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For me, the biggest problem with the whole maths ---> code mapping is that of nested brackets. For a random quick example, I mean things like

    (a*(1+exp(1i*theta[0,:]))+foo(x))/((b-cosh(bar(x))+(b+sinh(y[:,-1])).

The sort of thing where it just _looks_ far nicer on a page with like _real fractions_ -- where missing a bracket or changing the order of two brackets can _totally_ bugger you. Yes, changing the form of the expression a bit can make it "far nicer" or simpler -- for example, by defining intermediate terms -- but sometimes there's something to be said for <expression x> matches <equation y> in the paper.

Another example where I think ASCII actually _is_ limiting is for entries of matrices directly. I mean, we try, but I'm not convinced we succeed. For an example (picked at random), hands up if you think this is a nice Euler angle transformation, where cphi/sphi etc are the cosine and sine of phi? No matter how you write it, it's going to be ugly.

   alpha = [cpsi*cphi-ctheta*sphi*spsi   cpsi*sphi+ctheta*cphi*spsi  spsi*stheta;
            -spsi*cphi-ctheta*sphi*cpsi  -spsi*sphi+ctheta*cphi*cpsi cpsi*stheta;
            stheta*sphi                  -stheta*cphi                ctheta];

View on HN

double cf = cos(phi),sf = sin(phi); double cp = cos(psi),sp = sin(psi); double ct = cos(theta),st = sin(theta); alpha = [ cp*cf-ct*sf*sp cp*sf+ct*cf*sp sp*st; -sp*cf-ct*sf*cp -sp*sf+ct*cf*cp cp*st; st*sf -st*cf ct];

# 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];

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];

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 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, ) { … }

[[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]]