Markiyan Hirnyk

Markiyan Hirnyk
9 years, 72 days

These are answers submitted by Markiyan Hirnyk

By Transpose

10 hours ago Markiyan Hirnyk 6293

The Transpose command does the job:

lista := [[1, 10], [2, 20], [3, 30]]:
x,y:= op(ListTools:-Transpose(lista));

                    [1, 2, 3], [10, 20, 30]

By subsop

13 hours ago Markiyan Hirnyk 6293

How about this?

F := Vector(subsop(3 = NULL, [seq(f[j], j = -2 .. 2)]));

See ?set for info.

PS. Or this?


 I tried it with the DirectSearch package which should be downloaded  from and installed in your Maple >=12.

A := LinearAlgebra:-Transpose(Matrix([XA, YA, ZA]));
B := LinearAlgebra:-Transpose(Matrix([XB, YB, ZB]));
DirectSearch:-DataFit(Poly1, A, Vector([WA]), [x, y, z]);


DirectSearch:-DataFit(Poly1, B, Vector([WB]), [x, y, z])



January 20 2015 Markiyan Hirnyk 6293

That was discussed in 

few days ago. Carl did not indicate it.


January 18 2015 Markiyan Hirnyk 6293

Because  polygraphic workers dislike the black square which takes a lot of expensive dye-stuff,

I suggest □ (the Square symbol) or ○ (the cir symbol) or ▷ (the triangleright symbol)  to this end.

The first two ones can be inserted through the Miscellaneous palette and the third one is contained

in the Relational palette. It should be mentioned that these symbols look larger in a Standard worksheet.

Of course, other symbols from the Maple palettes can be used too. For completeness, it would be useful

to include the black square symbol in the Miscellaneous palette.



January 17 2015 Markiyan Hirnyk 6293

The cite from Maple Help to ?phaseportrait:

"A system of two first order differential equations also produces a direction field plot, provided the system is determined to be autonomous. In addition, a single first order differential equation also produces a direction field (as it can always be mapped to a system of two first order autonomous differential equations). For systems not meeting these criteria, no direction field is produced (only solution curves are possible in such instances). There can be ONLY one independent variable".

Is the ODE system under consideration autonomous?


See example 3 in  ?implicitplot to this end. This help can be reached in your worksheet  by typing and executing ?implicitplot or/and  by typing implicitplot in the Search windows of your Maple Help and pushing the Search button.

Two ways

January 13 2015 Markiyan Hirnyk 6293

1. This can be done with the DirectSearch package which should be downloaded from and installed in your Maple >=12. For example,

2. To this end, one may use the Dragilev method (see and 

and ).

By cfrac

January 12 2015 Markiyan Hirnyk 6293

This can be done as follows.



See ?cfrac for info. The reading of Maple Help is very useful.

PS. Maple treats

as 3/2.

PPS. IMHO, your question is "art for art's sake". Geometry is the earth measurement.


January 05 2015 Markiyan Hirnyk 6293


Acta Phys. Sin
5 черв. 2012 р. - He Ting-Ting, Luo Xiao-Shu, Liao Zhi-Xian, Wei Zheng-Cong ... With the help of the symbolic computation system Maple and using the improved .... 150 keV and 1.2 MeV) beams impinging on Au surface are measured. .... diode pumped free-running double-clad ytterbium-doped fiber laser are investigated.

Exact square

January 04 2015 Markiyan Hirnyk 6293

4^2-sqrt(7)^2=9=3^2, whereas
4^2-sqrt(6)^2=10 which is not an exact square. This makes the difference.
 The execution with prinlevel:=15 confirms that. Another example is
expr2 := sqrt(sqrt(26)-sqrt(10))*sqrt(sqrt(26)+sqrt(10)):


The Tolerances package computes ToleranceValue(a*b) for a:=x&+-Deltax and b:=y&+-Deltay by the formula max((x+Deltax)*(y+Deltay)-x*y,x*y- (x-Deltax)*(y-Deltay)) ( (x+Deltax)*(y+Deltay) - (x-Deltax)*(y-Deltay))/2, wheras the ScientificErrorAnalysis package,

up to Maple Help, uses

"The result of combine/errors is a quantity-with-error returned in a Quantity object.
• The uncertainty is calculated using the usual formula of error analysis involving a first-order expansion with the variances of the quantities-with-error.
The error   u(y) in   y, where  y is a function of variables   x[i], is

where   u(x[i]) is the error in   x[i], and the partials are evaluated at the central values of the   x[i]".
In you case y=x[1]*x[2]. These make the difference in the answers.

I think the error done with Tolerances is more reliable in your case.



By evalf@allvalues

December 29 2014 Markiyan Hirnyk 6293

This can be done in the standard way. The modification

does the job, outputing 

See ?allvalues and ?evalf for info (These codes should be typed and executed in your worksheet, e.g. ?allvalues .).

Another way

December 23 2014 Markiyan Hirnyk 6293

This can be done as follows.

restart; F := proc (eta) options operator, arrow; int((0.579160e-1*sqrt(x)*Ei(1., 0.500000e-4*x)+1072.23*(.999950+(-1)*1.*exp((-1)*0.500000e-4*x))/sqrt(x))/sqrt(x), x = 1. .. eta, numeric) end proc





plot(proc (eta) options operator, arrow; exp(18.1818*F(eta)+(-1)*9.10000*eta)/eta end proc, 1 .. 100, numpoints = 40)



int(proc (eta) options operator, arrow; exp(18.1818*F(eta)+(-1)*9.10000*eta)/eta end proc, 1. .. 100., numeric)





The cites from ?subs


The first form of the subs command substitutes a for x in the expression expr. Note that this command is similar to the eval command. Simple applications of replacing a symbol by a value in a formula should normally be done with the eval command. Differences between the two commands are highlighted in the examples below"

"Since Maple does simultaneous substitution in all parameters, the following call to subs will return an error. (However, eval will work correctly.)
p := piecewise(x = 0, 1, sin(x)/x);

subs(x = 0, p);
Error, numeric exception: division by zero
eval(p, x = 0);
1 "

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