/* metrics.mac
 *   version 0.02
 *  (C) Kenrou Adachi, 2004/06/25
 */

load(eigen)$

geom(a, b, G) := block([ta],
    ta : conjugate(transpose(a)),
    ratsimp(ta . G . b)
)$

absolute(a, G) := ratsimp(sqrt(geom(a, a, G)))$

anglcos(a, b, G) := block([denom],
    denom : absolute(a, G) * absolute(b, G),
    ratsimp(geom(a, b, G) / denom)
)$

MinkMatrix : ematrix(4, 4, 2, 1, 1) - ident(4)$

mink(a, b) := geom(a, b, MinkMatrix)$

tminknorm(a) := sqrt(mink(a,a))$

sminknorm(a) := sqrt(-mink(a,a))$

minknorm(a) := block(
    if mink(a, a) < 0 then
        sqrt(-mink(a, a))
    else
        sqrt(mink(a, a))
)$

hypangcos(a, b) := ratsimp(mink(a, b) / (tminknorm(a) * tminknorm(b)))$