(0,1,0)

(0,0,1)

(1,0,0)

(1,0,0)

(0,1,0)

(0,0,1)

(0,1,0)

(1,0,0)

(0,0,1)

(0,0,0)

\mathcal{R}

(x,y,z)

(0,0,0)

(1,0,0)

(0,1,0)

(0,0,1)

\operatorname{Vect}(v_1)

\operatorname{Vect}(v_1,v_2)

\operatorname{Vect}(v_1,v_2,v_3)

\operatorname{Vect}(

,

)

v=(x,y,z)

,

)

v_1

v_2

v_3

v_1

v_2

v_3

v_1

v_2

)

v_1

=

v_1

v_1

ax+by+cz=d

\tau(v_1,v_2,v_3)

t_1 v_1

,\quad t_2=

t_1v_1+t_2v_2

,\quad t_2=

,\quad t_3=

t_1v_1+t_2v_2+t_3v_3

\left\{\begin{array} ax+by+cz=d \ 
a'x+b'y+c'z=d' \end{array}\right.

\left\{\begin{array}\textcolor{white}{i} \ 
\textcolor{white}{i}\ 
\textcolor{white}{i}\end{array}\right. 

=

=

v_1

v_2

\text{unité sur }(Ox)=

\text{unité sur }(Oy)=

\text{angle entre }(Ox)\text{ et }(Oy)=

\text{unité sur }(Oz)=

\text{angle entre }(Oz)\text{ et }(Oxy)=

\text{angle entre }(Ox)\text{ et le projeté de }(Oz)\text{ sur }(Oxy)=

t_1=

t_1v_1

t_2v_2

t_1=

t_1v_1

t_2v_2

t_3v_3

v

[v]_{\mathcal{B}}

[v]_{\mathcal{B}}=P^{-1}\left(\begin{array}x \ y \ z\end{array}\right)=\left(\begin{array}\textcolor{orange}{t_1} \ \textcolor{blue}{t_2} \ \textcolor{green}{t_3}\end{array}\right)\

\vspace{10mm}

 v=(x,y,z),\quad\mathcal{B}=v_1,v_2,v_3  

t_1v_1

t_2v_2

t_3v_3

t_1v_1+t_2v_2+t_3v_3

t_1v_1+t_2v_2

t_1v_1

t_2v_2

[v]_{\mathcal{B}}

[v]_{\mathcal{B}}=\left(\begin{array}{} \textcolor{orange}{t_1} \ \textcolor{blue}{t_2} \end{array}\right),\quad \mathcal{B}=v_1,v_2

t_1v_1

[v]_{\mathcal{B}}

[v]_{\mathcal{B}}=\textcolor{orange}{t_1},\quad \mathcal{B}=v_1

=\textcolor{orange}{t_1v_1}

f(x,y,z)=(

,

,

)

f:\mathbb{R}^3\rightarrow\mathbb{R}^3

f(v)=f(x,y,z)

A

[v]_{\mathcal{B}}=\left(\begin{array}\textcolor{orange}{t_1} \ \textcolor{blue}{t_2} \ \textcolor{green}{t_3}\end{array}\right)\

\vspace{10mm}

 v=(x,y,z),\quad\mathcal{B}=v_1,v_2,v_3  

x(1,0,0)

y(0,1,0)

z(0,0,1)

