In Raku you can also use × (U+D7) for multiplication

    # this assumes that ϕ, ψ, and θ have already been set

    my \cϕ = ϕ.cos; my \sϕ = ϕ.sin;
    my \cψ = ψ.cos; my \sψ = ψ.sin;
    my \cθ = θ.cos; my \sθ = θ.sin;

    my \alpha = [ cψ×cϕ−cθ×sϕ×sψ,   cψ×sϕ+cθ×cϕ×sψ,   sψ×sθ;
               −sψ×cϕ−cθ×sϕ×cψ,  −sψ×sϕ+cθ×cϕ×cψ,   cψ×sθ;
                sθ×sϕ,           −sθ×cϕ,            cθ];

I'm not sure if using × helps or hurts in this case since I'm not really experienced in this area.

These all work because Unicode defines ϕψθ as "Letter lowercase"

    say "ϕψθ".uniprops;
    # (Ll Ll Ll)

---

I would like to note that I used the Unicode "Minus Sign" "−" U+2212 so that it wouldn't complain about not being able to find a routine named "cϕ-cθ". (A space next to the "-" would have also sufficed.)

> × (U+D7) for multiplication

Blech; looks like a letter and normalizes cross products. Better to use "·" (U+B7)[0]:

  alpha = [ cψ·cϕ−cθ·sϕ·sψ,  cψ·sϕ+cθ·cϕ·sψ,  sψ·sθ;
           −sψ·cϕ−cθ·sϕ·cψ, −sψ·sϕ+cθ·cϕ·cψ,  cψ·sθ;
            sθ·sϕ,          −sθ·cϕ,           cθ];

Minus sign is a nice-to-have, though.

0: Also "∧" (U+2227, wedge), the real other vector product[1], but that doesn't matter for scalar multiplication.

1: http://en.wikipedia.org/wiki/Wedge_product

It would be easy to just make `·` an alias. Then that code would work.

  my &infix:< · > = &infix:< × >;

(After all `×` itself is just an alias of `*` in the source for Rakudo.)

If you need more control you can write it out

  sub infix:< · > (+@vals)
    is equiv(&[×])       # uses the same precedence level etc.
    is assoc<chaining>   # may not be necessary given previous line
  {
    [×] @vals            # reduction using infix operator
  }

I made it chaining for the same reason `+` and `×` are chaining.

---

I don't know enough about the topic to know how to properly write `∧`.

It looks like it may be useful to write it using multis.

  # I don't know what precedence level it is supposed to be
  proto infix:< ∧ > (|) is tighter(&[×]) {*}

  multi infix:< ∧ > (
    Numeric $l,
    Numeric $r,
  ) {
    $l × $r
  }

  multi infix:< ∧ > (
    Vector $l, # need to define this somewhere, or use List/Array
    Vector $r,
  ) {
    …
  }

If it was as simple as just a normal cross product, that would have been easy.

  [[1,2,3],[4,5,6]] »×« [[10,20,30],[40,50,60]]
  # [[10,40,90],[160,250,360]]

  # generate a synthetic `»×«` operator, and give it an alias
  my &infix:< ∧ > = &infix:< »×« >;

  [[1,2,3],[4,5,6]] ∧ [[10,20,30],[40,50,60]]
  # [[10,40,90],[160,250,360]]

Of course, I'm fairly confident that is wrong.