basisCoeffs -- Expand a finite-dimensional algebra element into its basis

i1 : (A,B,FF,I)=setupCotangent(2,4,Presentation=>Borel,Ktheory=>true,Equivariant=>false)

o1 = (A, B, FF, {0 0 1 1, 0 1 0 1, 0 1 1 0, 1 0 0 1, 1 0 1 0, 1 1 0 0})

o1 : Sequence

i2 : basis A

o2 = | 1 x_(1,{3, 4}) x_(1,{3, 4})^2 x_(1,{3, 4})x_(2,{3, 4}) x_(2,{3, 4})
     ------------------------------------------------------------------------
     x_(2,{3, 4})^2 |

             1      6
o2 : Matrix A  <-- A

i3 : basisCoeffs(x_(1,{1,2})^2)

o3 = | 16 |
     | -8 |
     | 1  |
     | 0  |
     | 0  |
     | 0  |

              6       1
o3 : Matrix FF  <-- FF