2341.sagews

var("t, u, v, z")
g = t^3 + 5/u + 3*log(v) - 2*tan(z)
show(g)
show("variables:")
show(g.variables())

def quadruple_integral(f, x, a, b, y, c, d, z, e, g, w, h, i):
    return integral(integral(integral(integral(f, x, a, b), y, c, d), z, e, g), w, h, i)
show(quadruple_integral(g, t, 3, 4, u, 67, 89, v, 12, 22, z, -9, 3).n())

show(g.integrate(t, 3, 4).integrate(u, 67, 89).integrate(v, 12, 22).integrate(z, -9, 3).n())
show(g.limit(t=12).limit(u=13).limit(z=65).limit(v=23).n())
h=g(u=1,v=10,z=9)
h.plot()

\newcommand{\Bold}[1]{\mathbf{#1}}t^{3} + \frac{5}{u} + 3 \, \log\left(v\right) - 2 \, \tan\left(z\right)

\newcommand{\Bold}[1]{\mathbf{#1}}\hbox{variables:}

\newcommand{\Bold}[1]{\mathbf{#1}}\left(t, u, v, z\right)

\newcommand{\Bold}[1]{\mathbf{#1}}138028.662213126

\newcommand{\Bold}[1]{\mathbf{#1}}138028.662213126

\newcommand{\Bold}[1]{\mathbf{#1}}1740.73117454773

C = Matrix([[1 , i], [2 , 2*i]])
show(C)
#show(C.eigenvectors_left())
show(C.adjoint())
show(C^3)

\newcommand{\Bold}[1]{\mathbf{#1}}\left($$\begin{array}{rr} 1 & i \\ 2 & 2 i \end{array}$$\right)

\newcommand{\Bold}[1]{\mathbf{#1}}\left($$\begin{array}{rr} 2 i & -i \\ -2 & 1 \end{array}$$\right)

\newcommand{\Bold}[1]{\mathbf{#1}}\left($$\begin{array}{rr} 4 i - 3 & -3 i - 4 \\ 8 i - 6 & -6 i - 8 \end{array}$$\right)

f=41*x^2/12 - 21*x^3/10
g=x
f.plot()+g.plot()

B = Matrix([[i, 2, -1], [3, 1+i, 2], [-2*i, 1, 4-i]])
show(B)
#show(B.jordan_form())
show(B.det())
C = Matrix([[1, 0, -2, 3], [-3, 1, 1, 2], [0, 4, -1, 1], [2, 3, 0, 1]])
show(C)
show(C.decomposition())
show(C.det())

\newcommand{\Bold}[1]{\mathbf{#1}}\left($$\begin{array}{rrr} i & 2 & -1 \\ 3 & i + 1 & 2 \\ -2 i & 1 & -i + 4 \end{array}$$\right)

\newcommand{\Bold}[1]{\mathbf{#1}}-i - 28

\newcommand{\Bold}[1]{\mathbf{#1}}\left($$\begin{array}{rrrr} 1 & 0 & -2 & 3 \\ -3 & 1 & 1 & 2 \\ 0 & 4 & -1 & 1 \\ 2 & 3 & 0 & 1 \end{array}$$\right)

\newcommand{\Bold}[1]{\mathbf{#1}}\left[\left(\Bold{Z}^{4}, {\rm True}\right)\right]

\newcommand{\Bold}[1]{\mathbf{#1}}95

Matrix([[19, -43], [-11, 28]]).det()

\newcommand{\Bold}[1]{\mathbf{#1}}59

T=Matrix([[-3, 3, -2], [-7, 6, -3], [1, -1, 2]])
show(T)
show(T^2)

\newcommand{\Bold}[1]{\mathbf{#1}}\left($$\begin{array}{rrr} -3 & 3 & -2 \\ -7 & 6 & -3 \\ 1 & -1 & 2 \end{array}$$\right)

\newcommand{\Bold}[1]{\mathbf{#1}}\left($$\begin{array}{rrr} -14 & 11 & -7 \\ -24 & 18 & -10 \\ 6 & -5 & 5 \end{array}$$\right)

show(T.eigenvalues())
show(T.jordan_form())

