SamplePublisher`GrassmannCalculus`
EvaluateContractors  |
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Details and Options
Examples
(2)
Basic Examples
(1)
In[1]:=
<<GrassmannCalculus`
In[2]:=
 | SetCoordinateVectorSpace |
In[3]:=
〈
dw⋀(ady),be
y
〉
%// | EvaluateContractors |
Out[3]=
〈dw⋀(ady),b〉
e
y
Out[3]=
-abdw
In[4]:=
Outer
,
,
//MatrixForm%//
//MatrixForm
 | Contractor |
| FormBasis |
| VectorBasis |
 | EvaluateContractors |
Out[4]//MatrixForm=
〈dw, e w | 〈dw, e x | 〈dw, e y | 〈dw, e z |
〈dx, e w | 〈dx, e x | 〈dx, e y | 〈dx, e z |
〈dy, e w | 〈dy, e x | 〈dy, e y | 〈dy, e z |
〈dz, e w | 〈dz, e x | 〈dz, e y | 〈dz, e z |
Out[4]//MatrixForm=
1 | 0 | 0 | 0 |
0 | 1 | 0 | 0 |
0 | 0 | 1 | 0 |
0 | 0 | 0 | 1 |
The result is zero if the grade of the form is less than the grade of the k-vector. (Similar to interior products.)
In[5]:=
〈
dw⋀dx,e
w
e
x
e
y
〉
%// | EvaluateContractors |
Out[5]=
〈dw⋀dx,⋀⋀〉
e
w
e
x
e
y
Out[5]=
0
Left and Right contractors can also be evaluated.
In[6]:=
e
y
| EvaluateContractors |
Out[6]=
e
y
Out[6]=
dw⋀dx⋀dz
In[7]:=
dw⋀dx⋀dy⋀dz↤%//
e
y
| EvaluateContractors |
Out[7]=
dw⋀dx⋀dy⋀dz↤
e
y
Out[7]=
-(dw⋀dx⋀dz)
Examples from Edelen
(1)
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