Lua高斯消元：增广矩阵的逐列消元

local function eliminate(a, n)
    for col = 1, n do
        for row = col + 1, n do
            local f = a[row][col] / a[col][col]
            for j = col, n + 1 do
                a[row][j] = a[row][j] - f * a[col][j]
            end
        end
    end
end

local function solve(a, n)
    eliminate(a, n)
    local x = {}
    for i = n, 1, -1 do
        local s = a[i][n + 1]
        for j = i + 1, n do
            s = s - a[i][j] * x[j]
        end
        x[i] = s / a[i][i]
    end
    return x
end
local p = getplayerbyname("gauss01")
-- x+y=5, y+z=7, x+z=6
local x = solve({{1, 1, 0, 5},
    {0, 1, 1, 7}, {1, 0, 1, 6}}, 3)
sendmsg(p, 1, x[1] .. "," .. x[2] .. "," .. x[3])