jacobian R -- calculates the Jacobian matrix of the ring R
jacobian f -- calculates the Jacobian matrix of the matrix f,
which will normally be a matrix with one row.
jacobian I -- compute the matrix of derivatives of the
generators of I w.r.t. all of the variables
i1 : R = ZZ/101[a..d];
i2 : I = monomialCurve(R,{1,3,4})
3 2 2 2 3 2
o2 = ideal (b*c - a*d, c - b*d , a*c - b d, b - a c)
o2 : Ideal of R
i3 : A = R/I
o3 = A
o3 : QuotientRing
i4 : jacobian A
o4 = {1} | 0 c2 -d -2ac |
{1} | -d2 -2bd c 3b2 |
{1} | 3c2 2ac b -a2 |
{1} | -2bd -b2 -a 0 |
4 4
o4 : Matrix A <--- A
For a one row matrix, the derivatives w.r.t. all the variables
is given
i5 : R = ZZ/101[a..c]
o5 = R
o5 : PolynomialRing
i6 : p = symmetricPower(2,vars R)
o6 = {0} | a2 ab ac b2 bc c2 |
1 6
o6 : Matrix R <--- R
i7 : jacobian p
o7 = {1} | 2a b c 0 0 0 |
{1} | 0 a 0 2b c 0 |
{1} | 0 0 a 0 b 2c |
3 6
o7 : Matrix R <--- R
Caveat: if a matrix or ideal over a quotient polynomial ring S/J
is given, then only the derivatives of the given elements are
computed and NOT the derivatives of elements of J.
