Gonzalo Garcia

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16 years, 99 days

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Let C a square in the n-diemnsional Euclidean space. Somebody know how to divide C into 2^{n} congruent subsquares? 

For instance, for n=2 and  say C:=[0,1]x[0,1], the unit closed square, we will obtain the 2^{2}=4 subsquares [0,1/4]x[0,1/4], [0,1/4]x[1/2], [1/2,1]x[0,1/4] and [1/2,1]x[1/2,1].  

Many thanks in advance for your comments!!


Assume that we hace a set points in the plane, put X:=[a1,a2,...,aN] where each ai is given by its coordinates [x,y]. The commnad "convexhull(X)" give us the points of the convex hull of X, but how I can find to "lower-right" of these points? Please, see the attached image. I need to findo the points A,C,E and F, marked with a solid circle.

Many thanks in advances for your comments.




I have seen a Mathematica code which I would like to have it in Maple, since I do not know that program. Let f(z) an analytic function, say f(z):=1+2^{z+1}+3^{z}. To find the roots of f(z) in a regingion, we can use in Maple the command "Analytic" (of the package "RootFinding"). However, in Mathematica is used the following:

L = 20; Monitor[zeros = Flatten@Table[N[z /. Solve[f[z] ⩵ 0 && k L ≤ Re[z] ≤ k L + L && -10 < Im[z] < 10, z], 25],{k, 300}],k];

What means the "N[z/. Solve..." instruction? Also, the following command:

SortBy[zeros, Re]; 

Can be "translated" to Maple?


Many thaks in advance for your comments!

With Regards,



I have seen th following procedure to compute the image of the points of [0,1] under the so called Peano space-filling curve (sorry, I have to pasted the code in "text plane" mode):

P[0] := (x, y) -> ((1/3)*y, (1/3)*x);

P[1] := (x, y) -> (-(1/3)*x+1/3, (1/3)*y+1/3); 

P[2] := (x, y) -> ((1/3)*x, (1/3)*y+2/3); 

P[3] := (x, y) -> ((1/3)*x+1/3, -(1/3)*y+1);

P[4] := (x, y) -> (2/3-(1/3)*y, 2/3-(1/3)*x); 

P[5] := (x, y) -> ( (1/3)*x+1/3, 1/3-(1/3)*y));

 P[6] := (x, y) -> (1/3)*x+2/3, (1/3)*y);

P[7] := (x, y) -> (-(1/3)*x+1, (1/3)*y+1/3);

P[8] := (x, y) -> ((1/3)*x+2/3, (1/3)*y+2/3);

peano := proc (t::numeric, depth::integer)

local q, r; global P;

if depth = 0 then return 0, 0 end if;

q := floor(9*t); r := 9*t-q;

return P[q](peano(r, depth-1))

end proc;


Now, I need to use the procedure "peanofun" as a function. For instance, if we define f:=(x,y)->x+y, I need to use (plot, compute, etc) for instance, the function f(peanofun(t,5))

Can you help me with this issue, please?

Many thanks for your time!




I am an error with the use of the function "Analytic" of the packpage RootFinding. These are the procedures:


CreaCos := proc (C, n, m, t) local k, F; F := C[1][1]+(C[1][2]-C[1][1])*t; for k to n-1 do F := F, C[k+1][1]+((1/2)*C[k+1][2]-(1/2)*C[k+1][1])*(1-cos(Pi*m^k*t)) end do; return F end proc;


Then, for k=50, 100, 150... the instruction

works correctly. However, for higher values of k (for instance, k=250) returns the below error. Some idea or suggets about occurs this error?

Many thanks for your time! 

Error, (in RootFinding:-Analytic) unable to evaluate `@`(evalf, proc (x) option remember; table( [( 0.524900000000000000000000000000e-1+Float(undefined)*I ) = Float(undefined)+Float(undefined)*I ] ) 31250*Pi*sin(62500*Pi*x)/(7/18-(1/2)*cos(62500*Pi*x)) end proc) at the value 0.524900000000000000000000000000e-1+Float(undefined)*I. The expression to be solved was probably not analytic.




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