I believe that what you're looking for is some data structure Vector which has some list defining direction and some scalar which in part defines magnitude.

Here you go:

Vector[a_List] := Vector[1, a] Vector[b_, _]["scalar"] := b Vector[_, a_List]["vector"] := a Vector /: (b_ Vector[c_, a_List]) := Vector[c b, a] a = 3 Vector[{1, 1, 0}]; b = 2 Vector[.3, {3, 2, 0}]; 

If you want to "extract" the scalars, then use magicfunction:

Vector /: magicfunction[a__Vector, z_] := Times @@ (#["scalar"] &) /@ List[a] z @@ (#["vector"] &) /@ List[a] 

For instance:

magicfunction[a, b, Cross] (* {0., 0., -1.8} *) magicfunction[a, b, Hold] (* 1.8 Hold[{1, 1, 0}, {3, 2, 0}] *) 

In order to get the regular vector back, just use Normal. Make sure you have a copy of your Vector, however, as this transformation will lose the information about the scalar.

Vector /: Normal[Vector[b_, a_List]] := b a Normal[a] (* {3, 3, 0} *) 

I believe that what you're looking for is some data structure Vector which has some list defining direction and some scalar which in part defines magnitude.

Here you go:

Vector[a_List] := Vector[1, a] Vector[b_, _]["scalar"] := b Vector[_, a_List]["vector"] := a Vector /: (b_ Vector[c_, a_List]) := Vector[c b, a] a = 3 Vector[{1, 1, 0}]; b = 2 Vector[.3, {3, 2, 0}]; 

If you want to "extract" the scalars, then use magicfunction:

magicfunction[a__Vector, z_] := Times @@ (#["scalar"] &) /@ List[a] z @@ (#["vector"] &) /@ List[a] 

For instance:

magicfunction[a, b, Cross] (* {0., 0., -1.8} *) magicfunction[a, b, Hold] (* 1.8 Hold[{1, 1, 0}, {3, 2, 0}] *) 

In order to get the regular vector back, just use Normal. Make sure you have a copy of your Vector, however, as this transformation will lose the information about the scalar.

Vector /: Normal[Vector[b_, a_List]] := b a Normal[a] (* {3, 3, 0} *) 

I believe that what you're looking for is some data structure Vector which has some list defining direction and some scalar which in part defines magnitude.

Here you go:

Vector[a_List] := Vector[1, a] Vector[b_, _]["scalar"] := b Vector[_, a_List]["vector"] := a Vector /: (b_ Vector[c_, a_List]) := Vector[c b, a] a = 3 Vector[{1, 1, 0}]; b = 2 Vector[.3, {3, 2, 0}]; 

If you want to "extract" the scalars, then use magicfunction:

Vector /: magicfunction[a__Vector, z_] := Times @@ (#["scalar"] &) /@ List[a] z @@ (#["vector"] &) /@ List[a] 

For instance:

magicfunction[a, b, Cross] (* {0., 0., -1.8} *) magicfunction[a, b, Hold] (* 1.8 Hold[{1, 1, 0}, {3, 2, 0}] *) 

In order to get the regular vector back, just use Normal

Vector /: Normal[Vector[b_, a_List]] := b a Normal[a] (* {3, 3, 0} *) 

I believe that what you're looking for is some data structure Vector which has some list defining direction and some scalar which in part defines magnitude.

Here you go:

Vector[a_List] := Vector[1, a] Vector[b_, _]["scalar"] := b Vector[_, a_List]["vector"] := a Vector /: (b_ Vector[c_, a_List]) := Vector[c b, a] a = 3 Vector[{1, 1, 0}]; b = 2 Vector[.3, {3, 2, 0}]; 

If you want to "extract" the scalars, then use magicfunction:

Vector /: magicfunction[a__Vector, z_] := Times @@ (#["scalar"] &) /@ List[a] z @@ (#["vector"] &) /@ List[a] 

For instance:

magicfunction[a, b, Cross] (* {0., 0., -1.8} *) magicfunction[a, b, Hold] (* 1.8 Hold[{1, 1, 0}, {3, 2, 0}] *) 

In order to get the regular vector back, just use Normal. Make sure you have a copy of your Vector, however, as this transformation will lose the information about the scalar.

Vector /: Normal[Vector[b_, a_List]] := b a Normal[a] (* {3, 3, 0} *)