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Generating a Jacobian matrix for a set of multivariate polynomials

Hi I can see that this is implemented for schemes but I do not want it in such vast generality - I have a (long) list of variables vee=var('a b c d ... ') and a long list of explicit polynomials f1(vee), f2(vee), ... in those variables. What please is the neatest way in which to construct the Jacobian matrix of first derivatives in such a way that I obtain the symbolic matrix (and can calculate a symbolic determinant say), and also am able to evaluate it at a particular set of values for the variables? Thanks for any ideas.