Elliptic curve arithmetic: Difference between revisions

<syntaxhighlight lang="raku" line>unit module EC; {

our ($A, $B) = (0, 7);

$x, $y where $y**2 ~~== $x**3 + $A*$x + $B

) { self.bless(samewith :$x, :$y) }

multi method new(Horizon $)gist { self.bless"EC butPoint Horizonat x=$.x, y=$.y" }

multi method gist(::?CLASS:U:) { "EC 'Point at x=$.x, y=$.y"horizon' }

}

multi prefix:<->(Point $p) is export { Point.new: x => $p.x, y => -$p.y }

multi prefix:<->(HorizonPoint:: $) is export { HorizonPoint }

multi infix:<->(Point $a, Point $b) is export { $a + -$b }

multi infix:<+>(HorizonPoint:U $, Point $p) is export { $p }

multi infix:<+>(Point $p, HorizonPoint:U) is export { $p }

multi infix:<*>(Point $u, Int $n) is export { $n * $u }

multi infix:<*>(Int $n, HorizonPoint:U) is export { HorizonPoint }

multi infix:<*>(0, Point) is export { HorizonPoint }

multi infix:<*>(1, Point $p) is export { $p }

multi infix:<*>(2, Point $p) is export {

$p.blessnew(:$x, :$y);

}

multi infix:<*>(Int $n where $n > 2, Point $p) is export {

}

multi infix:<+>(Point $p, Point $q) is export {

return $p.y ~~ $q.y ?? 2 * $p !! HorizonPoint;

my $slope = ($q.y - $p.y) / ($q.x - $p.x);

my $y = $slope*($p.x - my $x = $slope**2 - $p.x - $q.x) - $p.y;

return $p.new(:$x, :$y);

say "checking alignment: ",is abs (($p.x - $q.x)*(-$s.y - $q.y) - ($p.y - $q.y)*($s.x - $q.x)), 0, "S, P and Q are aligned";</syntaxhighlight>