GrassmannCalculus`
EvenGradeQ  |
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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 even grade.
In[3]:=
2
x
e
x
 | EvenGradeQ |
Out[3]=
2
x
e
x
Out[3]=
True
The following is not because it contains one odd grade term.
In[4]:=
2
x
e
x
e
x
| EvenGradeQ |
Out[4]=
2
x
e
x
e
x
Out[4]=
False
Set a 4-dimensional space.
In[5]:=
★A;
;
| ★ℬ |
4
EvenGradeQ
In[6]:=
| EvenGradeQ |
Out[6]=
True
And with graded symbols:
In[7]:=
Table[,{m,0,4}]
[%]
α
m
| EvenGradeQ |
Out[7]=
,,,,
α
0
α
1
α
2
α
3
α
4
Out[7]=
{True,False,True,False,True}
Multigraded expressions give True only if all the element grades are even.
In[8]:=
,,
[%]
α
{0,2,4}
α
{1,3}
α
{0,1,2}
| EvenGradeQ |
Out[8]=
,,
α
{0,2,4}
α
{1,3}
α
{0,1,2}
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 symbols as long as you assert their grades, or you can override the grades of currently declared symbols.
In[10]:=
Clear[A];
A+x,A∈,x∈
| EvenGradeQ |
★Λ
4
★Λ
2
Out[10]=
True
The expression can contain powers (including reciprocals) of scalars. The quantity in brackets is multigraded and reduced to even grade by the interior product.
In[11]:=
Grade[(x⋀y)⋄z]
Out[11]=
{1,3}
In[12]:=
| EvenGradeQ |
1
+
(x⋀y)⋄z
a
(
x⊖y)+
2
(a⋀b)
Out[12]=
True
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""