$c=%v$

$d=%v$

m_{1,1} =

m_{1,2} =

μ_{1} =

m_{2,1} =

m_{2,2} =

μ_{2} =

$(d_1) : %v$

$(d_2) : %v$

$a=%v$

$b=%v$

$(δ_1) : %v$

$(δ_2) : %v$

Traitement par combinaisons linéaires

Présentation classique

Présentation complémentaire

m_{1,1} = 6
m_{1,2} = -2
n_1: (m_{1,1}, m_{1,2})
texte1 = LaTeX(n_1, true, false)
m_{2,1} = 1
m_{2,2} = -3
n_2: (m_{2,1}, m_{2,2})
texte2 = LaTeX(n_2, true, false)
m_{2,3} = 13
m_{1,3} = -4
c = 1 (slider from -30 to 30, step 1)
d = -6 (slider from -30 to 30, step 1)
c_2: (c * m_{1,3}) + (d * m_{2,3})
b_2: (c * m_{1,2}) + (d * m_{2,2})
truc2 = If(b_2 ≥ 0, "+" + b_2, "" + b_2)
a_2: (c * m_{1,1}) + (d * m_{2,1})
M: {{m_{1,1}, m_{1,2}}, {m_{2,1}, m_{2,2}}}
texte0 = LaTeX(M, true, true)
ChampTexte1 = Textfield(m_{1,1})
ChampTexte2 = Textfield(m_{1,2})
ChampTexte3 = Textfield(m_{1,3})
ChampTexte4 = Textfield(m_{2,1})
ChampTexte5 = Textfield(m_{2,2})
ChampTexte6 = Textfield(m_{2,3})
d_1: (m_{1,1} * x) + (m_{1,2} * y) = m_{1,3}
d_2: (m_{2,1} * x) + (m_{2,2} * y) = m_{2,3}
a = 3 (slider from -30 to 30, step 1)
b = -2 (slider from -30 to 30, step 1)
a_1: (a * m_{1,1}) + (b * m_{2,1})
b_1: (a * m_{1,2}) + (b * m_{2,2})
c_1: (a * m_{1,3}) + (b * m_{2,3})
δ_1: (a_1 * x) + (b_1 * y) = c_1
δ_2: (a_2 * x) + (b_2 * y) = c_2
T_2 = LaTeX(a_2 + "x" + truc2 + "y=" + c_2 + ": " + "   (δ_2)", true)
truc1 = If(b_1 ≥ 0, "+" + b_1, "" + b_1)
T_1 = LaTeX(a_1 + "x" + truc1 + "y=" + c_1 + ": " + "   (δ_1)", true)
n = 3.5
e = true
f = false
I = Intersect(d_1, d_2)
sa_1 = If((a_1  <  0) ∧ (c_1  <  0), ((-a_1)) / GCD[a_1, c_1], a_1 / GCD[a_1, c_1])
sb_2 = If((b_2  <  0) ∧ (c_2  <  0), ((-b_2)) / GCD[b_2, c_2], b_2 / GCD[b_2, c_2])
sc_2 = If((b_2  <  0) ∧ (c_2  <  0), ((-c_2)) / GCD[b_2, c_2], c_2 / GCD[b_2, c_2])
sc_1 = If((a_1  <  0) ∧ (c_1  <  0), ((-c_1)) / GCD[a_1, c_1], c_1 / GCD[a_1, c_1])
Legende = LaTeX("(\frac{" + sc_1 + "}{" + sa_1 + "},\frac{" + sc_2 + "}{" + sb_2 + "})", false)
AffichageCoordonnees = Text(Legende, I, true, true)
t_{1,1} = LaTeX(If[(n ≥ 1 / 2) ∧ e, "| \times" + ((-m_{2,2})), ""], true, true)
t_{1,2} = LaTeX(If[(n ≥ 1 / 2) ∧ e, "| \times" + m_{1,2}, ""], true, true)
t_{2,2} = LaTeX(If[(n ≥ 3 / 2) ∧ e, "| \times" + ((-m_{1,1})), ""], true, true)
t_{2,1} = LaTeX(If[(n ≥ 3 / 2) ∧ e, "| \times" + m_{2,1}, ""], true, true)
texte4 = TableText({{m_{1,1} + "x" + (If[m_{1,2} > 0, "+" + m_{1,2}, "" + m_{1,2}]) + "y=" + m_{1,3}, t_{1,1}, t_{2,1}}, {m_{2,1} + "x" + (If[m_{2,2} > 0, "+" + m_{2,2}, "" + m_{2,2}]) + "y=" + m_{2,3}, t_{1,2}, t_{2,2}}}, "{")
T01: m_{1,1} + "x" + (If[m_{1,2} > 0, "+" + m_{1,2}, "" + m_{1,2}]) + "y=" + m_{1,3}
T02: m_{2,1} + "x" + (If[m_{2,2} > 0, "+" + m_{2,2}, "" + m_{2,2}]) + "y=" + m_{2,3}
texte6 = If(n ≟ 0, TableText[{{T01}, {T02}}, "{"], If[n ≟ 1, TableText[{{T_1}, {T02}}, "{"], TableText[{{T_1}, {T_2}}, "{"]])
totonegal0 = TableText({{T01 + ": (d_1)"}, {T02 + ": (d_2)"}}, "{")
totonegal2 = TableText({{T_1}, {T_2}}, "{")
texte7 = LaTeX(totonegal0, true, true)
totonegal1 = TableText({{T_1}, {T02 + ":  (d_2)"}}, "{")
texte8 = LaTeX(M, true, true)
A = (-21.187687333632613, -2.9495290391104283)
texte10 = Text("\overrightarrow{n_1}" + texte1 + " non  // " + " \overrightarrow{n_2}" + texte2 + " \iff Déterminant[M] \neq 0", A, true, true)
faisceau = TableText({{T_1}, {T_2}}, "{")
TestCouleur = LaTeX("\fbox{ S= \{(x_I,y_I)\}=\{" + AffichageCoordonnees + "\}}")