User documentation for MatrixSpecial
Examples
Special Matrices
JacobianMat(f, indets)
-- wheref
(polynomials) andindets
(indeterminates) are vectors ofRingElem
, all belonging to the samePolyRing
. 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 bothf
andindets
are empty (cannot determine thering
for constructing the 0x0matrix
).JacobianMat(f)
-- Jacobian matrix with respect to all indets in the ring.
TensorMat(A, B)
-- whereA
andB
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 thematrix
A
.
A | 0 |
I | I |
SylvesterMat(f,g,x)
-- create Sylvester matrix for polysf
andg
w.r.t. indeterminatex
HilbertMat(n)
-- create ann
-by-n
matrix overQQ
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 argniters
is optional (it defaults to25*n
).RandomSparseNonSing01Mat(R,n)
-- create a random sparse non-singular (0,1) matrix of sizen
-by-n
Maintainer documentation
Bugs, shortcomings and other ideas
Many special matrices are not yet implemented: (from the source file)
- VandermondeMatrix
- HessianMatrix
- HilbertInverseMatrix
- ToeplitzMatrix
- WronskianMatrix
Main changes
2016
- November (v0.99544): added
RandomUnimodularMat
2011
- February (v0.9942): first release (
jacobian
) - March (v0.9943): added
TensorMat