GrassmannCalculus`
GeneralizedProduct  |
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| | ||||
Details and Options
Examples
(3)
Basic Examples
(1)
In[1]:=
<<GrassmannCalculus`
Set the book default and turn on Precedence showing.
In[2]:=
★A;
;
 | ★P |
These inputs are equivalent:
In[3]:=
y
 | GeneralizedProduct |
[
λ
]
[x,y],x | △ |
λ
Out[3]=
xy,xy
△
λ
△
λ
And so are these:
In[4]:=
y
z,x
y
z
| GeneralizedProduct |
[
λ
]
 | GeneralizedProduct |
[
μ
]
[x,y],z,x | △ |
μ
| △ |
λ
| △ |
μ
| △ |
λ
Out[4]=
xyz,xyz,xyz
△
μ
△
λ
△
μ
△
λ
△
μ
△
λ
Because the generalized Grassmann product is not necessarily associative the following inputs are not necessarily equivalent as can be verified by looking at the form with Precedence showing.
In[5]:=
x
y
z,x
y
z
| △ |
a
| △ |
a
| △ |
a
| △ |
a
Out[5]=
{x(yz),(xy)z}
△
a
△
a
△
a
△
a
The generalized product is listable.
In[6]:=
w
{u,v}
 | △ |
λ
Out[6]=
wu,wv
△
λ
△
λ
The following again illustrates listability and precedence.
In[7]:=
{w,z}
{u,v}
{x,y}
| △ |
μ
| △ |
λ
Out[7]=
wux,zvy
△
μ
△
λ
△
μ
△
λ
In[8]:=
{w,z}
{u,v}
{x,y}
| △ |
μ
| △ |
λ
Out[8]=
wux,zvy
△
μ
△
λ
△
μ
△
λ
In[9]:=
 | ★★P |
Clifford Products
(1)
Hypercomplex Products
(1)
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""