613.sagews

'Vektory'

'Vektory'

u = vector([2, -1, 0]) #definice vektoru
v = vector([-1, 5, 3])
u; v

(2, -1, 0) (-1, 5, 3)

u + v #scitani vektoru

(1, 4, 3)

u*v #nasobeni vektoru

-7

3*u - 2*v #linearni kombinace

(8, -13, -6)

'Matice'

'Matice'

A = matrix([[1, -6, 4, 0], [-4, 3, 8, 7]]) #definice matice
A

[ 1 -6 4 0] [-4 3 8 7]

B = matrix([[2, -5], [3, 4], [-7, 1], [-2, 8]])
B

[ 2 -5] [ 3 4] [-7 1] [-2 8]

A*B #nasobeni matic

[-44 -25] [-69 96]

B*A

[ 22 -27 -32 -35] [-13 -6 44 28] [-11 45 -20 7] [-34 36 56 56]

transpose(A) #vypocet transponovane matice

[ 1 -4] [-6 3] [ 4 8] [ 0 7]

rank(A) #hodnost matice

2

rank(B*A)

2

det(A*B) #vypocet determinantu matice

-5949

'Reseni rovnic a jejich soustav'

'Reseni rovnic a jejich soustav'

solve(x^2 + 4*x - 2 == 0, x) #reseni jednoduche rovnice

[x == -sqrt(6) - 2, x == sqrt(6) - 2]

x, y = var('x, y')
solve([x - y == 2, x + y == 10], [x, y]) #reseni soustavy rovnic

[[x == 6, y == 4]]

solve(sin(x) == 1, x) #Sage nevrati vzdy vsechna reseni

[x == 1/2*pi]

p = solve(x^2 + 4*x == 2, x, solution_dict = True); p

[{x: -sqrt(6) - 2}, {x: sqrt(6) - 2}]

for sol in p: print(n(sol[x], digits = 3)) #numericka aproxiamce reseni

-4.45 0.449