# oddOperators -- part of a CliffordModule

## Synopsis

• Usage:
uOdd = M.oddOperators
• Outputs:
• uOdd, a list, of the odd operators on M

## Description

The list of the odd operators uOdd_i: M_1\to M_0

 i1 : kk = ZZ/101 o1 = kk o1 : QuotientRing i2 : g = 1 o2 = 1 i3 : (S, qq, R, u, M1, M2, Mu1, Mu2)=randomNicePencil(kk,g); i4 : M = cliffordModule(M1,M2, R) o4 = CliffordModule{...6...} o4 : CliffordModule i5 : M.oddOperators o5 = {{-4} | 0 0 0 0 5t 0 0 0 |, {-4} | 0 0 0 0 -s 0 0 0 |, {-4} | {-3} | 0 0 5t 0 0 0 0 0 | {-3} | 0 0 -s 0 0 0 0 0 | {-3} | {-3} | 0 -5t 0 0 0 0 0 0 | {-3} | 0 s 0 0 0 0 0 1 | {-3} | {-3} | 5t 0 0 0 0 0 0 0 | {-3} | -s 0 0 0 0 0 -1 0 | {-3} | {-3} | 0 0 0 0 0 0 0 -1 | {-3} | 0 0 0 0 0 0 0 0 | {-3} | {-3} | 0 0 0 0 0 0 1 0 | {-3} | 0 0 0 0 0 0 0 0 | {-3} | {-3} | 0 0 0 0 0 -1 0 0 | {-3} | 0 0 0 0 1 0 0 0 | {-3} | {-2} | 0 0 0 -1 0 0 0 0 | {-2} | 0 0 1 0 0 0 0 0 | {-2} | ------------------------------------------------------------------------ 0 0 0 0 -12t 18t s+30t 0 |, {-4} | 0 0 0 0 0 0 -12t 18t 0 0 0 -1 | {-3} | 0 0 12t -10t 0 12t 0 s+30t 0 0 0 0 | {-3} | 0 -12t 0 -6t -12t 0 0 0 0 1 0 0 | {-3} | 12t 0 0 48t 0 -18t -s-30t 0 0 0 0 0 | {-3} | 0 10t 6t 0 18t 0 0 0 -1 0 0 0 | {-3} | -10t 0 -48t 0 s+30t 0 0 0 0 0 0 0 | {-3} | -6t 48t 0 0 0 -1 0 0 0 0 0 0 | {-2} | 1 0 0 0 ------------------------------------------------------------------------ 12t -10t -6t 48t |} 0 0 1 0 | 0 -1 0 0 | 0 0 0 0 | 1 0 0 0 | 0 0 0 0 | 0 0 0 0 | 0 0 0 0 | o5 : List