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GrassmannCalculus`

GradeBasis

GradeBasis[m]
	gives the list of basis elements of grade m constructed from the currently declared basis.

Details and Options



Examples

(1)

Basic Examples

(1)

In[1]:=

<<GrassmannCalculus`

In the algebra of 3-space, the bases are:

In[2]:=

★A;Table

GradeBasis

[m],{m,0,3}//Column

Out[2]=

{1}

{

e

1

,

e

2

,

e

3

}

{

e

1

⋀

e

2

,

e

1

⋀

e

3

,

e

2

⋀

e

3

}

{

e

1

⋀

e

2

⋀

e

3

}

If you now declare a 4-space, the bases are:

In[3]:=

★ℬ

4

;Table

GradeBasis

[m],{m,0,4}//Column

Out[3]=

{1}

{

e

1

,

e

2

,

e

3

,

e

4

}

{

e

1

⋀

e

2

,

e

1

⋀

e

3

,

e

1

⋀

e

4

,

e

2

⋀

e

3

,

e

2

⋀

e

4

,

e

3

⋀

e

4

}

{

e

1

⋀

e

2

⋀

e

3

,

e

1

⋀

e

2

⋀

e

4

,

e

1

⋀

e

3

⋀

e

4

,

e

2

⋀

e

3

⋀

e

4

}

{

e

1

⋀

e

2

⋀

e

3

⋀

e

4

}

For a point basis in 3-space:

In[4]:=

★

3

;Table

GradeBasis

[m],{m,0,4}//Column

Out[4]=

{1}

{★,

e

1

,

e

2

,

e

3

}

{★⋀

e

1

,★⋀

e

2

,★⋀

e

3

,

e

1

⋀

e

2

,

e

1

⋀

e

3

,

e

2

⋀

e

3

}

{★⋀

e

1

⋀

e

2

,★⋀

e

1

⋀

e

3

,★⋀

e

2

⋀

e

3

,

e

1

⋀

e

2

⋀

e

3

}

{★⋀

e

1

⋀

e

2

⋀

e

3

}

SeeAlso

▪

▪

RelatedGuides

▪

▪

▪

Grassmann Calculus

▪

Grassmann Calculus

▪

""