GrassmannCalculus`
EvenComplementaryGradeQ  |
Details and Options
Examples
(1)
Basic Examples
(1)
In[1]:=
<<GrassmannCalculus`
Set the GrassmannPlane.
In[2]:=
SetActiveAssociation
"Grassmann Plane"
 | PublicGrassmannAtlas |
The dimension is:
In[3]:=
 | ★D |
Out[3]=
3
In[4]:=
Print["The GrassmannBases and their grades:"]
Grade
Print["The GrassmannComplements of the basis elements and their grades:"]
Grade
Print["Whether the complementary grades of the bases are even:"]
| GrassmannBases |
 | GrassmannBases |
| GrassmannComplements |
| GrassmannComplements |
| EvenComplementaryGradeQ |
| GrassmannBases |
The GrassmannBases and their grades:
Out[4]=
{{1},{★,,},{★⋀,★⋀,⋀},{★⋀⋀}}
e
x
e
y
e
x
e
y
e
x
e
y
e
x
e
y
Out[4]=
{{0},{1,1,1},{2,2,2},{3}}
The GrassmannComplements of the basis elements and their grades:
Out[4]=
{{★⋀⋀},{⋀,-(★⋀),★⋀},{,-,★},{1}}
e
x
e
y
e
x
e
y
e
y
e
x
e
y
e
x
Out[4]=
{{3},{2,2,2},{1,1,1},{0}}
Whether the complementary grades of the bases are even:
Out[4]=
{{False},{True,True,True},{False,False,False},{True}}
Switching to the 4-dimensional book space.
EvenComplementaryGradeQ
In[5]:=
★A;
;
[1+3x⋀y+4u⋀v⋀x⋀y]
| ★ℬ |
4
 | EvenComplementaryGradeQ |
Out[5]=
True
You can also use new symbols as long as you assert their grades, or you can override the grades of currently declared symbols.
In[6]:=
| ★ℬ |
4
| EvenComplementaryGradeQ |
★Λ
2
★Λ
3
Out[6]=
True
The expression can contain powers (including reciprocals) of scalars.
In[7]:=
| ★ℬ |
4
| EvenComplementaryGradeQ |
1
+
(x⋀y)⊖x
a
(
x⊖y)+
2
(a⋀b)
Out[7]=
True
 |
|
 |
|
""