GrassmannCalculus`
OddGradeQ  |
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Details and Options
Examples
(1)
Basic Examples
(1)
In[1]:=
<<GrassmannCalculus`
Using the GrassmannPlane:
In[2]:=
SetActiveAssociation
"Grassmann Plane"
 | PublicGrassmannAtlas |
The following expression is of odd grade.
In[3]:=
2
x
e
x
2
y
e
y
e
x
e
y
 | OddGradeQ |
Out[3]=
2
x
e
x
2
y
e
y
e
x
e
y
Out[3]=
True
The following is not because it contains one even grade term.
In[4]:=
1+++xy★⋀⋀
[%]
2
x
e
x
2
y
e
y
e
x
e
y
| OddGradeQ |
Out[4]=
1+++xy★⋀⋀
2
x
e
x
2
y
e
y
e
x
e
y
Out[4]=
False
Set a 4-dimensional space.
In[5]:=
| ★ℬ |
4
OddGradeQ
In[6]:=
| OddGradeQ |
Out[6]=
True
And with graded symbols:
In[7]:=
Table[,{m,0,4}]
[%]
α
m
| OddGradeQ |
Out[7]=
,,,,
α
0
α
1
α
2
α
3
α
4
Out[7]=
{False,True,False,True,False}
Multigraded expressions give True only if all the element grades are odd.
In[8]:=
,,
[%]
α
{1,3}
α
{0,2,4}
α
{1,2,3}
| OddGradeQ |
Out[8]=
,,
α
{1,3}
α
{0,2,4}
α
{1,2,3}
Out[8]=
{True,False,False}
The grade of 0 is neither even nor odd.
In[9]:=
Grade[0]
[0],
[0]
 | EvenGradeQ |
| OddGradeQ |
Out[9]=
★0
Out[9]=
{False,False}
You can also use new (undefined) symbols as long as you assert their grades, or you can override the grades of currently declared symbols.
In[10]:=
Clear[A];
A+x⋀y,A∈,x∈
| OddGradeQ |
★Λ
3
★Λ
2
Out[10]=
True
The expression can contain powers (including reciprocals) of scalars.
In[11]:=
| OddGradeQ |
x
+
(x⋀y⋀z)⊖y
a
(
x⊖y)+
2
(a⋀b)
Out[11]=
True
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""