Ilya Zakharevich on Fri, 29 Jan 1999 00:19:31 -0500 |
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Partial derivatives |
I'm thinking about adding new type "a transcendental function" to PARI. It is going to be a slight modification of a user variable (undeterminate) with some additional rules of manipulation stored in some database, so that q=Trans(sin,x^2); deriv(q,x) may be calculated to be 2*x*Trans(cos,x^2). But first I want to understand what happens with algebraic functions, which *apparently* should be supported with the current implementation as well. Does not it look strange to you that ? q=Mod(z,x+y+z) %1 = Mod(z, x + (z + y)) ? deriv(q,x) %2 = 0 ? deriv(q,y) %3 = 0 ? deriv(q,z) %4 = Mod(1, x + (z + y)) ? Suppose that we have a modification deriv(a,x,[y,y1,y2]) with the meaning "partial derivative of a wrt x when y,y1,y2 remain constant". Then deriv(q,x,[y]) might be calculated and be Mod(-1,x+(z+y)). Any thoughts? Ilya P.S. Why is it that I cannot make a damn from Chapter2's PolMods? Is not it a codification of some bugs in PARI? Why should y+Mod(x,x^2+1) behave any differently than Mod(x+y,x^2+1)?