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SandBoxGrassmannIsometry

Edit detail for SandBoxGrassmannIsometry revision 2 of 7

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Editor: Bill Page Time: 2009/09/11 03:47:36 GMT-7
Note: pretty output

changed:
-idot:=operator(display(operator('dot,2),x+->x.1*x.2))$Expression(Integer)                       
idot:=display(operator('dot,2), (x:List OutputForm):OutputForm+->hconcat([x.1,_{_\cdot_} ,x.2]))

changed:
-ihat:=operator(operator('hat,2))$Expression(Integer)                       
ihat:=display(operator('hat,2), (x:List OutputForm):OutputForm+->hconcat([x.1,_{_\wedge_} ,x.2]))

added:
1+1

Grassmann Algebra Operators

Symmetric inner product

axiom

idot:=display(operator('dot,2), (x:List
OutputForm):OutputForm+->hconcat([x.1,_{_\cdot_} ,x.2]))

(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:=display(operator('hat,2), (x:List
OutputForm):OutputForm+->hconcat([x.1,_{_\wedge_} ,x.2]))

(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))

axiom

1+1

(5)

Type: PositiveInteger?