# Markiyan Hirnyk

Markiyan Hirnyk
9 years, 324 days

These are questions asked by Markiyan Hirnyk

### What is that limit?

September 20 2015 Maple
0 6

The following integral
f := u-> int(-1/(x*sqrt(-1+u^2*(x+1)^2*x^2)), x = (1/2)*(-u-sqrt(u^2-4*u))/u .. (1/2)*(-u+sqrt(u^2-4*u))/u);
arised in an applied research. I was asked about its properties:
plot on RealRange(4,infinity), limit(f(u),u=4,right), limit(f(u),u=infinity).
Unfortunately, I lost a file. As far as I remember it, I have had a problem with
the latter one only:

limit(f(u), u = infinity);

MultiSeries:-limit(f(u), u = infinity);

asympt(f(u), u, 2);

Error, (in asympt) unable to compute series

Hope my colleagues will make progress with it. The assumed value is Pi/2.

### How to create 2d Gaussian random field?

September 20 2015 Maple
0 10

Of course, with Maple. This object is described in Wiki.
Its plot looks like

Also the 2d Gaussian free field is of great interest. As far as I understand it, a one-dimensional Gaussian random field is formed by the
Finance[GaussMarkovProcess] command of Maple.

PS. The googling brings, in particular, http://mathematica.stackexchange.com/questions/4829/efficiently-generating-n-d-gaussian-random-fields.

### How is this nonstandard equation solved?

September 13 2015 Maple 2015
0 5

Here is a serious achievement of the Roots command:

Student[Calculus1]:-Roots(2^x+3^x+6^x-x^2);

[-1]

plot(2^x+3^x+6^x-x^2, x = -6 .. 2, gridlines = false);

The solve command also does the job here:

sol := solve(2^x+3^x+6^x-x^2);

allvalues(sol);

evalf(%):

The RealDomain:-solve command fails here.

I wonder how Maple solves it. It would be kind of Maple developers and experts to explain that.

PS. I tried printlevel:=10, but understood the output a little.

### Natural parametrization of curve

September 06 2015 Maple
0 13

Let a piecewise-linear curve be defined by a listlist. For example,

LL := [[1.1, 2.04], [1.97, 4.04], [2.96, 2.97], [4.5, 6.4], [5.08, 7.21], [1.1, 4.04], [1.1, 2.04]]:
plot(LL);

How to find its natural parametrization in Maple? A procedure is desired. See Wiki for info.

### Strange behavior of fsolve

July 26 2015 Maple
0 15

 > Let us define a piecewise-linear continuous function:
 > restart; VP := Vector[row](16, {(1) = 10, (2) = 177.9780267, (3) = 355.9560534, (4) = 533.9340801, (5) = 711.9121068, (6) = 889.8901335, (7) = 1067.868160, (8) = 1245.846187, (9) = 1423.824214, (10) = 1601.802240, (11) = 1779.780267, (12) = 1957.758294, (13) = 2135.736320, (14) = 2313.714347, (15) = 2491.692374, (16) = 2669.670400}); VE := Vector[row](16, {(1) = 5.444193931, (2) = .4793595141, (3) = .3166653569, (4) = .2522053489, (5) = .2123038784, (6) = .1822258228, (7) = .1544240625, (8) = .1277082078, (9) = .1055351619, (10) = 0.8639065510e-1, (11) = 0.6936612570e-1, (12) = 0.5388339810e-1, (13) = 0.3955702170e-1, (14) = 0.2612014630e-1, (15) = 0.1338216460e-1, (16) = 0.1203297900e-2}); for i to 15 do p[i] := VE[i+1] < x and x <= VE[i], (VP[i+1]-VP[i])*(x-VE[i])/(VE[i+1]-VE[i])+VP[i] end do; g := unapply(piecewise(seq(p[i], i = 1 .. 15)), x);
 > for i to 15 do print(fsolve(g(x) = VP[i])) end do;
 > Why doesn't the fsolve command work if i = 4, 7, 9, 11, 14? There are workarounds:
 > print(DirectSearch:-SolveEqutions(g(x) = VP[i]));
 > and/or
 > VP := convert(VP, rational); VE := convert(VE, rational); print(solve(g(x) = VP[i]));
 > How to explain such behavior of the fsolve command? That was asked but not answered in http://forum.exponenta.ru/viewtopic.php?t=13524&sid=025a140e7e00b99803c86060a5c0c33c .
 >

strange_behavior.mw

Edit. Replaced worksheet.

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