Annonymouse

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6 years, 98 days

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These are questions asked by Annonymouse

I am interested in taking a complex number and repeatedly raising it to a power and graphing the result to see if it looks cool (i think it will) to do this i wrote this program

iterativepower := proc (base, index, n)

local out, i;
out := vector(n+1, 1);

out[1] := base;

for i to n do out[i+1] := out[i]^index end do;

out;

end proc;


this can be run with:

iterativepower(2, 2, 5)


This doesn't return a vector, it returns the word out. Why is that, and how do i fix it?


How can you get maple to evaluate i^i?

when i type in
I^I

i just get

I^I

and similarly when i raise numbers to complex powers i get results like 2^(2I+6)

 

These are the timings for various algorithms, using different starting points deriving surfaces of dimension 5, 4, 3, 2, 1

times3:=[[], [.140], [1.344, .891], [1.578, 1.312, 1.375, 1.437, 1.922, 2.625, 6.406], [2.188, 2.312, 1.687, 2.110, 2.047, 1.578, 8.953, 1.891, 1.875, 9.344, 2.203, 55.969, 2.266, 2.531, 81.078, 2.172, 50.641, 2.500, 3.141, 61.656, 3.406, 3.375]]

times1:=[[.718], [.766, 4.703], [.750, .797, 7.594, 3.938], [6.594, 7.718, 11.969, 8.485, 11.391, 130.583, 548.284, 974.435], [7.281, 8.515, 65.569, 7.016, 8.312, 9.500, 8.562, 9.766, 10.641, 12.609, 13.281, 17.453, 18.640, 1763.860, 2659.990, 7812.89, 8189.139]]

So far i can get a boxplot of either:
Statistics:-BoxPlot(`~`[`~`[log10]](times3));
Statistics:-BoxPlot(`~`[`~`[log10]](times1));

but what I'd like is a boxplot like this but i can't work out how to do this.
 

I am working on a simple program (4 lines excluding header/footer and debug command) that calculates a Lie-derivatives of a function G, supplied by the user, with the rule:
 

derivative of x[i]=F[i]  (an input supplied by the user),
derivative of y[i]=y[i+1].


this calculation revolves around a dot product, and I can't seem to work out what has gone wrong. My impression is that is because nops of a Vector gives you  1 more than the length of the Vector, so the Vector handed to DotProduct is wrong- but i can't see why it doesn't work in the case of G2 and F2 but does for G and F.

lieDer2_problems_mwe.mw

I recently corresponded with maplesoft on whether the program Groebner:-Basis always produces reduced Groebner bases or not. They say it does. This mw appears to show it producing a non reduced Groebner Basis for a set of polynomials.

More specifically, the coefficient of the lead term of the first polynomial generated is not 1.

I'd like to be shown wrong here, but I am struggling to see what i could be doing wrong.

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