GrassmannCalculus`
SimplifyRegressiveProducts  |
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Details and Options
Examples
(1)
Basic Examples
(1)
In[1]:=
<<GrassmannCalculus`
Here is an expression which 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
SimplifyRegressiveProducts
In[3]:=
 | SimplifyRegressiveProducts |
Out[3]=
a⊖x+x⋄0+++x∘+u⋀v+v⋀u+xx
α
5
0
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 x is of grade 2, making the regressive product with itself non-zero. (Note also that although A is zero in a 4-space, since it is not a regressive product, it has not been simplified to zero).
In[4]:=
| ★ℬ |
4
 | SimplifyRegressiveProducts |
★Λ
5
★Λ
2
Out[4]=
A+x⋁x
In[5]:=
Clear[X]
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""