[f(v)]_{\mathcal{B}}

[f]_{\mathcal{B}}

[f(v)]_{\mathcal{B}}=[f]_{\mathcal{B}}[v]_{\mathcal{B}}

j_{12} = 4 (slider from 1 to 5, step 1)
n_2 = 1 (slider from 1 to 5, step 1)
j_5 = 1 (slider from -2 to 1, step 1)
n_6 = 1 (slider from 1 to 3, step 1)
h_8 = 0 (slider from -50 to 50, step 0.01)
u_7(x, y, z) = y
d_8: u_7(0, 0, 1)
c_8: u_7(0, 1, 0)
b_8: u_7(1, 0, 0)
P_4: (b_8, c_8, d_8)
f_8: b_8^(2) + c_8^(2) + d_8^(2)
c_7(x, y, z) = x
v_7: c_7(1, 0, 0)
w_7: c_7(0, 1, 0)
a_8: c_7(0, 0, 1)
m16: {{v_7, w_7, a_8}, {b_8, c_8, d_8}}
o_8 = MatrixRank(m16)
e_8: v_7^(2) + w_7^(2) + a_8^(2)
N_4: (v_7, w_7, a_8)
g_8 = 0 (slider from -50 to 50, step 0.01)
p: z = 0
C = PointIn(p)
D = (1.4197644572062842, 2.0630524240891077, 7.203530954474189)
B = Point(xAxis)
a = 1 (slider from 0 to 10, step 0.1)
E: (a, 0, 0)
b = 1 (slider from 0 to 10)
c = 1 (slider from 0 to 10)
α = 1.5707963267948966 rad (slider from -3.141592653589793 to 3.141592653589793, step 0.017453292519943295)
F: ((b * cos(α)), (b * sin(α)), 0)
β = 0 rad (slider from -3.141592653589793 to 3.141592653589793, step 0.017453292519943295)
γ = 1.5707963267948966 rad (slider from -1.5707963267948966 to 1.5707963267948966, step 0.017453292519943295)
G: (((c * cos(γ)) * cos(β)), ((c * cos(γ)) * sin(β)), (c * sin(γ)))
n = 0 (slider from 0 to 1, step 1)
I = If(n ≟ 0, C, F)
H = If(n ≟ 0, B, E)
J = If(n ≟ 0, D, G)
m1: {{x(H), x(I), x(J)}, {y(H), y(I), y(J)}, {z(H), z(I), z(J)}}
w = Determinant(m1)
m2 = If(w ≟ 0, {{0, 0, 0}, {0, 0, 0}, {0, 0, 0}}, m1^(-1))
m14 = Transpose(m2)
Q_4: (m14 * P_4)
q_8 = If(w ≟ 0 ∨ f_8 ≟ 0, z = 0, (x(Q_4) * x) + (y(Q_4) * y) + (z(Q_4) * z) = h_8)
O_4: (m14 * N_4)
p_8 = If(w ≟ 0 ∨ e_8 ≟ 0, z = 0, (x(O_4) * x) + (y(O_4) * y) + (z(O_4) * z) = g_8)
m_8 = If(o_8 ≟ 2, IntersectPath[p_8, q_8], Line[(0, 0, 0), (1, 0, 0)])
u_3(x, y, z) = x + y
w_3: u_3(1, 0, 0)
o_4: u_3(0, 1, 0)
u_4: u_3(0, 0, 1)
K_3: (w_3, o_4, u_4)
e_5: w_3^(2) + o_4^(2) + u_4^(2)
v_3 = 0 (slider from -60 to 60, step 0.1)
L_3: (m14 * K_3)
q_5 = If(w ≟ 0 ∨ e_5 ≟ 0, z = 0, (x(L_3) * x) + (y(L_3) * y) + (z(L_3) * z) = v_3)
F_1: (0, 0, 0)
E_1: (0, 0, 0)
s: (y(E_1) * z(F_1)) - (z(E_1) * y(F_1))
r: (x(E_1) * z(F_1)) - (z(E_1) * x(F_1))
q: (x(E_1) * y(F_1)) - (x(F_1) * y(E_1))
A: (0, 0, 0)
J_1: (m1 * F_1)
I_1: (m1 * E_1)
p_1 = If((q, r, s) ≟ (0, 0, 0) ∨ w ≟ 0, p, Plane[A, I_1, J_1])
n_3 = 1 (slider from -2 to 1, step 1)
N_1: (2, 3, 4)
m_2 = 0 (slider from 0 to 1, step 1)
O_1: (m1 * N_1)
H_3: (0, 0, 0)
h_{12}: ¬(H_3 ≟ (0, 0, 0))
I_3: (m1 * H_3)
l_5 = If(w ≟ 0 ∨ H_3 ≟ (0, 0, 0), Line[(0, 0, 0), (1, 0, 0)], Line[A, I_3])
K_1 = (6.024626150394312, 48.37006999218724, 12.290194142062902)
P_1 = If(m_2 ≟ 0, K_1, O_1)
C_3: (0, 0, 0)
B_3: (0, 0, 0)
m13: {{x(B_3), x(C_3)}, {y(B_3), y(C_3)}, {z(B_3), z(C_3)}}
o_3 = MatrixRank(m13)
E_3: (m1 * C_3)
D_3: (m1 * B_3)
p_5 = If((¬(o_3 ≟ 2)) ∨ w ≟ 0, p, Plane[A, D_3, E_3])
ChampTexte1 = Textfield(a)
ChampTexte2 = Textfield(b)
ChampTexte3 = Textfield(c)
ChampTexte4 = Textfield(α)
ChampTexte5 = Textfield(β)
ChampTexte6 = Textfield(γ)
K: (x(A), y(A), z(A))
f = Line(A, (1, 0, 0))
d = Distance(A, I)
g = If(d ≟ 0, f, Line[A, I])
e = Distance(A, J)
h = If(e ≟ 0, f, Line[A, J])
i = true
j = true
k = 0 (slider from 0 to 8, step 1)
L: (0, 0, 0)
ChampTexte7 = Textfield(L)
M: (0, 0, 0)
ChampTexte8 = Textfield(M)
N: (m1 * L)
O: (m1 * M)
texte3: "" + (LaTeX[L]) + ""
texte4: "" + (LaTeX[M]) + ""
P: (0, 0, 0)
Q: (0, 0, 0)
R: (0, 0, 0)
S: (0, 0, 0)
T: (0, 0, 0)
ChampTexte9 = Textfield(P)
ChampTexte10 = Textfield(Q)
ChampTexte11 = Textfield(R)
ChampTexte12 = Textfield(S)
ChampTexte13 = Textfield(T)
U: (0, 0, 0)
ChampTexte14 = Textfield(U)
V: (m1 * P)
W: (m1 * Q)
Z: (m1 * R)
A_1: (m1 * S)
B_1: (m1 * T)
C_1: (m1 * U)
texte5: "" + (LaTeX[P]) + ""
texte6: "" + (LaTeX[Q]) + ""
texte7: "" + (LaTeX[R]) + ""
texte8: "" + (LaTeX[S]) + ""
texte9: "" + (LaTeX[T]) + ""
texte10: "" + (LaTeX[U]) + ""
l = 1 (slider from 0 to 1, step 1)
m = 1 (slider from 0 to 1, step 1)
n_1 = 1 (slider from 0 to 1, step 1)
i_1 = 1 (slider from 0 to 1, step 1)
j_1 = 1 (slider from 0 to 1, step 1)
k_1 = 1 (slider from 0 to 1, step 1)
l_1 = 1 (slider from 0 to 1, step 1)
m_1 = 1 (slider from 0 to 1, step 1)
o = false
D_1 = (1.1, 10.02)
i_2 = 1 (slider from 1 to 2, step 1)
ChampTexte15 = Textfield(E_1)
ChampTexte16 = Textfield(F_1)
G_1 = (2.0400000000000014, 10.019999999999987)
