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lib/Math/Derivative.pm  view on Meta::CPAN

Take the references to two arrays containing the x and y ordinates of
the data, and return an array of approximate first derivatives at the
given x ordinates, using the forward difference approximation.

The last term is actually formed using a backward difference formula,
there being no array item to subtract from at the end of the array.
If you want to use derivatives strictly formed from the forward
difference formula, use only the values from [0 .. #y-1], e.g.:

    @dydx = (forwarddiff(\@x, \@y))[0 .. $#y-1];

or, more simply,

lib/Math/Derivative.pm  view on Meta::CPAN

given x ordinates.

The algorithm used three data points to calculate the derivative, except
at the end points, where by necessity the forward difference algorithm
is used instead. If you want to use derivatives strictly formed from
the central difference formula, use only the values from [1 .. #y-1],
e.g.:

    @dydx = (centraldiff(\@x, \@y))[1 .. $#y-1];

=cut

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lib/Math/DyckWords.pm  view on Meta::CPAN

    (())()
    (()())

There is also a relationship between Dyck words and Catalan numbers.
Catalan numbers have many applications in combinatorics and consists
of a sequence of ever increasing integers following the formula:

    (2n)!/(n!(n+1)!)

The first few numbers in the Catalan sequence are:

lib/Math/DyckWords.pm  view on Meta::CPAN

=over

=item catalan_number( $n )

Using the formula - (2n)!/(n!(n+1)!) - this function returns the
corresponding number $n from the Catalan sequence.

=back

=cut

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lib/Math/EMA.pm  view on Meta::CPAN

  $avg->add($some_value);
  my $ema=$avg->ema;

=head1 DESCRIPTION

This module computes an exponential moving average by the following formula

  avg(n+1) = (1 - alpha) * new_value + alpha * avg(n)

where alpha is a number between 0 and 1.

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Expr/FormulaDB.pm  view on Meta::CPAN

#!/usr/bin/perl 

#  FormulaDB.pm - A db of formulas and there properties
#  (c) Copyright 1998 Hakan Ardo <hakan@debian.org>
#
#  This program is free software; you can redistribute it and/or modify
#  it under the terms of the GNU General Public License as published by
#  the Free Software Foundation; either version 2 of the License, or

Expr/FormulaDB.pm  view on Meta::CPAN

#  along with this program; if not, write to the Free Software
#  Foundation, Inc., 675 Mass Ave, Cambridge, MA 02139, USA.

=head1 NAME

  Math::Expr::FormulaDB - A db of formulas and there properties

=head1 SYNOPSIS

  require Math::Expr::FormulaDB;
  $db=new Math::Expr::FormulaDB($file);

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Expression.pm  view on Meta::CPAN

Error messages may be via a user provided function.
This is not designed for high computation use.

=head1 EXAMPLE

Shipping cost depends on item price by some arbitrary formula. The VAT amount can also
vary depending on political edict. Rather than nail these formula into the application code the
formula are obtained at run time from some configuration source. These formula are
entered by a non technical manager and are thus not to be trusted.

    use Math::Expression;
    my $ArithEnv = new Math::Expression;

Expression.pm  view on Meta::CPAN

# Price of what you are selling, set the price variable:
    my $price = 100;
    $ArithEnv->VarSetScalar('Price', $price);

# Obtain VAT & Shipping using the configured formula:
    my $VatTax = $ArithEnv->ParseToScalar($VatFormula);
    my $Shipping  = $ArithEnv->ParseToScalar($ShippingFormula);

    say "Price=$price VatTax=$VatTax Shipping=$Shipping";

# If these will be run many times, parse the formula once:

    my $VatExpr = $ArithEnv->Parse($VatFormula);
    my $ShipExpr = $ArithEnv->Parse($ShippingFormula);

# Evaluate it with the current price many times:

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lib/Math/Formula.pm  view on Meta::CPAN

use warnings;
use strict;
use utf8;

use Log::Report 'math-formula';

use Math::Formula::Token ();
use Math::Formula::Type  ();

use Scalar::Util         qw/blessed/;

lib/Math/Formula.pm  view on Meta::CPAN

	(bless {}, $class)->init(\%self);
}

sub init($)
{	my ($self, $args) = @_;
	my $name    = $self->{MSBE_name} = $args->{_name} or panic "every formular requires a name";
	my $expr    = $args->{_expr} or panic "every formular requires an expression";
	my $returns = $self->{MSBE_returns} = $args->{returns};

	if(ref $expr eq 'SCALAR')
	{	$expr = MF::STRING->new(undef, $$expr);
	}

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example/2n-table.txt  view on Meta::CPAN

The first, and second methods, are recorded in the Kahun Papyrus and the Rhind
Mathematical Papyrus. Both texts solved arithmetic progression problems by
using rational number differences. Egyptian fraction series were used to write
final answers. Arithmetic progressions, an algebra topic that followed
interesting formulas, will not be discussed. The second method, an arithmetic
topic, 2/n tables, listing optimized unit fraction series, will be discussed
in terms of a likely ancient unifying theme.

Overly analytical views of possible 2/n table methods, especially potential
2/35, 2/91 and 2/95 conversion methods have been suggested by scholars for

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FresnelZone.pm  view on Meta::CPAN

None by default. You can export any of the 3 functions as in the synopsis example.

=head2 VARIABLES

These variables are used when using miles/feet instead of kilometers/meters to modify the input for the formula and the output for the user:

   $Math::FresnelZone::KILOMETERS_IN_A_MILE  (Default is 1.609344)
   $Math::FresnelZone::FEET_IN_A_METER (Defualt is 3.280839)

Feel free to change them if you need more or less than six decimal places and/or want really inaccurate results :)

=head1 SEE ALSO

To find out more about the fresnel zone (pronounced fray-NELL) you can google the man who this formula/zone is named after to learn more: Augustin Jean Fresnel.

Mr. Fresnel was a French physicist who supported the wave theory of light, investigated polarized light, 
and developed a compound lens for use in lighthouses (IE the "Fresnel lens") (1788-1827).

Also googling the phrase "Fresnel Zone" turns up some interesting glossary refernces to what the fresnel zone is.

Here is a link to an image illustrating what a fresnel zone is and the formula:
L<http://drmuey.com/images/fresnelzone.jpg>

=head1 AUTHOR

Daniel Muey, L<http://drmuey.com/cpan_contact.pl> 

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docs/index.md  view on Meta::CPAN

Now that we have a trick, we still have to find out one last way to
actually find an irreducible polynomial of the desired order \\(n\\) over
the field we are extending. There are some results about it:

- they actually exist! There is someone that calculated a formula to count
  them, which also implies that fields of order \\(p^n\\) exists, of
  course! See [this question][irred-count] for further information;
- there always exist *monic* ones, i.e. where the coefficient for the
  highest power of \\(x\\) is \\(1\\) (which simplifies the division and
  the rest calculation);

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lib/Math/GSL/Histogram.pm  view on Meta::CPAN

=item C<gsl_histogram_pdf_init($p, $h)> - This function initializes the probability distribution $p with the contents of the histogram $h. If any of the bins of $h are negative then the error handler is invoked with an error code of $GSL_EDOM because...

=item C<gsl_histogram_pdf_free($p)> - This function frees the probability distribution function $p and all of the memory associated with it.

=item C<gsl_histogram_pdf_sample($p, $r)> -     This function uses $r, a uniform random number between zero and one, to compute a single random sample from the probability distribution $p. The algorithm used to compute the sample s is given by the fo...

=back

=head1 EXAMPLES