A=

B=

E_ {\{2,4 \} } \wedge E_ {\{1,2,3\} } =-E_ {\{1,3,4\}}
\\
E_ {\{2,4 \} }=E_2  \wedge E_4\
E_ {\{1,3,4\}}=E_1 \wedge E_3 \wedge E_4\
E_1^2=\ldots=E_r^2=-1\\
E_{r+1}^2=E_{r+2}^2= \ldots =1\
\mbox{\small Die Verknüpfung ist assoziativ.}\
\mbox{\small Das Vertauschen zweier benachbarter, verschiedener  Elemente führt zu einem Vorzeichenwechsel.\
\mbox{\small Die Dimension und r charakterisieren die Clifford-Algebren. }

r=

r1: 2
L2: {1, 2, 3}
L1: {2, 4}
W = Sum(Sequence[If[Element[Intersection[L1, L2], i] ≤ r1, 1, 0], i, 1, Length[Intersection[L1, L2]]])
N = Sequence(Sequence[If[Element[L1, i] ≤ Element[L2, j], 0, -1], j, 1, Length[L2]], i, 1, Length[L1])
M = Sequence(Frequency[{-2, -1}, N(k)], k, 1, Length[L1])
L3 = Sequence(M(k, 1), k, 1, Length[L1])
V: (-1)^(Sum[L3] + W)
Eingabefeld1 = Textfield(L1)
Eingabefeld2 = Textfield(L2)
P = Sort(RemoveUndefined[Sequence[If[Element[Join[{L1, L2}], i] ∈ Intersection[L1, L2], NaN, Element[Join[{L1, L2}], i]], i, 1, Length[Join[{L1, L2}]]]])
V2 = Sequence(If[Element[Intersection[L1, L2], i] ≤ r1, 1, 0], i, 1, Length[Intersection[L1, L2]])
P1 = If(IsInteger[Element[P, 1]], P, {})
Text1: "\mbox{A} \wedge\mbox{B}=" + (LaTeX[V]) + "" + (LaTeX[P1]) + ""
Eingabefeld3 = Textfield(r1)