Math::NumSeq::PlanePathCoord -- sequence of coordinate values from a PlanePath module
use Math::NumSeq::PlanePathCoord; my $seq = Math::NumSeq::PlanePathCoord->new (planepath => 'SquareSpiral', coordinate_type => 'X'); my ($i, $value) = $seq->next;
This is a tie-in to present coordinates from a Math::PlanePath module as a NumSeq sequence. The NumSeq "i" index is the PlanePath "N" value.
Math::PlanePath
The coordinate_type choices are
coordinate_type
"X" X coordinate "Y" Y coordinate "Sum" X+Y sum "Product" X*Y product "DiffXY" X-Y difference "DiffYX" Y-X difference (negative of DiffXY) "AbsDiff" abs(Y-X) difference "Radius" sqrt(X^2+Y^2) radius "RSquared" X^2+Y^2 radius squared
"Sum" can be interpreted geometrically as a projection onto the X=Y leading diagonal, or equivalently as a measure of which anti-diagonal stripe contains the X,Y.
\ 2 \ \ 1 2 \ \ \ 0 1 2
"DiffXY" similarly, but a projection onto the X=-Y opposite diagonal, or a measure of which leading diagonal stripe has the X,Y.
/ / / / -1 0 1 2 / / / / -1 0 1 2 / / / 0 1 2
Some path coordinates are in Sloane's Online Encyclopedia of Integer Sequences. See each PlanePath module for details.
$seq->oeis_anum() returns the A-number in the usual way, if there's one known. This includes things like A000004 all-zeros for cases where a coordinate is simple or even trivial.
$seq->oeis_anum()
Known A-numbers are presented through Math::NumSeq::OEIS::Catalogue so path related sequences can be created with Math::NumSeq::OEIS in the usual way. A-numbers specific to the paths are catalogued, plus a few of the simpler things not otherwise covered by NumSeq modules yet (such as A002262 successive 0 to k runs 0, 0,1, 0,1,2, 0,1,2,3, which arises in the Diagonals).
Math::NumSeq::OEIS::Catalogue
Math::NumSeq::OEIS
See "FUNCTIONS" in Math::NumSeq for the behaviour common to all path classes.
$seq = Math::NumSeq::PlanePathCoord->new (planepath => $name, coordinate_type => 'X')
Create and return a new sequence object. The planepath option is the name of one of the Math::PlanePath modules.
planepath
coordinate_type (a string) is what coordinate from the path is wanted, per the choices above.
$value = $seq->ith($i)
Return the coordinate at N=$i in the PlanePath.
$i = $seq->i_start()
Return the first index $i in the sequence. This is the position rewind() returns to.
$i
rewind()
This is $path->n_start() from the PlanePath, since the i numbering is the N numbering of the underlying path. For some of the OEIS generated sequences there may be a higher i_start() corresponding to a higher starting point in the OEIS, though this is slightly experimental.
$path->n_start()
i_start()
Math::NumSeq, Math::NumSeq::OEIS
http://user42.tuxfamily.org/math-planepath/index.html
Copyright 2011 Kevin Ryde
This file is part of Math-PlanePath.
Math-PlanePath 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 3, or (at your option) any later version.
Math-PlanePath is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details.
You should have received a copy of the GNU General Public License along with Math-PlanePath. If not, see <http://www.gnu.org/licenses/>.
To install Math::PlanePath, copy and paste the appropriate command in to your terminal.
cpanm
cpanm Math::PlanePath
CPAN shell
perl -MCPAN -e shell install Math::PlanePath
For more information on module installation, please visit the detailed CPAN module installation guide.