GrassmannCalculus`
DeclareExtraVectorSymbols (★★V)  |
| DeclareExtraVectorSymbols[ lists UserVectorSymbols CurrentSpacePreferences | |
Details and Options
Examples
(1)
Basic Examples
(1)
In[1]:=
<<GrassmannCalculus`
In[2]:=
 | SetActiveSpacePreferences |
 | PublicGrassmannAtlas |
The following are the current and , which also includes all basis vectors and :
UserVectorSymbols
VectorSymbols
UserFormSymbols
In[3]:=
UserVectorSymbols
 | ★v |
Out[3]=
{p,q,r,s}
Out[3]=
dx,dy,p,q,r,s,α,β,ψ,ω,,,,
e
x
e
y
e
x
e
y
The following expression does not simplify because has not been declared a vector symbol.
In[4]:=
⋀%//
| ★ |
Out[4]=
⋀
Out[4]=
⋀
Add to the list of .
UserVectorSymbols
In[5]:=
| ★★V |
| ★v |
Out[5]=
{p,q,r,s,}
Out[5]=
dx,dy,p,q,r,s,,α,β,ψ,ω,,,,
e
x
e
y
e
x
e
y
The expression now simplifies;
In[6]:=
⋀%//
| ★ |
Out[6]=
⋀
Out[6]=
0
The new vector now appear on the GrassmannCalculus palette and also on the if recreated.
GrassmannSymbolsPalette
In[7]:=
| GrassmannSymbolsPalette |
You can add extra vector symbols or patterns in any argument or list form:
In[8]:=
| ★★V |
f
| ★v |
Out[8]=
{p,q,r,s,t,u,v,w,,}
f
Out[8]=
dx,dy,p,q,r,s,t,u,v,w,,α,β,ψ,ω,,,,,
e
x
e
y
e
x
e
y
f
The Grassmann algebra routines will now simplify expressions using the vector pattern.
In[9]:=
(a+b)⋀(c+d)%//
f
1
f
2
f
1
f
2
| ★ |
Out[9]=
(a+b)⋀(c+d)
f
1
f
2
f
1
f
2
Out[9]=
(-bc+ad)⋀
f
1
f
2
Existing scalars, basis symbols or forms cannot be declared as user vector symbols.
In[10]:=
| ★★V |
e
x
DeclareVectorSymbols::scalarsymbol:The symbols in the list {a,x,y} have already been declared as scalar symbols. Scalar symbols cannot also be declared as vector or form symbols, since they are of different grade.
DeclareVectorSymbols::form:The symbols in the list {ω} have already been declared as forms. Forms cannot also be declared as vectors.
DeclareVectorSymbols::basis:The symbols in the list {dy,} have already been declared as basis elements. Basis elements cannot also be declared as vector or form symbols.
e
x
Out[10]=
DeclareUserVectorSymbols[{a,dy,★,p,q,r,s,t,u,v,w,x,y,,ω,,}]
e
x
f
 |
|
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