resolvent

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These are questions asked by resolvent

Recently, I submitted for publication to a peer-reviewed math journal

a formula for the n-th order implicit derivative given an implicit function G(z,w)=0.

i.e. dz/dw = - Gw/Gz where Gw and Gz are partial derivatives of G with respect to w and z, respectively. Anyway, I proved the general formula for d^n z/ dw^n.   I have since proved the generalization of this to implicit functions of several variables, G(z,w1,w2,...,w(N))=0. A good mathematician...

I have a multivariable function, F(n, g(1,0),g(0,1),g(0,2),g(1,1),g(2,1),...,g(n,1),g(n-1,2),...,g(1,n)), of indeterminates g(i,j) (omitting g(0,0) - in other words - let L = set of all pairs of nonnegative integers, (i,j), which satsify 1<= i+j <=n) of the following form F = product over all the (i,j) in L of g(i,j)^h(i,j) / ((i!

I want to graph a real-valued function e.g. plot y=x^2 from x=1 to 2.  There used to be a function called "plot2D". But it does not exist any more. When I call up the glossary or Help list, I get hundreds of plot-related functions - countourplot, loglogplot, etc - but not a plot for doing a real-valued function.  It is not under with(plots): 

My goal: given G(z,w), find the polynomial, P(n), in the partial derivatives of G(z,w) over the integer such that 

d^n z/ dw^n = P(n) / Gz^(2n-1)    where Gz= partial derivative of G with respect to z.

Step 1. Differentiate G(z(w),w) w.r.t w n times. Formulae are known for doing that (Mishkov, Tsoy-Wo Ma),

I need to formally partial-differentiate a given arbitrary function G(z,w) with respect to two other variables z=z(s,t) w=w(s,t) and then to express the p-th-total-order partial derivatives of z with respect to s and t as a polynomial in the partial derivatives of G with respect to z and w and the partial derivatives of w with respect to s and t, divided by the partial derivative of G with respect to z raised to the power 2p+1.   The eliminate function allows me to eliminate all partial derivatives of z w.r.t. s and t of total order lower than p.

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