# symMatrix -- part of a CliffordModule

## Synopsis

• Usage:
s = symMatrix(eOdd,eEv)
• Inputs:
• eOdd, a list,
• eEv, a list, operators on a Clifford Module
• Outputs:
• s, , over k[s,t], the base of the Clifford algebra

## Description

Computes the matrix given by the pencil of quadrics defining the Clifford algebra.

 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.evenOperators o5 = {{-1} | 0 0 0 -1 0 0 0 0 |, {-1} | 0 0 0 0 0 -1 0 0 |, {-1} {-1} | 0 0 1 0 0 0 0 0 | {-1} | 0 0 0 0 1 0 0 0 | {-1} {-1} | 0 -1 0 0 0 0 0 0 | {-1} | 0 0 0 0 0 0 0 0 | {-1} {-1} | 0 0 0 0 0 0 0 5t | {-1} | 0 -1 0 0 0 0 0 -s | {-1} {-2} | -1 0 0 0 0 0 0 0 | {-2} | 0 0 0 0 0 0 0 0 | {-2} {-2} | 0 0 0 0 0 0 5t 0 | {-2} | -1 0 0 0 0 0 -s 0 | {-2} {-2} | 0 0 0 0 0 -5t 0 0 | {-2} | 0 0 0 0 0 s 0 0 | {-2} {-2} | 0 0 0 0 5t 0 0 0 | {-2} | 0 0 0 0 -s 0 0 0 | {-2} ------------------------------------------------------------------------ | 0 0 0 0 0 0 -1 0 |, {-1} | 0 0 0 0 | 0 0 0 0 0 0 0 s+30t | {-1} | 0 0 0 0 | 0 0 0 0 1 0 0 -18t | {-1} | 0 0 0 0 | 0 0 -1 0 0 0 0 -12t | {-1} | 0 0 0 -1 | 0 0 0 0 0 s+30t -18t 0 | {-2} | 0 0 0 0 | 0 0 0 -s-30t 0 0 -12t 0 | {-2} | 0 0 48t 6t | -1 0 0 18t 0 12t 0 0 | {-2} | 0 -48t 0 -10t | 0 s+30t -18t 0 -12t 0 0 0 | {-2} | -1 -6t 10t 0 ------------------------------------------------------------------------ 0 0 0 -48t |} 0 0 -1 -6t | 0 1 0 10t | 0 0 0 12t | -48t -6t 10t 0 | 0 0 12t 0 | 0 -12t 0 0 | 12t 0 0 0 | o5 : List i6 : symMatrix(M.evenOperators,M.oddOperators) o6 = | -5t -50s 6t -6t | | -50s 0 -9t 5t | | 6t -9t -s-30t 3t | | -6t 5t 3t -48t | 4 4 o6 : Matrix R <--- R