symbolic-math

I have a function f(t)=2/(2-t) . It is not so hard to get the rth derivative at t=0 (i.e. 2^(-r)*r! ) without using Mathematica. In the case of Mathematica calculation, I can get the r-th derivative when r=4 like this: D[2/(2-t), {t, 4}] . But how can I get the rth derivative at t=0 in Mathematica when r is ANY integer? I tried to use this expression, but it didn't work as expected: Simplify[D[2/(2 - t), {t, r}], Assumptions -> Element[r, Integers]] /. {t->0} Is it possible to do the above math symbolically in Mathematica just as we humans do? f = FindSequenceFunction[Table[D[2/(2 - t), {t, n}

Does anybody know of any resources (books, classes, lecture notes, or anything) about the general theory of computer algebra systems (e.g. mathematica , sympy )? "Introductory" materials are preferred, but I realize that with such a specialized subject anything is bound to be fairly advanced. "General Theory" of CAS is a pretty huge scope for a question. That being said, I'll do my best to cover as much as I can in the hopes that something helps you find what you're looking for :) The proceedings of the ISSAC and SIGSAM groups would no doubt have some good stuff about techniques for building

I am trying to find intersection points of two curves syms x y g(x) = 20*(exp(-(x+30)/3.5)-1); [sol_x, sol_y] = solve((x+22.3097)^2+(y+16.2497)^2 == 25, y == g(x),x,y,'Real',true) ; It is giving only one solution. But according to the plot of the two equations, there should be two intersection points. How can I rectify this problem? The solver can not find a analytic solution, thus a numeric solver is used. There is no reliable way in finding all solutions with a numeric method, but if you have a good guess (e.g. from a plot) try vpasolve with a reasonable set initial value. In this case, with

I tried using the .. command in MATLAB to generate Laguerre polynomials but I keep getting this error every time: I found this in the help section: Since I have defined x as symbolic I shouldn't be getting this error. Also on website I found this which says that the function does not run in MATLAB. Can anyone help? Thanks in advance Like you say, and the matlab help says this function only works inside mupad, maybe in later versions it works in matlab console. If you want to use it, write mupad in Matlab Command window and then use it in the mupad, matlab will return you the result as I show

I am trying to run the function mtaylor from the MuPAD engine in MatLab, which provides a multivariate Taylor expansion of a function. However, it keeps telling me I am trying to expand around an invalid point. Here is a minimal working example of what I tried: syms x y; feval(symengine,'mtaylor',exp(x^2 - y), [x, y], 4) Error message: vError using mupadengine/feval (line 157) MuPAD error: Error: Invalid expansion point. [mtaylor] Why doesn't this work? The reason this works with MuPAD's mtaylor syms x y; feval(symengine,'mtaylor',exp(x^2 - y), x, 4) % [x] is fine too and this doesn't syms x y

The following command syms x real; f = @(x) log(x^2)*exp(-1/(x^2)); fp(x) = diff(f(x),x); fpp(x) = diff(fp(x),x); and solve(fpp(x)>0,x,'Real',true) return the result solve([0.0 < (8.0*exp(-1.0/x^2))/x^4 - (2.0*exp(-1.0/x^2))/x^2 - (6.0*log(x^2)*exp(-1.0/x^2))/x^4 + (4.0*log(x^2)*exp(-1.0/x^2))/x^6], [x == RD_NINF..RD_INF]) which is not what I expect. The first question: Is it possible to force Matlab's solve to return the set of all solutions? (This is related to this question .) Moreover, when I try to solve the equation solve(fpp(x)==0,x,'Real',true) which returns ans = -1