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GradedLieAlgebras :: signExtLie

signExtLie -- returns the sign of a generator in the Ext-algebra

Synopsis

Usage:
s=signExtLie(r)
Inputs:
- r, a ring element, a generator in extAlgRing
Outputs:
- s, an integer, the sign of the input element

Description

To get the multi-degree of the element, use degree.

i1 : L=lieAlgebra({a,b},{[a,a,b],[b,b,a]},genWeights=>{{1,1},{1,1}})

o1 = L

o1 : LieAlgebra

i2 : extAlgLie 3

o2 = | 2 0 0 |
     | 0 0 2 |
     | 0 0 0 |

              3        3
o2 : Matrix ZZ  <--- ZZ

i3 : L.cache.extAlgRing

o3 = QQ[ext , ext , ext , ext ]
           0     1     2     3

o3 : PolynomialRing

i4 : signExtLie(ext_2)

o4 = 0

i5 : degree ext_2

o5 = {3, 3, 2}

o5 : List

See also

extAlgLie -- the matrix of dimensions of the Ext-algebra
extAlgRing -- the ring representation of the Ext-algebra

Ways to use `signExtLie` :

signExtLie(RingElement)