list0 = [6,3,1,8,7,1,2,5,8,4,3,4,8]
list1 = [1,1,2,3,3,4,4,5,6,7,8,8,8]
list2 = [1,1,2,3,3,4,4,5,6,7,8,8,8]
list3 = [1,1,2,3,3,4,4,5,6,7,8,8,8]
list4 = [1,1,2,3,3,4,4,5,6,7,8,8,8]
list5 = [8,8,8,7,6,5,4,4,3,3,2,1,1]
list6 = [8,8,8,7,6,5,4,4,3,3,2,1,1]

f(x) = 5x^3+7x^2+5x+9
f(0) = 9.0
f(1) = 26.0
f(2) = 87.0
f(3) = 222.0

v1        = [2.0,3.0,4.0]
v2        = [6.0,7.0,8.0]

id        = [[1.0,0.0,0.0],[0.0,1.0,0.0],[0.0,0.0,1.0]]
m1        = [[2.0,0.0,0.0],[0.0,2.0,0.0],[0.0,0.0,2.0]]
m2        = [[1.0,2.0,3.0],[4.0,5.0,6.0],[7.0,8.0,9.0]]

v1 * v1   = 29.0
v1 * v2   = 65.0
v2 * v1   = 65.0
v1 * v2   = 65.0

id * v1   = [2.0,3.0,4.0]
m1 * v1   = [4.0,6.0,8.0]
m2 * v1   = [20.0,47.0,74.0]

trn(id)   = [[1.0,0.0,0.0],[0.0,1.0,0.0],[0.0,0.0,1.0]]
trn(m1)   = [[2.0,0.0,0.0],[0.0,2.0,0.0],[0.0,0.0,2.0]]
trn(m2)   = [[1.0,4.0,7.0],[2.0,5.0,8.0],[3.0,6.0,9.0]]

[v1] * id = [[2.0,3.0,4.0]]
[v1] * m1 = [[4.0,6.0,8.0]]
[v1] * m2 = [[42.0,51.0,60.0]]

id * [v1] = [[2.0,3.0,4.0],[0.0,0.0,0.0],[0.0,0.0,0.0]]
m1 * [v1] = [[4.0,6.0,8.0],[0.0,0.0,0.0],[0.0,0.0,0.0]]
m2 * [v1] = [[2.0,3.0,4.0],[8.0,12.0,16.0],[14.0,21.0,28.0]]

id * id   = [[1.0,0.0,0.0],[0.0,1.0,0.0],[0.0,0.0,1.0]]
id * m1   = [[2.0,0.0,0.0],[0.0,2.0,0.0],[0.0,0.0,2.0]]
m1 * id   = [[2.0,0.0,0.0],[0.0,2.0,0.0],[0.0,0.0,2.0]]
m1 * m1   = [[4.0,0.0,0.0],[0.0,4.0,0.0],[0.0,0.0,4.0]]
id * m2   = [[1.0,2.0,3.0],[4.0,5.0,6.0],[7.0,8.0,9.0]]
m2 * id   = [[1.0,2.0,3.0],[4.0,5.0,6.0],[7.0,8.0,9.0]]
m1 * m2   = [[2.0,4.0,6.0],[8.0,10.0,12.0],[14.0,16.0,18.0]]
m2 * m1   = [[2.0,4.0,6.0],[8.0,10.0,12.0],[14.0,16.0,18.0]]
m2 * m2   = [[30.0,36.0,42.0],[66.0,81.0,96.0],[102.0,126.0,150.0]]