GrassmannCalculus`
MetricDeterminant (★g)  |
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Details and Options
Examples
(1)
Basic Examples
(1)
In[1]:=
<<GrassmannCalculus`
Set the Grassmann plane and display the metric.
In[2]:=
 | SetActiveSpacePreferences |
 | PublicGrassmannAtlas |
In[3]:=
Metric//MatrixForm
Out[3]//MatrixForm=
1 | 0 |
0 | 1 |
In[4]:=
 | ★g |
| ToMetricElements |
Out[4]=
★g
Out[4]=
1
Declaring a general symbolic metric.
In[5]:=
| DeclareMetric |
Out[5]//MatrixForm=
g x,x | g x,y |
g x,y | g y,y |
In[6]:=
| ★g |
| ToMetricElements |
Out[6]=
★g
Out[6]=
-+
2
()
g
x,y
g
x,x
g
y,y
The value can also be obtained from
In[7]:=
2
GrassmannVolumeFactor
Out[7]=
-+
2
()
g
x,y
g
x,x
g
y,y
We can obtain the volume factor from any of the available Grassmann Associations even if they are not the currently active one.
In[8]:=
volFactor=
"Spherical""Metrics","VolumeFactor"metric=
"Spherical""Metrics","Metric"
"Spherical""Coordinates","CoordinateDomain"&
 | PublicGrassmannAtlas |
| PublicGrassmannAtlas |
Det[metric]
//Simplify#, | PublicGrassmannAtlas |
Out[8]=
2
r
Out[8]=
{{1,0,0},{0,,0},{0,0,}}
2
r
2
r
2
Sin[θ]
Out[8]=
2
r
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