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.
| a_11 B | a_12 B | ... | a_1c B |
| a_21 B | a_22 B | ... | a_2c B |
| ... | |||
| a_r1 B | a_r2 B | ... | a_rc B |
LawrenceMat(A) --
Lawrence lifting of the matrix A.
| A | 0 |
| I | I |
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
Many special matrices are not yet implemented: (from the source file)
2016
RandomUnimodularMat
2011
jacobian)
TensorMat