use math.la: vector, matrix
use sys: exit

function error(s)
   print("Error in test-la: test ", s, " failed.")
   exit(1)
end

if 2*vector(1,2) != vector(2,4)
   error("#1.1")
end

if vector(1,2)+vector(3,4) != vector(4,6)
   error("#1.2")
end

if vector(1,2)*vector(3,4) != 11
   error("#1.3")
end

v = vector(1,2,3)
w = vector(4,5,6)

if 2*v+4*w != vector(18,24,30)
   error("#1.4")
end

if 5*v-3*w != vector(-7,-5,-3)
   error("#1.5")
end

if v*w != 32 or w*v != 32
   error("#1.6")
end

if (11*v)*(12*w) != 132*(v*w)
   error("#1.7")
end

if (v+w)*(v-w) != v*v-v*w+w*v-w*w
   error("#1.8")
end

if (v+w)*(v-w) != v*v-w*w
   error("#1.9")
end

if (v+w)*(v+w) != v*v+2*w*v+w*w
   error("#1.10")
end

A = matrix(
   [1,2],
   [3,4]
)

B = matrix(
   [5,6],
   [7,8]
)

v = vector(1,2)

if 2*A != matrix([2,4],[6,8])
   error("#2.1")
end

if 2*A != A+A or 3*A != A+A+A or 4*A != A+A+A+A
   error("#2.2")
end

if A.T.T != A
   error("#2.3")
end

if A*B != matrix([19,22],[43,50])
   error("#2.4")
end

if A*B != (B.T*A.T).T
   error("#2.5")
end

if A*B-(B.T*A.T).T != matrix([0,0],[0,0])
   error("#2.6")
end

if A*v != vector(5,11)
   error("#2.7")
end

if (A*A)*v != A*(A*v)
   error("#2.8")
end

if (A*B)*v != A*(B*v)
   error("#2.9")
end

if (A*v)*v != v*(A*v)
   error("#2.10")
end

A = matrix(
   [1,2,3],
   [4,5,6]
)

B = matrix(
   [7,8,9],
   [10,11,12]
)

Z2 = matrix([0,0],[0,0])
Z3 = matrix([0,0,0],[0,0,0],[0,0,0])
v = vector(1,2,3)

if A*B.T != matrix([50,68],[122,167])
   error("#3.1")
end

if A.T*B != matrix([47,52,57],[64,71,78],[81,90,99])
   error("#3.2")
end

if (A*B.T).T != B*A.T
   error("#3.3")
end

if (A*B.T).T-B*A.T != Z2 or B*A.T-(A*B.T).T != Z2
   error("#3.4")
end

if A*B.T != (B*A.T).T
   error("#3.5")
end

if A*B.T-(B*A.T).T != Z2 or (B*A.T).T-A*B.T != Z2
   error("#3.6")
end

if (A.T*B).T != B.T*A
   error("#3.7")
end

if (A.T*B).T-B.T*A != Z3 or B.T*A-(A.T*B).T != Z3
   error("#3.8")
end

if A*v != vector(14,32)
   error("#3.9")
end

A = matrix(
   [1,2,3],
   [4,5,6]
)

B = matrix(
   [7,10],
   [8,11],
   [9,12]
)

if A*B != matrix([50,68],[122,167])
   error("#4.1")
end

if (A*B).T != B.T*A.T
   error("#4.2")
end

if (A*B).T-B.T*A.T != Z2 or B.T*A.T-(A*B).T != Z2
   error("#4.3")
end

if B*A != matrix([47,64,81],[52,71,90],[57,78,99])
   error("#4.4")
end

if (B*A).T != A.T*B.T or A.T*B.T != (B*A).T
   error("#4.5")
end

if (B*A).T-A.T*B.T != Z3 or A.T*B.T-(B*A).T != Z3
   error("#4.6")
end