H_1 = (4.240000000000002, 10.039999999999987)
texte21: "" + (LaTeX[E_1]) + ""
texte22: "" + (LaTeX[F_1]) + ""
j_2 = 1 (slider from -3 to 1, step 1)
u: q^(2) + r^(2) + s^(2)
v: (x(E_1))^(2) + (y(E_1))^(2) + (z(E_1))^(2) + (x(F_1))^(2) + (y(F_1))^(2) + (z(F_1))^(2)
l_2 = 1 (slider from -2 to 2, step 1)
ChampTexte17 = Textfield(N_1)
M_1 = If((¬(u ≟ 0)) ∧ P_1 ∈ p_1 ∧ (¬(w ≟ 0)), Intersect[Line[A, J_1], Line[P_1, Vector[A, I_1]]], (0, 0, 0))
L_1 = If((¬(u ≟ 0)) ∧ P_1 ∈ p_1 ∧ (¬(w ≟ 0)), Intersect[Line[A, I_1], Line[P_1, Vector[A, J_1]]], (0, 0, 0))
t = If((q, r, s) ≟ (0, 0, 0) ∧ (¬(E_1 ≟ (0, 0, 0))) ∧ (¬(w ≟ 0)), Line[A, I_1], (q, r, s) ≟ (0, 0, 0) ∧ (¬(F_1 ≟ (0, 0, 0))) ∧ (¬(w ≟ 0)), Line[A, J_1], Line[(0, 0, 0), (1, 0, 0)])
f_1 = If(u ≟ 0 ∨ w ≟ 0, Line[(0, 0, 0), (0, 0, 1)], Line[A, J_1])
g_1 = If(u ≟ 0 ∨ w ≟ 0, Line[(0, 0, 0), (0, 0, 1)], Line[A, I_1])
poly1, h_1, q_1, r_1, s_1, t_1 = Polygon(A, L_1, P_1, M_1, A)
a_1 = Segment(P_1, L_1)
b_1 = Segment(P_1, M_1)
Q_1: (m2 * P_1)
R_1: (x(Q_1) * H)
S_1: (y(Q_1) * I)
T_1: R_1 + S_1
U_1: (z(Q_1) * J)
V_1: U_1 + R_1
W_1: U_1 + S_1
c_1 = Segment(P_1, V_1)
d_1 = Segment(P_1, W_1)
e_1 = Segment(P_1, T_1)
f_2 = Segment(U_1, V_1)
g_2 = Segment(R_1, V_1)
h_2 = Segment(W_1, S_1)
p_2 = Segment(U_1, W_1)
q_2 = Segment(R_1, T_1)
r_2 = Segment(T_1, S_1)
s_2 = Segment(R_1, A)
t_2 = Segment(U_1, A)
a_2 = Segment(S_1, A)
Z_1: (0, 0, 0)
A_2: (0, 0, 0)
B_2: (0, 0, 0)
ChampTexte18 = Textfield(Z_1)
ChampTexte19 = Textfield(A_2)
ChampTexte20 = Textfield(B_2)
C_2: (m1 * Z_1)
D_2: (m1 * A_2)
E_2: (m1 * B_2)
i_3 = 1 (slider from -2 to 1, step 1)
j_3 = 1 (slider from -1 to 2, step 1)
texte30: "" + (LaTeX[Z_1]) + ""
texte31: "" + (LaTeX[A_2]) + ""
texte32: "" + (LaTeX[B_2]) + ""
m3: {{x(Z_1), x(A_2), x(B_2)}, {y(Z_1), y(A_2), y(B_2)}, {z(Z_1), z(A_2), z(B_2)}}
o_1 = Determinant(m3)
u_1: (w * o_1)
m4 = If(o_1 ≟ 0, {{0, 0, 0}, {0, 0, 0}, {0, 0, 0}}, m3^(-1))
F_2: ((m4 * m2) * P_1)
G_2: (x(F_2) * C_2)
H_2: (y(F_2) * D_2)
I_2: (z(F_2) * E_2)
J_2: I_2 + H_2
K_2: H_2 + G_2
L_2: I_2 + G_2
e_2 = Segment(P_1, L_2)
f_3 = Segment(P_1, K_2)
g_3 = Segment(P_1, J_2)
h_3 = Segment(G_2, L_2)
k_3 = Segment(I_2, L_2)
l_3 = Segment(K_2, H_2)
m_3 = Segment(J_2, H_2)
p_3 = Segment(I_2, J_2)
q_3 = Segment(G_2, K_2)
r_3 = Segment(A, I_2)
s_3 = Segment(A, H_2)
t_3 = Segment(G_2, A)
v_1 = MatrixRank(m3)
m5: {{x(Z_1), x(A_2)}, {y(Z_1), y(A_2)}, {z(Z_1), z(A_2)}}
m6: {{x(Z_1), x(B_2)}, {y(Z_1), y(B_2)}, {z(Z_1), z(B_2)}}
m7: {{x(A_2), x(B_2)}, {y(A_2), y(B_2)}, {z(A_2), z(B_2)}}
w_1 = MatrixRank(m5)
o_2 = MatrixRank(m6)
u_2 = MatrixRank(m7)
f_4 = If((¬(v_1 ≟ 2)) ∨ w ≟ 0, p, w_1 ≟ 2, Plane[A, C_2, D_2], o_2 ≟ 2, Plane[A, C_2, E_2], Plane[A, D_2, E_2])
c_2 = If(w ≟ 0 ∨ A_2 ≟ (0, 0, 0), Line[A, (1, 0, 0)], Line[A, D_2])
d_2 = Textfield(B_2)
a_3 = If(w ≟ 0 ∨ B_2 ≟ (0, 0, 0), Line[A, (1, 0, 0)], Line[A, E_2])
b_3 = If((¬(v_1 ≟ 1)) ∨ w ≟ 0, Line[(0, 0, 0), (1, 0, 0)], ¬(Z_1 ≟ (0, 0, 0)), Line[A, C_2], ¬(A_2 ≟ (0, 0, 0)), Line[A, D_2], ¬(B_2 ≟ (0, 0, 0)), Line[A, E_2])
b_2 = If(w ≟ 0 ∨ Z_1 ≟ (0, 0, 0), Line[A, (1, 0, 0)], Line[A, C_2])
n_4 = 1 (slider from 1 to 2, step 1)
M_2: (0, 0, 0)
N_2: (0, 0, 0)
O_2: (0, 0, 0)
ChampTexte21 = Textfield(M_2)
ChampTexte22 = Textfield(N_2)
ChampTexte23 = Textfield(O_2)
i_4 = 1 (slider from -2 to 1, step 1)
j_4 = 1 (slider from -1 to 2, step 1)
P_2: (m1 * M_2)
Q_2: (m1 * N_2)
R_2: (m1 * O_2)
texte36: "" + (LaTeX[M_2]) + ""
texte37: "" + (LaTeX[N_2]) + ""
texte38: "" + (LaTeX[O_2]) + ""
m8: {{x(M_2), x(N_2), x(O_2)}, {y(M_2), y(N_2), y(O_2)}, {z(M_2), z(N_2), z(O_2)}}
v_2 = MatrixRank(m8)
m9: {{x(M_2), x(N_2)}, {y(M_2), y(N_2)}, {z(M_2), z(N_2)}}
m10: {{x(M_2), x(O_2)}, {y(M_2), y(O_2)}, {z(M_2), z(O_2)}}
m11: {{x(N_2), x(O_2)}, {y(N_2), y(O_2)}, {z(N_2), z(O_2)}}
w_2 = MatrixRank(m9)
c_3 = MatrixRank(m10)
d_3 = MatrixRank(m11)
g_4 = If((¬(v_2 ≟ 2)) ∨ w ≟ 0, p, w_2 ≟ 2, Plane[A, P_2, Q_2], c_3 ≟ 2, Plane[A, P_2, R_2], Plane[A, Q_2, R_2])
e_3 = If((¬(v_2 ≟ 1)) ∨ w ≟ 0, Line[(0, 0, 0), (1, 0, 0)], ¬(M_2 ≟ (0, 0, 0)), Line[A, P_2], ¬(N_2 ≟ (0, 0, 0)), Line[A, Q_2], ¬(O_2 ≟ (0, 0, 0)), Line[A, R_2])
h_4 = If(w ≟ 0 ∨ M_2 ≟ (0, 0, 0), Line[A, (1, 0, 0)], Line[A, P_2])
k_4 = If(w ≟ 0 ∨ N_2 ≟ (0, 0, 0), Line[A, (1, 0, 0)], Line[A, Q_2])
l_4 = If(w ≟ 0 ∨ O_2 ≟ (0, 0, 0), Line[A, (1, 0, 0)], Line[A, R_2])
m12 = If(v_2 ≟ 3, m8^(-1), {{0, 0, 0}, {0, 0, 0}, {0, 0, 0}})
