# boundaries -- make the subalgebra of boundaries

## Synopsis

• Usage:
B=boundaries(L)
• Inputs:
• Outputs:
• B, an instance of the type LieSubAlgebra, the image of the differential

## Description

 i1 : L=lieAlgebra({a,b},Signs=>{1,0},Weights=>{{2,0},{2,1}}, LastWeightHomological=>true,Field=>ZZ/3) o1 = L o1 : LieAlgebra i2 : L=differentialLieAlgebra{0_L,a} o2 = L o2 : LieAlgebra i3 : B=boundaries L o3 = B o3 : LieSubAlgebra i4 : dims(10,B) o4 = | 0 1 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 1 0 1 | | 0 0 0 0 0 0 0 1 0 1 | | 0 0 0 0 0 0 0 0 0 1 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | 10 10 o4 : Matrix ZZ <--- ZZ

## See also

• cycles -- make the subalgebra of cycles
• lieHomology -- make the homology as a vector space

## Ways to use boundaries :

• "boundaries(LieAlgebra)"

## For the programmer

The object boundaries is .