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firstDegree -- get the degree of an element

Description

The degree of an element $x$ in a Lie algebra or an Ext-algebra is the first degree of the homogeneous element $x$. The zero element has degree 0; however, its degree should be thought of as arbitrary. The degree of a Lie derivation $d$ is the first degree of $d$ considered as a graded map.

Synopsis

  • Usage:
    n=firstDegree(x)
  • Inputs:
  • Outputs:
    • n, an integer, the first degree of $x$

Synopsis

  • Usage:
    n=firstDegree(x)
  • Inputs:
  • Outputs:
    • n, an integer, the first degree of $x$

Synopsis

  • Usage:
    n=firstDegree(d)
  • Inputs:
  • Outputs:
    • n, an integer, the first degree of $d$
i1 : L = lieAlgebra({a,b,c},Weights=>{1,2,3})

o1 = L

o1 : LieAlgebra
 
i2 : firstDegree(c a b+a b c)

o2 = 6
 
i3 : E = extAlgebra(5,L)

o3 = E

o3 : ExtAlgebra
 
i4 : apply(gens E,firstDegree)

o4 = {1, 2, 3}

o4 : List
 
i5 : d=lieDerivation({a c b,b b c,c c b})

o5 = d

o5 : LieDerivation
 
i6 : firstDegree d

o6 = 5

See also

Ways to use firstDegree:

  • firstDegree(ExtElement)
  • firstDegree(LieDerivation)
  • firstDegree(LieElement)

For the programmer

The object firstDegree is a method function.

The source of this document is in GradedLieAlgebras/doc2.m2:537:0.