S_2: ((m12 * m2) * P_1)
T_2: (x(S_2) * P_2)
U_2: (y(S_2) * Q_2)
V_2: (z(S_2) * R_2)
W_2: T_2 + V_2
Z_2: T_2 + U_2
A_3: V_2 + U_2
m_4 = Segment(P_1, Z_2)
p_4 = Segment(Z_2, U_2)
q_4 = Segment(P_1, W_2)
r_4 = Segment(P_1, A_3)
s_4 = Segment(A_3, U_2)
t_4 = Segment(W_2, V_2)
a_4 = Segment(T_2, Z_2)
b_4 = Segment(A_3, V_2)
c_4 = Segment(W_2, T_2)
ChampTexte24 = Textfield(B_3)
ChampTexte25 = Textfield(C_3)
n_5 = 2 (slider from -1 to 2, step 1)
i_5 = 1 (slider from -3 to 1, step 1)
texte42: "" + (LaTeX[B_3]) + ""
texte43: "" + (LaTeX[C_3]) + ""
d_4 = If((¬(o_3 ≟ 1)) ∨ w ≟ 0, Line[(0, 0, 0), (1, 0, 0)], ¬(B_3 ≟ (0, 0, 0)), Line[A, D_3], ¬(C_3 ≟ (0, 0, 0)), Line[A, E_3])
e_4 = If(w ≟ 0 ∨ B_3 ≟ (0, 0, 0), Line[(0, 0, 0), (1, 0, 0)], Line[A, D_3])
f_5 = If(w ≟ 0 ∨ C_3 ≟ (0, 0, 0), Line[(0, 0, 0), (1, 0, 0)], Line[A, E_3])
F_3 = If(w ≟ 0 ∨ (¬(o_3 ≟ 2)) ∨ (¬(P_1 ∈ p_5)), (0, 0, 0), Intersect[Line[A, D_3], Line[P_1, Vector[A, E_3]]])
G_3 = If(w ≟ 0 ∨ (¬(o_3 ≟ 2)) ∨ (¬(P_1 ∈ p_5)), (0, 0, 0), Intersect[Line[A, E_3], Line[P_1, Vector[A, D_3]]])
g_5 = Segment(P_1, F_3)
h_5 = Segment(P_1, G_3)
ChampTexte26 = Textfield(H_3)
texte47: "" + (LaTeX[H_3]) + ""
k_5 = -1 (slider from -1 to 2, step 1)
ChampTexte27 = Textfield(u_3)
ChampTexte28 = Textfield(v_3)
m_5 = 1 (slider from 0 to 1, step 1)
J_3: (0, 0, 0)
ChampTexte29 = Textfield(J_3)
i_6 = 2 (slider from -1 to 2, step 1)
texte51: "" + (LaTeX[J_3]) + ""
j_6 = 1 (slider from -1 to 1, step 1)
M_3: (m1 * J_3)
r_5 = If(w ≟ 0 ∨ J_3 ≟ (0, 0, 0), Line[(0, 0, 0), (1, 0, 0)], Line[A, M_3])
N_3: (0, 0, 0)
ChampTexte30 = Textfield(N_3)
texte53: "" + (LaTeX[N_3]) + ""
k_6 = 1 (slider from -1 to 1, step 1)
l_6 = 2 (slider from -1 to 2, step 1)
O_3: (m1 * N_3)
s_5 = If(w ≟ 0 ∨ N_3 ≟ (0, 0, 0), Line[(0, 0, 0), (1, 0, 0)], Line[A, O_3])
m_6 = 1 (slider from 1 to 3, step 1)
n_7 = 1 (slider from 0 to 1, step 1)
v_4(x, y, z) = x
texte54 = LaTeX(v_4, true, true)
ChampTexte31 = Textfield(v_4)
w_4 = 0 (slider from -60 to 60)
ChampTexte32 = Textfield(w_4)
a_5: v_4(1, 0, 0)
b_5: v_4(0, 1, 0)
c_5: v_4(0, 0, 1)
P_3: (a_5, b_5, c_5)
Q_3: (m14 * P_3)
d_5: a_5^(2) + b_5^(2) + c_5^(2)
p_6 = If(w ≟ 0 ∨ d_5 ≟ 0, z = 0, (x(Q_3) * x) + (y(Q_3) * y) + (z(Q_3) * z) = w_4)
o_5(x, y, z) = x
t_5: o_5(1, 0, 0)
u_5: o_5(0, 1, 0)
v_5: o_5(0, 0, 1)
w_5: t_5^(2) + u_5^(2) + v_5^(2)
a_6 = 0 (slider from -60 to 60)
ChampTexte33 = Textfield(a_6)
ChampTexte34 = Textfield(o_5)
R_3: (t_5, u_5, v_5)
S_3: (m14 * R_3)
q_6 = If(w ≟ 0 ∨ w_5 ≟ 0, z = 0, (x(S_3) * x) + (y(S_3) * y) + (z(S_3) * z) = a_6)
i_7 = 1 (slider from 0 to 1, step 1)
T_3: C_2 + D_2
U_3: C_2 + E_2
V_3: D_2 + E_2
W_3: C_2 + D_2 + E_2
f_6 = Segment(A, C_2)
g_6 = Segment(A, D_2)
h_6 = Segment(A, E_2)
r_6 = Segment(C_2, T_3)
s_6 = Segment(C_2, U_3)
t_6 = Segment(D_2, V_3)
b_6 = Segment(D_2, T_3)
c_6 = Segment(T_3, W_3)
d_6 = Segment(W_3, U_3)
e_6 = Segment(W_3, V_3)
f_7 = Segment(E_2, V_3)
g_7 = Segment(E_2, U_3)
h_7 = Segment(A, P_2)
j_7 = Segment(A, Q_2)
Z_3: P_2 + Q_2
k_7 = Segment(P_2, Z_3)
l_7 = Segment(Q_2, Z_3)
m_7 = Segment(A, R_2)
A_4: P_2 + R_2
p_7 = Segment(P_2, A_4)
q_7 = Segment(A_4, R_2)
B_4: Q_2 + R_2
r_7 = Segment(Q_2, B_4)
s_7 = Segment(B_4, R_2)
C_4: B_4 + P_2
t_7 = Segment(A_4, C_4)
a_7 = Segment(B_4, C_4)
b_7 = Segment(C_4, Z_3)
o_6 = false
n_8 = 0 (slider from 0 to 2, step 1)
u_6 = 0 (slider from -5 to 5, step 0.01)
v_6 = 0 (slider from -5 to 5, step 0.01)
w_6 = 0 (slider from -5 to 5, step 0.01)
ChampTexte35 = Textfield(u_6)
ChampTexte36 = Textfield(v_6)
ChampTexte37 = Textfield(w_6)
i_8 = 0 (slider from 0 to 2, step 1)
D_4: I_3
E_4: (u_6 * D_4)
F_4: (u_6 * H_3)
texte59: "" + (LaTeX[F_4]) + ""
G_4: (v_6 * J_1) + (w_6 * I_1)
j_8 = 0 (slider from 0 to 2, step 1)
d_7 = 0 (slider from -5 to 5, step 0.01)
e_7 = 0 (slider from -5 to 5, step 0.01)
o_7 = 0 (slider from -5 to 5, step 0.01)
ChampTexte38 = Textfield(d_7)
texte57: "t_1 v_1\,,\quad v_1=" + (LaTeX[H_3]) + ",\,\quad t_1="
ChampTexte39 = Textfield(e_7)
ChampTexte40 = Textfield(o_7)
l_8 = 0 (slider from 0 to 2, step 1)
I_4: (d_7 * Z_1)
J_4: (e_7 * A_2)
K_4: (o_7 * B_2)
H_4: (d_7 * C_2) + (e_7 * D_2) + (o_7 * E_2)
L_4: (v_6 * F_1)
M_4: (w_6 * E_1)
texte63: "" + (LaTeX[L_4]) + "+" + (LaTeX[M_4]) + ""
ChampTexte41 = Textfield(c_7)
ChampTexte42 = Textfield(u_7)
ChampTexte43 = Textfield(g_8)
ChampTexte44 = Textfield(h_8)
