GrassmannCalculus`
MPlaneElementFormQ  |
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Details and Options
Examples
(1)
Basic Examples
(1)
In[1]:=
<<GrassmannCalculus`
In[2]:=
SetGrassmannNSpace[5,{v,w,x,y,z},"Vector"]
The following are m-plane elements of various grades.
In[3]:=
 | MPlaneElementFormQ |
e
v
e
v
e
v
e
x
e
v
e
w
e
x
e
y
e
x
e
v
e
x
e
v
e
v
e
w
e
x
e
y
e
z
Out[3]=
{True,True,True,True,True,True,True,True}
The principal forms that are not m-planes are ones that are mixed grade, contain graded symbols, or lack an Origin.
In[4]:=
| MPlaneElementFormQ |
e
v
α
2
e
v
e
w
e
x
e
y
Out[4]=
{False,False,False}
The test can be confined to a single m-dimensional plane using an additional argument specifying m.
In[5]:=
| MPlaneElementFormQ |
e
v
e
x
| MPlaneElementFormQ |
e
v
e
x
| MPlaneElementFormQ |
Out[5]=
True
Out[5]=
False
Out[5]=
True
Switch to a non-Point space.
In[6]:=
SetEuclideanNSpace[5,{v,w,x,y,z},"Vector"]
The following are no longer weighted point forms because we are no longer in a Point space.
In[7]:=
| WeightedPointFormQ |
e
x
e
y
e
z
e
x
e
y
e
z
Out[7]=
{False,False,False,False,False}
You can compose an m-plane element form by using .
ComposeMPlaneElement
In[8]:=
★A;
;Π=
[3,a]
 | ★ |
5
 | ComposeMPlaneElement |
Out[8]=
(★+++++)⋀(++++)⋀(++++)⋀(++++)
a
1
e
1
a
2
e
2
a
3
e
3
a
4
e
4
a
5
e
5
a
6
e
1
a
7
e
2
a
8
e
3
a
9
e
4
a
10
e
5
a
11
e
1
a
12
e
2
a
13
e
3
a
14
e
4
a
15
e
5
a
16
e
1
a
17
e
2
a
18
e
3
a
19
e
4
a
20
e
5
In[9]:=
| MPlaneElementFormQ |
 | ★ |
 | ★ |
| ★ |
| ★ |
Out[9]=
{True,True,True,False}
In[10]:=
★A;Clear[Π]
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""