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) = 9.0
f(1) = 26.0
f(2) = 87.0
f(3) = 222.0

v1        = List(2.0,3.0,4.0)
v2        = List(6.0,7.0,8.0)

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

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

id * v1   = List(2.0,3.0,4.0)
m1 * v1   = List(4.0,6.0,8.0)
m2 * v1   = List(20.0,47.0,74.0)

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

List(v1) * id = List(List(2.0,3.0,4.0))
List(v1) * m1 = List(List(4.0,6.0,8.0))
List(v1) * m2 = List(List(42.0,51.0,60.0))

id * List(v1) = List(List(2.0,3.0,4.0),List(0.0,0.0,0.0),List(0.0,0.0,0.0))
m1 * List(v1) = List(List(4.0,6.0,8.0),List(0.0,0.0,0.0),List(0.0,0.0,0.0))
m2 * List(v1) = List(List(2.0,3.0,4.0),List(8.0,12.0,16.0),List(14.0,21.0,28.0))

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