GrassmannCalculus`
SimplifyVectorSpaceComplements  |
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Details and Options
Examples
(1)
Basic Examples
(1)
In[1]:=
<<GrassmannCalculus`
Here is an expression that simplifies to zero.
GrassmannSimplify
In[2]:=
★A;X=u⋀v+v⋀u+x⋁y+a⊖x+x⋄0+x∘+x
x++GrassmannSimplify[X]
z
4
 | △ |
0
α
5
0
Out[2]=
a⊖x+x⋄0+++x∘+x⋁y+u⋀v+v⋀u+xx
α
5
0
z
4
△
0
Out[2]=
0
SimplifyVectorSpaceComplements
In[3]:=
 | SimplifyVectorSpaceComplements |
Out[3]=
a⊖x+x⋄0++x∘+x⋁y+u⋀v+v⋀u+xx
α
5
z
4
△
0
You can also use new symbols as long as you assert their grades, or you can override the grades of currently declared symbols. Here we assert that (a declared vector symbol) and (an undeclared symbol) are both of grade 4, making them (and their vector space complement) zero in a 3-space. (Note that the Grassmann complement , although also zero, is not simplified by .
x
A
A+x
SimplifyVectorSpaceComplements
In[4]:=
| ★ℬ |
3
 | SimplifyVectorSpaceComplements |
A+x
A+x
★Λ
4
Out[4]=
A+x
In[5]:=
Clear[X]
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""