symExt -- from linear presentation matrices over S to linear presentation matrices over E and conversely

i1 : n={1,2}

o1 = {1, 2}

o1 : List

i2 : (S,E) = productOfProjectiveSpaces n

o2 = (S, E)

o2 : Sequence

i3 : vars S, vars E

o3 = (| x_(0,0) x_(0,1) x_(1,0) x_(1,1) x_(1,2) |, | e_(0,0) e_(0,1) e_(1,0)
     ------------------------------------------------------------------------
     e_(1,1) e_(1,2) |)

o3 : Sequence

i4 : m=map(S^4,S^{{ -1,0},{0,-1}}, transpose matrix{{S_0,S_1,0,0},{S_2,0,S_3,S_4}})

o4 = | x_(0,0) x_(1,0) |
     | x_(0,1) 0       |
     | 0       x_(1,1) |
     | 0       x_(1,2) |

             4      2
o4 : Matrix S  <-- S

i5 : mE=symExt(m,E)

o5 = {-1, 0} | 0        e_(0,0) 0       0       |
     {-1, 0} | 0        0       e_(0,0) 0       |
     {-1, 0} | 0        0       0       e_(0,0) |
     {-1, 0} | e_(0,1)  0       0       0       |
     {-1, 0} | -e_(0,0) e_(0,1) 0       0       |
     {-1, 0} | 0        0       e_(0,1) 0       |
     {-1, 0} | 0        0       0       e_(0,1) |
     {0, -1} | 0        e_(1,0) 0       0       |
     {0, -1} | 0        0       e_(1,0) 0       |
     {0, -1} | 0        0       0       e_(1,0) |
     {0, -1} | e_(1,1)  0       0       0       |
     {0, -1} | 0        e_(1,1) 0       0       |
     {0, -1} | -e_(1,0) 0       e_(1,1) 0       |
     {0, -1} | 0        0       0       e_(1,1) |
     {0, -1} | e_(1,2)  0       0       0       |
     {0, -1} | 0        e_(1,2) 0       0       |
     {0, -1} | 0        0       e_(1,2) 0       |
     {0, -1} | -e_(1,0) 0       0       e_(1,2) |

             18      4
o5 : Matrix E   <-- E