;### SIMPLE COMPUTATIONS WITH POLYTOPES
$c=cube(3);
print $c->FACETS;
print_constraints($c);
print $c->F_VECTOR;
$c_polar=polarize($c);
print $c_polar->F_VECTOR;
$c_polar->VISUAL;
product(n_gon(5),n_gon(7))->SCHLEGEL(FACET=>1,EdgeColor=>"blue");
;# how to do it yourself: BEG, visualization: VIS, polytopes: SEM
;
;### RULE BASED COMPUTATION
$p=permutahedron(3);
print join(", ", $p->list_properties);
$schedule=$p->get_schedule("SIMPLE");
print join("\n", $schedule->list);
$schedule->apply($p);
print join(", ", $p->list_properties);
print $p->SIMPLE;
;# rules and such for beginners: PRL, ... for experts: EXT
;
;### GETTING HELP
help 'objects';
help 'objects/Polytope';
$t=typeof $c;
print join(", ", sorted_uniq(sort { $a cmp $b } map { keys %{$_->properties} } $t, @{$t->super}));
;# you already tried, but now you are stuck: STK, more help: HLP
;
;### LONG INTEGER ARITHMETIC
$f = new Integer(1);
for ($i = new Integer(100); $i>0; --$i) { $f *= $i; }
print $f;
;
;### NEW: POLYNOMIALS
$r=new Ring("x","y");
($x,$y)=$r->variables;
$p=1*(1+$x*$y)-1*($x+($y^2))+2*(($x^2)+$y);
$N=newton($p);
print $N->VERTICES;
print fac($N->DIM)*$N->VOLUME;
;
;### PERL POWER
use Benchmark qw(:all);
$r=rand_sphere(3,100); $t=timeit(1,'$r->FACETS;'); print timestr($t);
$r=rand_sphere(3,100); $t=timeit(1,'prefer_now("beneath_beyond");$r->FACETS;'); print timestr($t);
;# using Perl: PRL
;
;### OTHER KINDS OF OBJECTS
application 'topaz';
$rp2=projective_plane();
print $rp2->HOMOLOGY;
print $rp2->CONNECTED;
print rows_labeled($rp2->HOMOLOGY);
$t=torus();
print $t->FACETS;
$t->VISUAL;
;# other applications: APP, tropical geometry: TRP
;