# randomExtension -- a random extension of a vector bundle on E by another vector bundle

## Synopsis

• Usage:
V=randomExtension(V1,V2)
V=randomExtension(Y1,Y2)
• Inputs:
• V1, an instance of the type VectorBundleOnE,
• V2, an instance of the type VectorBundleOnE,
• Y1, , a matrix which is the yAction of some VectorBundleOnE
• Y2, , a matrix which is the yAction of some VectorBundleOnE
• Outputs:

## Description

Chooses a random extension of V2 by V1, where V1, V2 are vector bundles on E represented by the type VectorBundleOnE.

 i1 : kk=ZZ/101; i2 : g=1; i3 : rNP=randNicePencil(kk,g); i4 : cM=cliffordModule(rNP.matFact1,rNP.matFact2,rNP.baseRing); i5 : f=cM.hyperellipticBranchEquation 3 2 2 3 4 o5 = - 12s t - 50s t - 16s*t + 47t o5 : kk[s, t] i6 : L1=randomLineBundle(0,f) o6 = VectorBundleOnE{...1...} o6 : VectorBundleOnE i7 : L2=randomLineBundle(2,f) o7 = VectorBundleOnE{...1...} o7 : VectorBundleOnE i8 : V=randomExtension(L1,L2) o8 = VectorBundleOnE{...1...} o8 : VectorBundleOnE i9 : V.yAction o9 = {-1} | -18s2-13st-43t2 13s2+45st-16t2 40s4+37s3t+16s2t2+35st3 {-1} | 45s2-14st-t2 18s2+13st+43t2 11s4+45s3t+6s2t2-5st3+3t4 {1} | 0 0 48s2+36st+35t2 {-1} | 0 0 44s4+s3t-22s2t2+33st3-t4 ------------------------------------------------------------------------ -42s2-33st-48t2 | 39s2-30st+32t2 | -34 | -48s2-36st-35t2 | 4 4 o9 : Matrix (kk[s, t]) <--- (kk[s, t]) i10 : degOnE V o10 = 2 i11 : V1=randomExtension(L2,V) o11 = VectorBundleOnE{...1...} o11 : VectorBundleOnE i12 : V1.yAction o12 = {1} | 48s2+36st+35t2 -34 36 {-1} | 44s4+s3t-22s2t2+33st3-t4 -48s2-36st-35t2 29s2+40st-43t2 {-1} | 0 0 -18s2-13st-43t2 {-1} | 0 0 45s2-14st-t2 {1} | 0 0 0 {-1} | 0 0 0 ----------------------------------------------------------------------- -38 -22s2-40st+6t2 -29 | 41s2-19st-15t2 -28s4-20s3t+11s2t2+31st3-5t4 29s2-3st+50t2 | 13s2+45st-16t2 40s4+37s3t+16s2t2+35st3 -42s2-33st-48t2 | 18s2+13st+43t2 11s4+45s3t+6s2t2-5st3+3t4 39s2-30st+32t2 | 0 48s2+36st+35t2 -34 | 0 44s4+s3t-22s2t2+33st3-t4 -48s2-36st-35t2 | 6 6 o12 : Matrix (kk[s, t]) <--- (kk[s, t]) i13 : degOnE V1 o13 = 4