GrassmannCalculus`
SimplifyScalars  |
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Details and Options
Examples
(1)
Basic Examples
(1)
In[1]:=
<<GrassmannCalculus`
Set the book default to establish scalars and vectors.
In[2]:=
★A;
SimplifyScalars
In[3]:=
 | ★P |
| SimplifyScalars |
 | ★★P |
Out[3]=
b+(2⋀f⋀(-c)⋀(-a)⋀f⋀a)⊖(x⋀x)
Out[3]=
b+(2c)⊖0
2
a
2
f
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 0, making the exterior product with itself non-zero. Here, A is a new symbol.
In[4]:=
Clear[A];
b+(2⋀A⋀-c⋀-a⋀x⋀a)⊖(x⋀x),{A,x}∈
| SimplifyScalars |
★Λ
0
Out[4]=
b+2Ac
2
a
3
x
The following is a more complicated AngleBracket scalar expression that simplifies to zero.
In[5]:=
 | ★ℬ |
3
| ★★S |
a
b
c
In[6]:=
Clear[ss,tt,uu];BF=〈p⋀q⋀ss〉〈p⋀r⋀uu〉〈q⋀r⋀tt〉-〈p⋀q⋀tt〉〈p⋀r⋀ss〉〈q⋀r⋀uu〉-〈p⋀q⋀r〉〈p⋀r⋀uu〉〈q⋀ss⋀tt〉+〈p⋀q⋀r〉〈p⋀q⋀tt〉〈r⋀ss⋀uu〉;BF=BF/.{ssp+q+r,ttp+q+r,uup+q+r};BF//
a
1
a
2
a
3
b
1
b
2
b
3
c
1
c
2
c
3
| SimplifyScalars |
Out[6]=
0
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""