function solve(m, v) {
if(v.length !== m.length) {
return null
}
var decomp = lu(m)
if(!decomp) {
return null
}
var n = m.length
var Y = new Array(n)
for(var j=0; j<n; j++) {
var c = rat(0)
for(var i=0; i<j; i++) {
c = add(c, mul(L[i][j], Y[i]))
}
Y[j] = div(sub(v[j], c), L[j][j])
}
var X = new Array(n)
for(var j=n-1; j>=0; j--) {
var c = rat(0)
for (var i=n-1; i>j; i--) {
c = add(c, mul(U[i][j], X[i]));
}
X[j] = sub(Y[j], c)
}
return X
}
function det(m) {
var U = lu(m)
if(!U) {
return 0
}
U = U[0]
var d = rat(1)
for(var i=0; i<U.length; ++i) {
d = mul(d, U[i][i])
}
return d
}