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Macaulay2Doc :: jacobian(Ring)

jacobian(Ring) -- the Jacobian matrix of the polynomials defining a quotient ring

Synopsis

Description

This is identical to jacobian presentation R, except that the resulting matrix is over the ring R. See jacobian(Matrix) for more information.
i1 : R = QQ[x,y,z]/(y^2-x^3-x^7);
i2 : jacobian R

o2 = {1} | -7x6-3x2 |
     {1} | 2y       |
     {1} | 0        |

             3       1
o2 : Matrix R  <--- R
If the ring R is a (quotient of a) polynomial ring over a polynomial ring, then the top set of indeterminates is used, on the top set of quotients:
i3 : A = ZZ[a,b,c]/(a^2+b^2+c^2);
i4 : R = A[x,y,z]/(a*x+b*y+c*z-1)

o4 = R

o4 : QuotientRing
i5 : jacobian R

o5 = {1, 0} | a |
     {1, 0} | b |
     {1, 0} | c |

             3       1
o5 : Matrix R  <--- R