GrassmannCalculus`
ToCommonFactorA  |
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Details and Options
Examples
(1)
Basic Examples
(1)
In[1]:=
<<GrassmannCalculus`
Here is the common factor of two simple 2-elements in a 3-space. and give the same form of the result, since the first factor is decomposable and uses the A form by default in this case. Since the second factor is decomposable also, ToCommonFactorB decomposes this factor and hence gives a different form of the result.
ToCommonFactor
ToCommonFactorA
ToCommonFactor
In[2]:=
★A;X=
,
,
[X]//Through//Column
(
x
⋀y)⋁(u⋀v) | ToCommonFactor |
| ToCommonFactorA |
| ToCommonFactorB |
Out[2]=
x⋀y⋁u⋀v
Out[2]=
★c(y〈u⋀v⋀x〉-x〈u⋀v⋀y〉) |
★c(y〈u⋀v⋀x〉-x〈u⋀v⋀y〉) |
★c(-v〈u⋀x⋀y〉+u〈v⋀x⋀y〉) |
When the first factor is not decomposable, but the second factor is decomposable, and both use the B form, giving the same form of result in all three cases.
ToCommonFactor
ToCommonFactorA
In[3]:=
X=⋁(u⋀v)
,
,
[X]//Through//Column
α
2
| ToCommonFactor |
| ToCommonFactorA |
| ToCommonFactorB |
Out[3]=
α
2
Out[3]=
★c-vu⋀ α 2 α 2 |
★c-vu⋀ α 2 α 2 |
★c-vu⋀ α 2 α 2 |
When the first factor is decomposable, but the second factor is not decomposable gives the same form of result as and .
ToCommonFactorB
ToCommonFactor
ToCommonFactorA
In[4]:=
X=
,
,
[X]//Through//Column
(
x
⋀y)⋁β
2
| ToCommonFactor |
| ToCommonFactorA |
| ToCommonFactorB |
Out[4]=
x⋀y⋁
β
2
Out[4]=
★cyx⋀ β 2 β 2 |
★cyx⋀ β 2 β 2 |
★cyx⋀ β 2 β 2 |
When neither factor is decomposable, no expansions are effected.
In[5]:=
X=⋁
,
,
[X]//Through//Column
α
2
β
2
| ToCommonFactor |
| ToCommonFactorA |
| ToCommonFactorB |
Out[5]=
α
2
β
2
Out[5]=
α 2 β 2 |
α 2 β 2 |
α 2 β 2 |
However, an additional decomposable factor may allow an expansion to occur, in this case in only one way.
In[6]:=
X=⋁
,
,
[X]//Through//Column
α
2
(
x
⋀y)⋁β
2
| ToCommonFactor |
| ToCommonFactorA |
| ToCommonFactorB |
Out[6]=
α
2
β
2
Out[6]=
2 ★c β 2 α 2 α 2 β 2 |
2 ★c β 2 α 2 α 2 β 2 |
2 ★c β 2 α 2 α 2 β 2 |
In[7]:=
Clear[X]
 |
|
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