m15: {{v_7, w_7, a_8, g_8}, {b_8, c_8, d_8, h_8}}
k_8 = MatrixRank(m15)
r_8 = If(o_8 ≟ 1 ∧ k_8 ≟ 2, z = 0, ¬(e_8 ≟ 0), p_8, q_8)
n_9 = 1 (slider from -5 to 5, step 1)
i_9 = 1 (slider from -1 to 1, step 1)
j_9 = 2 (slider from -1 to 2, step 1)
k_9 = -1 (slider from -1 to 2, step 1)
l_9 = -1 (slider from -1 to 2, step 1)
m_9 = 1 (slider from -1 to 2, step 1)
n_{10} = 1 (slider from -1 to 2, step 1)
i_{10} = 1 (slider from -1 to 2, step 1)
j_{10} = 1 (slider from -1 to 2, step 1)
texte60: "t_1v_1+t_2v_2\,,\quad v_1= " + (LaTeX[F_1]) + ",\quad v_2=" + (LaTeX[E_1]) + ""
R_4: (v_6 * J_1)
S_4: (w_6 * I_1)
k_2 = Segment(A, R_4)
s_8 = Segment(R_4, G_4)
t_8 = Segment(A, S_4)
f_9 = Segment(S_4, G_4)
texte23: "" + (LaTeX[L_4]) + ""
texte24: "" + (LaTeX[M_4]) + ""
T_4: (d_7 * C_2)
U_4: (e_7 * D_2)
V_4: (o_7 * E_2)
W_4: (d_7 * C_2) + (e_7 * D_2)
Z_4: (e_7 * D_2) + (o_7 * E_2)
A_5: (d_7 * C_2) + (o_7 * E_2)
g_9 = Segment(A, T_4)
h_9 = Segment(U_4, W_4)
p_9 = Segment(Z_4, H_4)
q_9 = Segment(V_4, A_5)
r_9 = Segment(A, U_4)
s_9 = Segment(V_4, Z_4)
t_9 = Segment(A_5, H_4)
a_9 = Segment(W_4, T_4)
b_9 = Segment(A, V_4)
c_9 = Segment(T_4, A_5)
d_9 = Segment(W_4, H_4)
e_9 = Segment(U_4, Z_4)
texte88: "" + (LaTeX[I_4]) + ""
texte89: "" + (LaTeX[J_4]) + ""
texte90: "" + (LaTeX[K_4]) + ""
k_{10} = 0 (slider from -1 to 1, step 1)
texte27: "v=" + (LaTeX[N_1]) + ""
texte91: "v=" + (LaTeX[Q_1]) + ""
u_8: i_3 ≟ -2 ∧ n_4 ≟ 1 ∧ n_2 ≟ 3 ∧ o ∧ j ∧ n_3 ≤ 0 ∧ v_1 ≟ 3 ∧ (j_{12} < 3 ∨ j_{12} ≟ 4)
v_8 = false
l_{10} = 0 (slider from 0 to 2, step 1)
w_8: j_3 ≟ -1 ∧ m_9 ≟ -1 ∧ n_{10} ≟ -1
o_9: j_3 ≟ 1 ∧ m_9 ≟ 1 ∧ n_{10} ≟ 1
m17 = If(v_1 ≟ 3, m3^(-1), {{0, 0, 0}, {0, 0, 0}, {0, 0, 0}})
u_9(x, y, z) = (m17(1, 1) * x) + (m17(1, 2) * y) + (m17(1, 3) * z)
v_9(x, y, z) = (m17(2, 1) * x) + (m17(2, 2) * y) + (m17(2, 3) * z)
w_9(x, y, z) = (m17(3, 1) * x) + (m17(3, 2) * y) + (m17(3, 3) * z)
texte97: "(" + (LaTeX[u_9]) + ")" + (LaTeX[Z_1]) + ""
texte98: "(" + (LaTeX[v_9]) + ")" + (LaTeX[A_2]) + ""
texte99: "(" + (LaTeX[w_9]) + ")" + (LaTeX[B_2]) + ""
Z_{5}: (1, 1, 0)
A_{6}: (0, 1, 1)
B_{5}: (0.5, 0, 1)
ChampTexte18_{1} = Textfield(Z_{5})
ChampTexte19_{1} = Textfield(A_{6})
ChampTexte20_{1} = Textfield(B_{5})
m3_{1}: {{x(Z_{5}), x(A_{6}), x(B_{5})}, {y(Z_{5}), y(A_{6}), y(B_{5})}, {z(Z_{5}), z(A_{6}), z(B_{5})}}
o_{10} = Determinant(m3_{1})
v_{10} = MatrixRank(m3_{1})
d_{10} = Textfield(B_{5})
m17_{1} = If(v_{10} ≟ 3, m3_{1}^(-1), {{0, 0, 0}, {0, 0, 0}, {0, 0, 0}})
u_{10}(x, y, z) = (m17_{1}(1, 1) * x) + (m17_{1}(1, 2) * y) + (m17_{1}(1, 3) * z)
v_{11}(x, y, z) = (m17_{1}(2, 1) * x) + (m17_{1}(2, 2) * y) + (m17_{1}(2, 3) * z)
w_{10}(x, y, z) = (m17_{1}(3, 1) * x) + (m17_{1}(3, 2) * y) + (m17_{1}(3, 3) * z)
a_{10}: x(Q_1)
b_{10}: y(Q_1)
c_{10}: z(Q_1)
e_{10}: x(F_2)
f_{10}: y(F_2)
g_{10}: z(F_2)
h_{10}: m17(3, 1)
m_{10}: m17(3, 2)
p_{10}: m17(3, 3)
q_{10}: m17(1, 1)
r_{10}: m17(1, 2)
s_{10}: m17(1, 3)
t_{10}: m17(2, 1)
a_{11}: m17(2, 2)
b_{11}: m17(2, 3)
c_{11}: n_2 ≟ 3 ∧ o ∧ n_4 ≟ 1 ∧ i_3 ≤ 0 ∧ i_3 ≥ -1 ∧ j_{12} < 3
texte65: "v_1=" + (LaTeX[Z_1]) + ",\quad v_2=" + (LaTeX[A_2]) + ",\quad v_3=" + (LaTeX[B_2]) + ""
d_{11} = false
Z_{6}: (1, 1, 0)
A_{7}: (0, 1, 1)
B_{6}: (0.5, 0, 1)
ChampTexte18_{2} = Textfield(Z_{6})
ChampTexte19_{2} = Textfield(A_{7})
ChampTexte20_{2} = Textfield(B_{6})
m3_{2}: {{x(Z_{6}), x(A_{7}), x(B_{6})}, {y(Z_{6}), y(A_{7}), y(B_{6})}, {z(Z_{6}), z(A_{7}), z(B_{6})}}
o_{11} = Determinant(m3_{2})
v_{12} = MatrixRank(m3_{2})
d_{12} = Textfield(B_{6})
m17_{2} = If(v_{12} ≟ 3, m3_{2}^(-1), {{0, 0, 0}, {0, 0, 0}, {0, 0, 0}})
u_{11}(x, y, z) = (m17_{2}(1, 1) * x) + (m17_{2}(1, 2) * y) + (m17_{2}(1, 3) * z)
v_{13}(x, y, z) = (m17_{2}(2, 1) * x) + (m17_{2}(2, 2) * y) + (m17_{2}(2, 3) * z)
w_{11}(x, y, z) = (m17_{2}(3, 1) * x) + (m17_{2}(3, 2) * y) + (m17_{2}(3, 3) * z)
texte69: "\textcolor{orange}{" + (LaTeX[I_4]) + "}+\textcolor{blue}{" + (LaTeX[J_4]) + "}+\textcolor{green}{" + (LaTeX[K_4]) + "}"
texte100: "" + (LaTeX[e_{10}]) + "" + (LaTeX[Z_1]) + ""
texte101: "" + (LaTeX[f_{10}]) + "" + (LaTeX[A_2]) + ""
texte102: "" + (LaTeX[g_{10}]) + "" + (LaTeX[B_2]) + ""
texte93_{1}: "[v]_{\mathcal{B}}=" + (LaTeX[m3]) + "^{-1}\left(\begin{array}x \\ y \\ z\end{array}\right)=\left(\begin{array}\textcolor{orange}{" + (LaTeX[u_9]) + "} \\ \textcolor{blue}{" + (LaTeX[v_9]) + "} \\ \textcolor{green}{" + (LaTeX[w_9]) + "}\end{array}\right)\\

