list0 = List(6,3,1,8,7,1,2,5,8,4,3,4,8)
list1 = List(1,1,2,3,3,4,4,5,6,7,8,8,8)
list2 = List(1,1,2,3,3,4,4,5,6,7,8,8,8)
list3 = List(1,1,2,3,3,4,4,5,6,7,8,8,8)
list4 = List(1,1,2,3,3,4,4,5,6,7,8,8,8)
list5 = List(8,8,8,7,6,5,4,4,3,3,2,1,1)
list6 = List(8,8,8,7,6,5,4,4,3,3,2,1,1)

list0: List() -> List()
list1: List(0) -> List(0)
list2: List(0,1) -> List(0,1)
list3: List(1,0) -> List(0,1)
list4: List(0,1,2) -> List(0,1,2)
list5: List(1,0,2) -> List(0,1,2)
list6: List(0,1,2) -> List(0,1,2)
list7: List(1,0,2) -> List(0,1,2)
list8: List(2,0,1) -> List(0,1,2)
list9: List(2,1,0) -> List(0,1,2)
listA: List(6,3,1,8,7,1,2,5,8,4) -> List(1,1,2,3,4,5,6,7,8,8)

f(x) = 5x^3+7x^2+5x+9
f(0) = 9
f(1) = 26
f(2) = 87
f(3) = 222

v1        = List(2,3,4)
v2        = List(6,7,8)

id        = List(List(1,0,0),List(0,1,0),List(0,0,1))
m1        = List(List(2,0,0),List(0,2,0),List(0,0,2))
m2        = List(List(1,2,3),List(4,5,6),List(7,8,9))

v1 * v1   = 29
v1 * v2   = 65
v2 * v1   = 65
v1 * v2   = 65

id * v1   = List(2,3,4)
m1 * v1   = List(4,6,8)
m2 * v1   = List(20,47,74)

trn(id)   = List(List(1,0,0),List(0,1,0),List(0,0,1))
trn(m1)   = List(List(2,0,0),List(0,2,0),List(0,0,2))
trn(m2)   = List(List(1,4,7),List(2,5,8),List(3,6,9))

List(v1) * id = List(List(2,3,4))
List(v1) * m1 = List(List(4,6,8))
List(v1) * m2 = List(List(42,51,60))

id * List(v1) = List(List(2,3,4),List(0,0,0),List(0,0,0))
m1 * List(v1) = List(List(4,6,8),List(0,0,0),List(0,0,0))
m2 * List(v1) = List(List(2,3,4),List(8,12,16),List(14,21,28))

id * id   = List(List(1,0,0),List(0,1,0),List(0,0,1))
id * m1   = List(List(2,0,0),List(0,2,0),List(0,0,2))
m1 * id   = List(List(2,0,0),List(0,2,0),List(0,0,2))
m1 * m1   = List(List(4,0,0),List(0,4,0),List(0,0,4))
id * m2   = List(List(1,2,3),List(4,5,6),List(7,8,9))
m2 * id   = List(List(1,2,3),List(4,5,6),List(7,8,9))
m1 * m2   = List(List(2,4,6),List(8,10,12),List(14,16,18))
m2 * m1   = List(List(2,4,6),List(8,10,12),List(14,16,18))
m2 * m2   = List(List(30,36,42),List(66,81,96),List(102,126,150))