\newcommand{\Bold}[1]{\mathbf{#1}}\left[1, 2, 2\right]

\newcommand{\Bold}[1]{\mathbf{#1}}\left(ParseError: KaTeX parse error: Expected '\right', got 'EOF' at end of input: …} 1 \end{array}\right) & \left($$\begin{array}{rr} 0 & 0 \end{array}$$\right) \\ \left($$\begin{array}{r} 0 \\ 0 \end{array}$$\right) & \left($$\begin{array}{rr} 2 & 1 \\ 0 & 2 \end{array}$$\right) \end{array}\right)

var('a')
T=Matrix([[-3-a, 3, -2], [-7, 6-a, -3], [1, -1, 2-a]])
show(T.det().expand().factor())

\newcommand{\Bold}[1]{\mathbf{#1}}-{\left(a - 2\right)}^{2} {\left(a - 1\right)}

T=Matrix([[-3, -7, 1], [3, 6, -1], [-2, -3, 2]])
U=Matrix([[-3, 3, -2], [-7, 6, -3], [1, -1, 2]])
I=identity_matrix(3)
a=1
show((T-a*I).kernel())
show(((T-a*I)^2).kernel())
show(((T-a*I)^3).kernel())
M=Matrix([[3],[6],[3]])
show(((U-a*I)^1)*M)

\newcommand{\Bold}[1]{\mathbf{#1}}\mathrm{RowSpan}_{\Bold{Z}}\left($$\begin{array}{rrr} 1 & 2 & 1 \end{array}$$\right)

\newcommand{\Bold}[1]{\mathbf{#1}}\mathrm{RowSpan}_{\Bold{Z}}\left($$\begin{array}{rrr} 1 & 2 & 1 \end{array}$$\right)

\newcommand{\Bold}[1]{\mathbf{#1}}\mathrm{RowSpan}_{\Bold{Z}}\left($$\begin{array}{rrr} 1 & 2 & 1 \end{array}$$\right)

\newcommand{\Bold}[1]{\mathbf{#1}}\left($$\begin{array}{r} 0 \\ 0 \\ 0 \end{array}$$\right)

var('a1, a2, a3, b1, b2, b3, c1, c2, c3, k')
M=Matrix([[b1+c1, b2+c2, b3+c3],[a1+c1, a2+c2, a3+c3],[a1+b1, a2+b2, a3+b3]])
N=Matrix([[a1, a2, a3],[b1, b2, b3],[c1, c2, c3]])
show(M)
show(N)
show(M.det().expand())
show(N.det().expand())
solve([M.det()==k*N.det()],k)

\newcommand{\Bold}[1]{\mathbf{#1}}\left($$\begin{array}{rrr} b_{1} + c_{1} & b_{2} + c_{2} & b_{3} + c_{3} \\ a_{1} + c_{1} & a_{2} + c_{2} & a_{3} + c_{3} \\ a_{1} + b_{1} & a_{2} + b_{2} & a_{3} + b_{3} \end{array}$$\right)

\newcommand{\Bold}[1]{\mathbf{#1}}\left($$\begin{array}{rrr} a_{1} & a_{2} & a_{3} \\ b_{1} & b_{2} & b_{3} \\ c_{1} & c_{2} & c_{3} \end{array}$$\right)

\newcommand{\Bold}[1]{\mathbf{#1}}2 \, a_{1} b_{2} c_{3} - 2 \, a_{1} b_{3} c_{2} - 2 \, a_{2} b_{1} c_{3} + 2 \, a_{2} b_{3} c_{1} + 2 \, a_{3} b_{1} c_{2} - 2 \, a_{3} b_{2} c_{1}

\newcommand{\Bold}[1]{\mathbf{#1}}a_{1} b_{2} c_{3} - a_{1} b_{3} c_{2} - a_{2} b_{1} c_{3} + a_{2} b_{3} c_{1} + a_{3} b_{1} c_{2} - a_{3} b_{2} c_{1}

\newcommand{\Bold}[1]{\mathbf{#1}}\left[k = 2\right]