\vspace{10mm}

 v=(x,y,z),\quad\mathcal{B}=" + (LaTeX[Z_1]) + "," + (LaTeX[A_2]) + "," + (LaTeX[B_2]) + "  "
e_{11} = false
f_{11}: j_2 ≤ 0 ∧ j_2 ≥ -2 ∧ n_2 ≟ 2 ∧ i_2 ≟ 1 ∧ j_{12} < 3
m18: {{x(F_1), y(F_1), z(F_1)}, {x(E_1), y(E_1), z(E_1)}}
g_{11} = MatrixRank(m18)
n_{11} = 1 (slider from 0 to 1, step 1)
i_{11} = 0 (slider from 0 to 1, step 1)
C_5 = If(m_2 ≟ 0, Q_1, N_1)
m19: {{x(F_1), x(E_1)}, {y(F_1), y(E_1)}}
m20: {{x(F_1), x(E_1)}, {z(F_1), z(E_1)}}
m21: {{y(F_1), y(E_1)}, {z(F_1), z(E_1)}}
h_{11} = Determinant(m19)
j_{11} = Determinant(m20)
k_{11} = Determinant(m21)
m22 = If(h_{11} ≟ 0, {{0, 0}, {0, 0}}, m19^(-1))
m23 = If(j_{11} ≟ 0, {{0, 0}, {0, 0}}, m20^(-1))
m24 = If(k_{11} ≟ 0, {{0, 0}, {0, 0}}, m21^(-1))
D_5: (x(C_5), y(C_5))
E_5: (x(C_5), z(C_5))
F_5: (y(C_5), z(C_5))
G_5 = If(¬(h_{11} ≟ 0), (m22 * D_5), ¬(j_{11} ≟ 0), (m23 * E_5), ¬(k_{11} ≟ 0), (m23 * F_5), A)
l_{11}: x(G_5)
m_{11}: y(G_5)
texte105: "" + (LaTeX[l_{11}]) + "" + (LaTeX[F_1]) + ""
texte106: "" + (LaTeX[m_{11}]) + "" + (LaTeX[E_1]) + ""
p_{11} = true
q_{11}: n_3 ≤ 0 ∧ j_2 ≟ -3 ∧ P_1 ∈ p_1 ∧ g_{11} ≟ 2 ∧ n_2 ≟ 2 ∧ i_2 ≟ 1 ∧ j_{12} < 3
n_{12} = 0 (slider from 0 to 2, step 1)
r_{11} = false
s_{11}: n_2 ≟ 1 ∧ n_6 ≟ 1 ∧ j_5 ≤ 0 ∧ j_5 ≥ -1 ∧ j_{12} < 3
t_{11} = Segment(A, E_4)
a_{12}: n_2 ≟ 1 ∧ n_6 ≟ 1 ∧ n_3 ≤ 0 ∧ j_5 ≟ -2 ∧ P_1 ∈ l_5 ∧ h_{12} ∧ (k_5 ≟ -1 ∧ k_{10} ≟ 0 ∨ k_{10} ≟ 1 ∧ k_5 ≟ 1) ∧ j_{12} < 3
b_{12} = false
c_{12}: x(H_3)
e_{12}: y(H_3)
f_{12}: z(H_3)
g_{12} = If(¬(c_{12} ≟ 0), x(C_5) / c_{12}, ¬(e_{12} ≟ 0), y(C_5) / e_{12}, ¬(f_{12} ≟ 0), z(C_5) / f_{12}, 0)
texte115: "[v]_{\mathcal{B}}=\textcolor{orange}{" + (LaTeX[g_{12}]) + "},\quad \mathcal{B}=" + (LaTeX[H_3]) + ""
i_{12} = 0 (slider from 0 to 1, step 1)
H_5: (g_{12} * I_3)
texte111: "[v]_{\mathcal{B}}=\left(\begin{array}\textcolor{orange}{" + (LaTeX[l_{11}]) + "} \\\textcolor{blue}{ " + (LaTeX[m_{11}]) + "} \end{array}\right),\quad \mathcal{B}=" + (LaTeX[F_1]) + "," + (LaTeX[E_1]) + ""
texte93_{2}: "[v]_{\mathcal{B}}=" + (LaTeX[m3]) + "^{-1}\left(\begin{array}" + (LaTeX[a_{10}]) + " \\ " + (LaTeX[b_{10}]) + " \\ " + (LaTeX[c_{10}]) + "\end{array}\right)=\left(\begin{array}\textcolor{orange}{" + (LaTeX[e_{10}]) + "} \\ \textcolor{blue}{" + (LaTeX[f_{10}]) + "} \\ \textcolor{green}{" + (LaTeX[g_{10}]) + "}\end{array}\right)\\

