Lösungen/Solutions/E1S1AlUe/Ex8

L=Lektion/Leçon-- Sprechstunde/heures de consultation
W=Work/Arbeit/Travail
A  =Anhang/  Annexe / Appendice

1 L / W

2 L / W

3 L / W

4

Plot[{x - 1, 1 - x, 2  x - 6}, {x, -1, 8}];

{x - y ≤ 1, x + y ≥ 1, 
      y ≥  2  x - 6}

Gut / Bien:    (Bsp./Ex.)

{x = 0, y = 4, x - y ≤ 1, x + y ≥ 1, 
      y ≥  2  x - 6}

{x = 2, y = 10, x - y ≤ 1, x + y ≥ 1, 
      y ≥  2  x - 6}

Schlecht / Ne pas bien:    (Bsp./Ex.)

{x = 0, y = 0, x - y ≤ 1, x + y ≥ 1, 
      y ≥  2  x - 6}

{x = 0, y = -4, x - y ≤ 1, x + y ≥ 1, 
      y ≥  2  x - 6}

{x = 0, y = -6, x - y ≤ 1, x + y ≥ 1, 
      y ≥  2  x - 6}

{x = 2, y = 0, x - y ≤ 1, x + y ≥ 1, 
      y ≥  2  x - 6}

{x = 5, y = 0, x - y ≤ 1, x + y ≥ 1, 
      y ≥  2  x - 6}

{x = 6.5, y = 6, x - y ≤ 1, x + y ≥ 1, 
      y ≥  2  x - 6}

Oben z.B. x=0, y=4       ===> o.k.
En haut p.ex. x=0, y=4  ===> o.k.

<< Graphics`InequalityGraphics`

InequalityPlot[{x - y ≥  1, x + y ≥ 1, 
          y ≤ 2  x - 6},  {x,  -3,  10},  {y, -10, 
          10} ];

5

a

Körper / Corps

b

Remove[a, b];
s = 
      Solve[{a + b == 10,  a^2 ==  10 b}, {a, b}]

s[[1]]

===>  a,b nicht rational, nur positive Lösungen / 
  ===>  a,b ne pas rationnel, seulement les solutions positives comptent

NSolve[{a + b == 10,  a^2 ==  10 b}, {a, b}]

6

Programm/ Programme

\(\(Wtab[f_, m_] := 
        Module[{tabb, tabZ, res, newtabX, u, exttabX, output, 
            output1}, \ 
Attributes[
              f] = {Listable}; 
tabb[
              1] = {{0}, {1}}; 
tabb[u_] := 
            Flatten[Table[
                Append[\(tabb[u - 1]\)[\([k]\)], w], {k, 1, 
                  Length[tabb[u - 1]]}, {w, 0, 1}], 1]; 
          tabZ[u_] := \ tabb[u] /. {0 -> False, 1 -> True}; 
          res = Table[
              Apply[f, \(tabZ[m]\)[\([n]\)]], {n, 1, Length[tabZ[m]]}]; 
          newtabX = Transpose[tabZ[m]]; 
u = 
            Length[newtabX]; 
\ \ \ \ \ exttabX = 
            Transpose[
              Append[newtabX, res]]; 
\ \ \ \ \ Prepend[exttabX, 
                Append[Range[u], {expr}]] /. {True -> 1, False -> 0} // 
            MatrixForm];\)\)
asUsual[f_] := 
        StringReplace[
          ToString[
            TraditionalForm[
              f]], {"!" -> "¬"}];
sub[x_, y_] := Or[Not[x], y]; 
    Attributes[sub] = {Listable};
bij[x_, y_] := And[sub[x, y], sub[y, x]]; 
    Attributes[bij] = {Listable};

Anwendung/ Application

f[a_, b_, c_] := Or[And[a, b], c];
f[a, b, c]  // asUsual

Wtab[f, 3]

7

a = 99; b = 98; c = 97; ab = 30; ac = 27; bc = 28; abc = 26;

a

aUbUc = a + b + c - ab - ac - bc + abc

b

ab - abc

8

a

Tan[60 Degree]

b

ArcCos[1/2]

Unendlich viele Lösungen! / Nombre infini de solutions!   ===>  (π/3) + 2 n π, -(π/3) + 2 n π

Plot[{Cos[x], 1/2}, {x, -2 Pi, 4  Pi}, 
        AspectRatio -> Automatic];

In Altgrad / En degrés

Plot[{Cos[x Degree], 1/2}, {x, -360, 720}];