Sequence;
  my $seq = Math::Sequence->new('x+a', 0, 'x');
  print($seq->current_index(), ' => ', $seq->next(), "\n") for 1..10;


Math::Sequence defines the following package variables:


This scalar contains a Parse::RecDescent parser to parse formulas. It is derived from the Math::Symbolic::Parser grammar.


This scalar indicates whether Math::Sequence should warn about the performance implications of using the back() method on uncached sequences. It defaults to true.



The constructor for Math::Sequence objects. Takes two or three arguments. In the two argument form, the first argument specifies the recursion definition. It must be either a string to be parsed by a Math::Symbolic parser or a Math::Symbolic tree. In the two argument version, the recursion variable (the one which will be recursively replaced by its predecessor) will be inferred from the function signature. Thus, the formula must contain exactly one variable. The second argument must be a starting value. It may either be a constant or a Math::Symbolic tree or a string to be parsed as such.

The three argument version adds to the two argument version a string indicating a variable name to be used as the recursion variable. Then, the recursion formula may contain any number of variables.


The next() method returns the next element of the sequence and advances the iterator by one. This is the prefered method of walking down a sequence's recursion.


Returns a true value if the sequence is currently being cached, false if it isn't. By default, new objects have caching enabled. It is suggested that you only disable caching if space is an issue and you will only walk the sequence uni-directionally and only once.

cached() can be used to change the caching behaviour. If the first argument is true, caching will be enabled. If it is false, caching will be disabled.


Returns the index of the current element. That is, the index of the element that will be returned by the next call to the next() method.

This method also allows (re-)setting the element that will be next returned by the next() method. In that case, the first argument shoudl be the appropriate index.

Returns undef and doesn't set the current index if the argument is below 0.


This method returns the sequence element with the index denoted by the first argument to the method. It does not change the state of the iterator. This method is extremely slow for uncached sequences.

Returns undef for indices below 0.


This methods returns the sequence element previously returned by the next() method. Since it is extremely slow on uncached sequences, it warns about this performance hit by default. To turn this warning off, set the $Math::Sequence::warnings scalar to a false value.

This method decrements the current iterator sequence element.

Returns undef if the current index goes below 0.


Steffen Mueller, <sequence-module at steffen-mueller dot net<gt>


Math::Symbolic and Math::Symbolic::Parser for the kinds of formulas accepted by Math::Sequence.