\vspace{10mm}

 v=" + (LaTeX[Q_1]) + ",\quad\mathcal{B}=" + (LaTeX[Z_1]) + "," + (LaTeX[A_2]) + "," + (LaTeX[B_2]) + "  "
k_{12}(x, y, z) = 0
l_{12}(x, y, z) = 0
m_{12}(x, y, z) = 0
ChampTexte45 = Textfield(k_{12})
ChampTexte46 = Textfield(l_{12})
ChampTexte47 = Textfield(m_{12})
o_{12} = false
p_{12}: j_{12} ≟ 3 ∨ j_{12} ≟ 4
m25: {{k_{12}(1, 0, 0), k_{12}(0, 1, 0), k_{12}(0, 0, 1)}, {l_{12}(1, 0, 0), l_{12}(0, 1, 0), l_{12}(0, 0, 1)}, {m_{12}(1, 0, 0), m_{12}(0, 1, 0), m_{12}(0, 0, 1)}}
I_5 = Textfield(k_{12})
J_5: (((m1 * m25) * m2) * P_1)
K_5: (m25 * Q_1)
texte124: "f(v)=" + (LaTeX[K_5]) + ""
i_{13} = 1 (slider from -1 to 1, step 1)
L_5: (0.05 * J_5) + (0.95 * P_1)
M_5: (0.95 * J_5) + (0.05 * P_1)
u_{12} = Vector(L_5, M_5)
O_5: (y(K_5) * I)
N_5: (x(K_5) * H)
P_5: (z(K_5) * J)
q_{12} = Segment(A, N_5)
r_{12} = Segment(A, O_5)
s_{12} = Segment(A, P_5)
t_{12} = Segment(N_5 + P_5, N_5)
f_{13} = Segment(N_5 + O_5, N_5)
g_{13} = Segment(O_5, O_5 + N_5)
h_{13} = Segment(O_5 + P_5, O_5)
j_{13} = Segment(O_5 + P_5, P_5)
k_{13} = Segment(N_5 + P_5, P_5)
l_{13} = Segment(O_5 + P_5 + N_5, O_5 + P_5)
m_{13} = Segment(O_5 + P_5 + N_5, O_5 + N_5)
n_{13} = Segment(O_5 + P_5 + N_5, N_5 + P_5)
n_{14} = 0 (slider from 0 to 1, step 1)
a_{13}: x(H_3)
b_{13}: y(H_3)
c_{13}: z(H_3)
d_{13} = If(¬(a_{13} ≟ 0), m25(1, 1) / a_{13}, 0)
e_{13} = If(¬(a_{13} ≟ 0), m25(1, 2) / a_{13}, 0)
o_{13} = If(¬(a_{13} ≟ 0), m25(1, 3) / a_{13}, 0)
p_{13} = If(¬(b_{13} ≟ 0), m25(2, 1) / b_{13}, 0)
q_{13} = If(¬(b_{13} ≟ 0), m25(2, 2) / b_{13}, 0)
r_{13} = If(¬(b_{13} ≟ 0), m25(2, 3) / b_{13}, 0)
s_{13} = If(¬(c_{13} ≟ 0), m25(3, 1) / c_{13}, 0)
t_{13} = If(¬(c_{13} ≟ 0), m25(3, 2) / c_{13}, 0)
u_{13} = If(¬(c_{13} ≟ 0), m25(3, 3) / c_{13}, 0)
w_{12} = If(¬(a_{13} ≟ 0), (d_{13} * x) + (e_{13} * y) + (o_{13} * z), ¬(b_{13} ≟ 0), (p_{13} * x) + (q_{13} * y) + (r_{13} * z), ¬(c_{13} ≟ 0), (s_{13} * x) + (t_{13} * y) + (u_{13} * z), x + y + z)
w_{13} = MatrixRank(m25)
m26: {{k_{12}(1, 0, 0), k_{12}(0, 1, 0), k_{12}(0, 0, 1)}, {l_{12}(1, 0, 0), l_{12}(0, 1, 0), l_{12}(0, 0, 1)}}
m27: {{k_{12}(1, 0, 0), k_{12}(0, 1, 0), k_{12}(0, 0, 1)}, {m_{12}(1, 0, 0), m_{12}(0, 1, 0), m_{12}(0, 0, 1)}}
m28: {{l_{12}(1, 0, 0), l_{12}(0, 1, 0), l_{12}(0, 0, 1)}, {m_{12}(1, 0, 0), m_{12}(0, 1, 0), m_{12}(0, 0, 1)}}
m29 = If(q ≟ 0, {({0, 0} * {0, 0})}, m19^(-1))
m30 = If(r ≟ 0, {({0, 0} * {0, 0})}, m20^(-1))
m31 = If(s ≟ 0, {{0, 0}, {0, 0}}, m21^(-1))
m32: (m29 * m26)
m33: (m30 * m27)
m34: (m31 * m28)
a_{14} = If(¬(q ≟ 0), (m32(1, 1) * x) + (m32(1, 2) * y) + (m32(1, 3) * z), ¬(r ≟ 0), (m33(1, 1) * x) + (m33(1, 2) * y) + (m33(1, 3) * z), ¬(s ≟ 0), (m34(1, 1) * x) + (m34(1, 2) * y) + (m34(1, 3) * z), x + y + z)
c_{14} = If(¬(q ≟ 0), (m32(2, 1) * x) + (m32(2, 2) * y) + (m32(2, 3) * z), ¬(r ≟ 0), (m33(2, 1) * x) + (m33(2, 2) * y) + (m33(2, 3) * z), ¬(s ≟ 0), (m34(2, 1) * x) + (m34(2, 2) * y) + (m34(2, 3) * z), x + y + z)
m35: {{k_{12}(1, 0, 0), k_{12}(0, 1, 0), k_{12}(0, 0, 1), x(H_3)}, {l_{12}(1, 0, 0), l_{12}(0, 1, 0), l_{12}(0, 0, 1), y(H_3)}, {m_{12}(1, 0, 0), m_{12}(0, 1, 0), m_{12}(0, 0, 1), z(H_3)}}
d_{14} = MatrixRank(m35)
b_{14}: j_5 ≤ -1 ∧ (¬(w ≟ 0)) ∧ w_{13} ≟ 1 ∧ (¬(H_3 ≟ (0, 0, 0))) ∧ o_{12} ∧ p_{12} ∧ i_{13} ≤ 0 ∧ n_3 ≤ 0 ∧ d_{14} ≟ 1
i_{14} = 0 (slider from 0 to 1, step 1)
m36: {{k_{12}(1, 0, 0), k_{12}(0, 1, 0), k_{12}(0, 0, 1), x(F_1), x(E_1)}, {l_{12}(1, 0, 0), l_{12}(0, 1, 0), l_{12}(0, 0, 1), y(F_1), y(E_1)}, {m_{12}(1, 0, 0), m_{12}(0, 1, 0), m_{12}(0, 0, 1), z(F_1), z(E_1)}}
f_{14} = MatrixRank(m36)
e_{14}: j_2 ≤ -1 ∧ (¬(w ≟ 0)) ∧ w_{13} ≟ 2 ∧ (¬((q, r, s) ≟ (0, 0, 0))) ∧ o_{12} ∧ p_{12} ∧ i_{13} ≤ 0 ∧ n_3 ≤ 0 ∧ f_{14} ≟ 2
j_{14} = 1 (slider from 0 to 1, step 1)
g_{14}: a_{14}(Q_1)
h_{14}: c_{14}(Q_1)
Q_5: (g_{14} * J_1)
R_5: (h_{14} * I_1)
k_{14} = Segment(J_5, R_5)
l_{14} = Segment(J_5, Q_5)
m_{14}: w_{12}(Q_1)
texte125: "\fbox{f(x,y,z)=(" + (LaTeX[w_{12}]) + ")" + (LaTeX[H_3]) + "}"
texte129: "\fbox{f" + (LaTeX[Q_1]) + "=" + (LaTeX[m_{14}]) + "" + (LaTeX[H_3]) + "}"
texte126: "\fbox{f(x,y,z)=(" + (LaTeX[a_{14}]) + ")" + (LaTeX[F_1]) + "+(" + (LaTeX[c_{14}]) + ")" + (LaTeX[E_1]) + "}"
texte127: "\fbox{f" + (LaTeX[Q_1]) + "=" + (LaTeX[g_{14}]) + "" + (LaTeX[F_1]) + "+" + (LaTeX[h_{14}]) + "" + (LaTeX[E_1]) + "}"
texte128: "\fbox{f" + (LaTeX[Q_1]) + "=" + (LaTeX[g_{14}]) + "" + (LaTeX[F_1]) + "" + (LaTeX[h_{14}]) + "" + (LaTeX[E_1]) + "}"
o_{14} = true
texte131: "A=" + (LaTeX[m25]) + ""
m37 = If(¬(a_{13} ≟ 0), {{d_{13}, e_{13}, o_{13}}}, ¬(b_{13} ≟ 0), {{p_{13}, q_{13}, r_{13}}}, ¬(c_{13} ≟ 0), {{s_{13}, t_{13}, u_{13}}}, {{1, 1, 1}})
m38: {{a_{13}}, {b_{13}}, {c_{13}}}
texte132: "=" + (LaTeX[m38]) + "" + (LaTeX[m37]) + ""
m40 = If(¬(q ≟ 0), {{m32(2, 1), m32(2, 2), m32(2, 3)}}, ¬(r ≟ 0), {{m33(2, 1), m33(2, 2), m33(2, 3)}}, ¬(s ≟ 0), {{m34(2, 1), m34(2, 2), m34(2, 3)}}, {{1, 1, 1}})
m39 = If(¬(q ≟ 0), {{m32(1, 1), m32(1, 2), m32(1, 3)}}, ¬(r ≟ 0), {{m33(1, 1), m33(1, 2), m33(1, 3)}}, ¬(s ≟ 0), {{m34(1, 1), m34(1, 2), m34(1, 3)}}, {{1, 1, 1}})
u_{14} = Vector(A, F_1)
v_{14} = Vector(A, E_1)
texte133: "=" + (LaTeX[u_{14}]) + "" + (LaTeX[m39]) + "+" + (LaTeX[v_{14}]) + "" + (LaTeX[m40]) + ""
p_{14}: j_{12} ≟ 3 ∨ j_{12} ≟ 4
q_{14}: j_2 ≤ -0 ∧ (¬(w ≟ 0)) ∧ w_{13} ≟ 2 ∧ (¬((q, r, s) ≟ (0, 0, 0))) ∧ o_{12} ∧ p_{12} ∧ o_{14} ∧ f_{14} ≟ 2
n_{15} = 1 (slider from 0 to 1, step 1)
r_{14}: j_5 ≤ 0 ∧ (¬(w ≟ 0)) ∧ w_{13} ≟ 1 ∧ (¬(H_3 ≟ (0, 0, 0))) ∧ o_{12} ∧ p_{12} ∧ o_{14} ∧ d_{14} ≟ 1
i_{15} = 0 (slider from 0 to 1, step 1)
j_{15} = 0 (slider from 0 to 2, step 1)
texte135: "[v]_{\mathcal{B}}=\left(\begin{array}\textcolor{orange}{" + (LaTeX[e_{10}]) + " } \\ \textcolor{blue}{ " + (LaTeX[f_{10}]) + "} \\ \textcolor{green}{ " + (LaTeX[g_{10}]) + "}\end{array}\right)\\

