Examples

Special Matrices

• JacobianMat(f, indets) -- where f (polynomials) and indets (indeterminates) are vectors of RingElem, all belonging to the same PolyRing. The (i,j)-th element of the Jacobian matrix is defined as the derivative of i-th function with respect to the j-th indeterminate.
  Throws if both f and indets are empty (cannot determine the ring for constructing the 0x0 matrix).

• JacobianMat(f) -- Jacobian matrix with respect to all indets in the ring.

• TensorMat(A, B) -- where A and B are matrices with the same BaseRing.

• LawrenceMat(A) -- Lawrence lifting of the matrix A.

• SylvesterMat(f,g,x) -- create Sylvester matrix for polys f and g w.r.t. indeterminate x

• HilbertMat(n) -- create an n-by-n matrix over QQ whose (i,j) entry is 1/(i+j-1)

• RandomUnimodularMat(R,n,niters) -- create a random matrix with integer entries and determinant +1 or -1; last arg niters is optional (it defaults to 25*n).

• RandomSparseNonSing01Mat(R,n) -- create a random sparse non-singular (0,1) matrix of size n-by-n