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SandBoxGrassmannIsometry

Edit detail for SandBoxGrassmannIsometry revision 1 of 7

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Editor: Bill Page Time: 2009/09/10 13:29:45 GMT-7
Note: dot and hat

changed:
-
Grassmann Algebra Operators

  Symmetric inner product

\begin{axiom}
idot:=operator(display(operator('dot,2),x+->x.1*x.2))$Expression(Integer)                       
dot(A:EXPR INT,B:EXPR INT):EXPR INT == (smaller?(A,B)=>idot(A,B);idot(B,A))
dot(P, Q)=dot(Q,P)
\end{axiom}

  Exterior product

\begin{axiom}
ihat:=operator(operator('hat,2))$Expression(Integer)                       
hat(A:EXPR INT,B:EXPR INT):EXPR INT == (smaller?(A,B)=>ihat(A,B);-ihat(B,A))
hat(P, Q)=-hat(Q,P)
\end{axiom}

Grassmann Algebra Operators

Symmetric inner product

axiom

idot:=operator(display(operator('dot,2),x+->x.1*x.2))$Expression(Integer)

(1)

Type: BasicOperator?

axiom

dot(A:EXPR INT,B:EXPR INT):EXPR INT == (smaller?(A,B)=>idot(A,B);idot(B,A))

   Function declaration dot : (Expression(Integer),Expression(Integer))
       -> Expression(Integer) has been added to workspace.

Type: Void

axiom

dot(P, Q)=dot(Q,P)

axiom

Compiling function dot with type (Expression(Integer),Expression(
      Integer)) -> Expression(Integer)

(2)

Type: Equation(Expression(Integer))

Exterior product

axiom

ihat:=operator(operator('hat,2))$Expression(Integer)

(3)

Type: BasicOperator?

axiom

hat(A:EXPR INT,B:EXPR INT):EXPR INT == (smaller?(A,B)=>ihat(A,B);-ihat(B,A))

   Function declaration hat : (Expression(Integer),Expression(Integer))
       -> Expression(Integer) has been added to workspace.

Type: Void

axiom

hat(P, Q)=-hat(Q,P)

axiom

Compiling function hat with type (Expression(Integer),Expression(
      Integer)) -> Expression(Integer)

(4)

Type: Equation(Expression(Integer))