\vspace{10mm}

 v= " + (LaTeX[Q_1]) + ",\quad\mathcal{B}=" + (LaTeX[Z_1]) + " ," + (LaTeX[A_2]) + " ,  " + (LaTeX[B_2]) + " "
texte117: "=" + (LaTeX[g_{12}]) + "" + (LaTeX[H_3]) + ""
S_5 = If(m_2 ≟ 0, Q_1, N_1)
s_{14}: x(S_5)
texte139: "" + (LaTeX[s_{14}]) + "(1,0,0)"
t_{14}: y(S_5)
texte140: "" + (LaTeX[t_{14}]) + "(0,1,0)"
w_{14}: z(S_5)
texte141: "" + (LaTeX[w_{14}]) + "(0,0,1)"
a_{15}: j_{12} ≟ 4
b_{15} = false
c_{15} = false
k_{15} = 0 (slider from 0 to 1, step 1)
T_5: ((m4 * m2) * J_5)
U_5: (x(T_5) * C_2)
V_5: (y(T_5) * D_2)
W_5: (z(T_5) * E_2)
f_{15} = Segment(A, W_5)
g_{15} = Segment(A, U_5)
h_{15} = Segment(A, V_5)
C_6: U_5 + W_5
l_{15} = Segment(C_6, U_5)
m_{15} = Segment(C_6, W_5)
D_6: U_5 + V_5
E_6: W_5 + V_5
p_{15} = Segment(W_5, E_6)
q_{15} = Segment(E_6, V_5)
r_{15} = Segment(D_6, V_5)
s_{15} = Segment(D_6, U_5)
t_{15} = Segment(J_5, C_6)
d_{15} = Segment(J_5, E_6)
e_{15} = Segment(J_5, D_6)
texte145: "[f]_{\mathcal{B}}=" + (LaTeX[m3]) + "^{-1}" + (LaTeX[m25]) + "" + (LaTeX[m3]) + ""
m41: ((m4 * m25) * m3)
texte146: "[f]_{\mathcal{B}}=" + (LaTeX[m41]) + ""
n_{16} = 0 (slider from 0 to 1, step 1)
i_{16} = 0 (slider from 0 to 1, step 1)