GrassmannCalculus`
Metric (★m)  |
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Details and Options
Examples
(2)
Basic Examples
(1)
In[1]:=
<<GrassmannCalculus`
Establish the book default preferences and display the metric.
In[2]:=
★A;Metric//MatrixForm
//MatrixForm
 | ★m |
Out[2]//MatrixForm=
1 | 0 | 0 |
0 | 1 | 0 |
0 | 0 | 1 |
Out[2]//MatrixForm=
1 | 0 | 0 |
0 | 1 | 0 |
0 | 0 | 1 |
Declare a new metric using subscripted g symbols.
In[3]:=
| DeclareMetric |
| ★m |
Out[3]//MatrixForm=
g 1,1 | g 1,2 | g 1,3 |
g 1,2 | g 2,2 | g 2,3 |
g 1,3 | g 2,3 | g 3,3 |
Use a bound vector space (with an Origin), The metric has an extra row and column.
In[4]:=
| SetBookBoundVectorSpace |
| ★m |
| DeclareMetric |
| ★m |
Out[4]=
{★,,,}
e
1
e
2
e
3
Out[4]//MatrixForm=
1 | 0 | 0 | 0 |
0 | 1 | 0 | 0 |
0 | 0 | 1 | 0 |
0 | 0 | 0 | 1 |
Out[4]//MatrixForm=
1 | 0 | 0 | 0 |
0 | g 1,1 | g 1,2 | g 1,3 |
0 | g 1,2 | g 2,2 | g 2,3 |
0 | g 1,3 | g 2,3 | g 3,3 |
Use a coordinate system from the PublicGrassmannAtlas. 'Grassmann' indicates a space with points.
In[5]:=
Keys
| PublicGrassmannAtlas |
Out[5]=
{Grassmann Line,Grassmann Plane,Grassmann 3-Space,Euclidean Line,Euclidean Plane,Euclidean 3-Space,Grassmann Polar,Polar,Elliptic Plane,Grassmann Elliptic Plane,Cylindrical,Grassmann Cylindrical,Spherical,Grassmann Spherical,Minkowski Space,Minkowski Grassmann Space}
In[6]:=
| SetActiveSpacePreferences |
 | PublicGrassmannAtlas |
Out[6]//MatrixForm=
1 | 0 | 0 | 0 |
0 | 1 | 0 | 0 |
0 | 0 | 2 ρ | 0 |
0 | 0 | 0 | 1 |
Calculations with a Metric
(1)
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