GrassmannCalculus`
GradeOfZero (★0)  |
|
| | ||||
Details and Options
Examples
(1)
Basic Examples
(1)
In[1]:=
<<GrassmannCalculus`
Set book default preferences.
In[2]:=
★A
When an exterior product or expression overruns the dimension of the space a is returned.
GradeOfZero
In[3]:=
{1,,⋀,⋀⋀,⋀⋀⋀x,⋀⋀⋀x⋀y}Grade[%]
e
1
e
1
e
2
e
1
e
2
e
3
e
1
e
2
e
3
e
1
e
2
e
3
Out[3]=
{1,,⋀,⋀⋀,⋀⋀⋀x,⋀⋀⋀x⋀y}
e
1
e
1
e
2
e
1
e
2
e
3
e
1
e
2
e
3
e
1
e
2
e
3
Out[3]=
{0,1,2,3,★0,★0}
RawGrade does not consider the dimension of the space.
In[4]:=
{1,,⋀,⋀⋀,⋀⋀⋀x,⋀⋀⋀x⋀y}
[%]
e
1
e
1
e
2
e
1
e
2
e
3
e
1
e
2
e
3
e
1
e
2
e
3
 | RawGrade |
Out[4]=
{1,,⋀,⋀⋀,⋀⋀⋀x,⋀⋀⋀x⋀y}
e
1
e
1
e
2
e
1
e
2
e
3
e
1
e
2
e
3
e
1
e
2
e
3
Out[4]=
{0,1,2,3,4,5}
The grade of expressions that are manifestly zero, without need for further evaluation, is returned as .
GradeOfZero
In[5]:=
{0,⋁,⊖(⋀),⋀⋀⋀x,⋀,x⋀x}Grade[%]
e
1
e
2
e
1
e
1
e
2
e
1
e
2
e
3
e
1
e
1
Out[5]=
{0,⋁,⊖⋀,⋀⋀⋀x,⋀,x⋀x}
e
1
e
2
e
1
e
1
e
2
e
1
e
2
e
3
e
1
e
1
Out[5]=
{★0,★0,★0,★0,2,2}
But upon evaluation these would all be zero and have a grade of zero.
In[6]:=
{0,⋁,⊖(⋀),⋀,x⋀x}//
Grade[%]
e
1
e
2
e
1
e
1
e
2
e
1
e
1
| ★ |
Out[6]=
{0,0,0,0,0}
Out[6]=
{★0,★0,★0,★0,★0}
Only a scalar that is zero gives , otherwise the grade is .
GradeOdZero
0
In[7]:=
Grade[{0,1,2,3}]
Out[7]=
{★0,0,0,0}
 |
|
""