GrassmannCalculus | Wolfram Resource Object

GrassmannCalculus`

RawGradeCobasis

RawGradeCobasis[m][ B ]
	gives the list of all the essentially different exterior products of (Dimension-m) factors whose products with the elements of the list RawGradeBasis [m][ B ] give the exterior product of the elements of B .

RawGradeCobasis[][ B ]
	gives a list of all the lists in B . The elements of B may be arbitrary expressions.

Details and Options



Examples

(1)

Basic Examples

(1)

In[1]:=

<<GrassmannCalculus`

RawGradeCobasis

does not depend on any preference declarations.

In[2]:=

RawGradeCobasis

[2][{9,a,Sin[θ],x,

e

1

}]

Out[2]=

{Sin[θ]⋀x⋀

e

1

,-(a⋀x⋀

e

1

),a⋀Sin[θ]⋀

e

1

,-(a⋀Sin[θ]⋀x),9⋀x⋀

e

1

,-(9⋀Sin[θ]⋀

e

1

),9⋀Sin[θ]⋀x,9⋀a⋀

e

1

,-(9⋀a⋀x),9⋀a⋀Sin[θ]}

RawGradeCobasis

can also compose products of expressions. Notice that only the essentially different products have been retained.

In[3]:=

RawGradeCobasis

[2][{u,v⋀w,x⋀y⋀z,x⋀y⊖z}]

Out[3]=

{x⋀y⋀z⋀(x⋀y⊖z),-(v⋀w⋀(x⋀y⊖z)),v⋀w⋀x⋀y⋀z,u⋀(x⋀y⊖z),-(u⋀x⋀y⋀z),u⋀v⋀w}

If you leave the grade argument blank in

RawGradeCobasis

you will get a list of all the lists.

In[4]:=

RawGradeCobasis

[][{a,b,c,d}]

Out[4]=

{{a⋀b⋀c⋀d},{b⋀c⋀d,-(a⋀c⋀d),a⋀b⋀d,-(a⋀b⋀c)},{c⋀d,-(b⋀d),b⋀c,a⋀d,-(a⋀c),a⋀b},{d,-c,b,-a},{1}}

SeeAlso

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Grade

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