Algebra.pm6

unit role Algebra;

proto method ADD($) {*}
multi method ADD(Real $) {...}
multi method ADD(::?CLASS $) {...}

proto method MULTIPLY($) {*}
multi method MULTIPLY(::?CLASS $) {...}
multi method MULTIPLY(Real $) {...}

multi prefix:<->(::?CLASS $a) { (-1)*$a }
multi infix:<+>(::?CLASS $a, ::?CLASS $b) { $a.ADD($b) }
multi infix:<->(::?CLASS $a, ::?CLASS $b) { $a.ADD($b.MULTIPLY(-1)) }

multi infix:<*>(::?CLASS $a, ::?CLASS $b) { $a.MULTIPLY($b) }
multi infix:<*>(Real $a, ::?CLASS $b) { $b.MULTIPLY($a) }
multi infix:<*>(::?CLASS $a, Real $b) { $a.MULTIPLY($b) }
multi infix:</>(::?CLASS $a, Real $b) { $a.MULTIPLY(1/$b) }

multi infix:<**>(::?CLASS $a, 0) { 1 }
multi infix:<**>(::?CLASS $a, 1) { $a }
multi infix:<**>(::?CLASS $a, UInt $n) { ($a*$a)**($n div 2) * $a**($n mod 2) }