GrassmannCalculus`
OddRawGradeQ  |
Details and Options
Examples
(1)
Basic Examples
(1)
In[1]:=
<<GrassmannCalculus`
Set the book 3-dimensional space.
In[2]:=
★A;
OddRawGradeQ
In[3]:=
 | OddRawGradeQ |
Out[3]=
True
And with graded symbols:
In[4]:=
Table[,{m,0,6}]
[%]
[%%]
α
m
| OddGradeQ |
| OddRawGradeQ |
Out[4]=
,,,,,,
α
0
α
1
α
2
α
3
α
4
α
5
α
6
Out[4]=
{False,True,False,True,False,False,False}
Out[4]=
{False,True,False,True,False,True,False}
Multigraded expressions give True only if all the element grades are odd.
In[5]:=
,,
[%]
α
{1,3,5,7}
α
{0,6}
α
{3,4,5}
| OddRawGradeQ |
Out[5]=
,,
α
{1,3,5,7}
α
{0,6}
α
{3,4,5}
Out[5]=
{True,False,False}
The raw grade of 0 is neither even nor odd.
In[6]:=
Grade[0]
[0],
[0]
 | EvenRawGradeQ |
| OddRawGradeQ |
Out[6]=
★0
Out[6]=
{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[7]:=
Clear[A];
A+x,A∈,x∈
 | OddRawGradeQ |
★Λ
3
★Λ
3
Out[7]=
True
The expression can contain powers (including reciprocals) of scalars. The quantity in brackets is multigraded and reduced to odd grade by the interior product.
In[8]:=
| RawGrade |
Out[8]=
{4,6}
In[9]:=
| OddRawGradeQ |
x
+
(x⋀y⋀p⋀q⋀r)⋄z
a
(
x⊖y)+
2
(a⋀b)
Out[9]=
True
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""