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lib/Math/DifferenceSet/Planar.pm  view on Meta::CPAN

=item I<iterate_known_lex_refs>

=item I<iterate_known_gap_refs>

The class methods
C<Math::DifferenceSet::Planar-E<gt>iterate_known_I<E<lt>typeE<gt>>_refs(@args)>
with I<E<lt>typeE<gt>> one of C<std>, C<lex>, or C<gap>, provide
iterators analogous to I<iterate>, but iterating over the reference
sets of the respective type rather than unspecified samples.  Note that
these iterations may terminate sooner than I<iterate> and may even skip
some orders.

=item I<known_std_ref_min_order>

=item I<known_std_ref_max_order>

=item I<known_std_ref_count>

=item I<known_lex_ref_min_order>

lib/Math/DifferenceSet/Planar.pm  view on Meta::CPAN

an extra.  Lacking more efficient algorithms, a substantial extension of
gap reference sets would require massive computing power, but we expect
to at least gradually increase their number over time.

More important perhaps is double- and triple-checking the data that is
already present, before it can be regarded as scientifically acceptable.
For each order, we used Singer's construction to generate a sample
set, which is provably valid, and iterated through its multiples
to find reference sets with their respective optimality properties.
As this was of course performed by computer programs and computers may
malfunction, repetitions or, even better, independent reiterations
will increase confidence in the results and weed out actual errors.

Verifying difference set properties using complete difference tables is
impractical for large sets.  Verification using reference sets, on the
other hand, relies partly on conjectures.  Therefore, we are still looking
for an efficient and proven verification method for very large sets.

=head1 SEE ALSO

=over 4

t/07_principals.t  view on Meta::CPAN

$di = $it->();
is($di->zeta,  0, 'second set zeta');
is($di->eta,   0, 'second set eta');
is($di->theta, 0, 'second set theta');

my $c = 2;
while ($it->()) {
    ++$c;
}
is($c, 12, 'number of iterations');

my $dp = MDP->new(25);
$it = $dp->iterate_principal_planes_zc;
is(ref($it), 'CODE', 'iterate principal planes using zeta-canonical sets');

my $uc = $c = 0;
while (my $di = $it->()) {
    ++$c;
    ++$uc if $di->contains(1);
}