I am using Maple's CodeTools[Usage] to check memory measurement for a few lines of code i have.

One line is calling a custom function and the usage reports ~16 GB usage, the other line is a Groebner Basis computation and reports ~200 MB of memory usage. The usage is reported via 'bytesused' flag in the CodeTools[Usage] input.

However, GNU time command returns 6 GB total for the whole code iteration. Why is there such a discrepancy? Does maple's bytesused mean something different than GNU time's max resident set size?

When asking dsolve to use specific ode type to solve an ode, in particular, dAlembert type, which typically generate complicated solutions, sometimes dsolve solution shows up using parameter T.

But odetest gets confused by this expression it seems. I am not able to figure if I am doing something wrong in using odetest, or may be odetest does not know how to handle such form of a solution.

Here is an example. This ode

is of these types:

restart;
ode:=diff(y(x), x) = (y(x)^3 + 2*x*y(x)^2 + x^2*y(x) + x^3)/(x*(y(x) + x)^2);
DEtools:-odeadvisor(ode);

By default, dsolve was smart to use homogeneous type to solve the ODE, as this gives the simplest solution. 

One can force dsolve to use the other types. When using dAlembert, odetest gives an error trying to verify any one of the solutions returned from dsolve due to the way the solution is returned. Here is the result

restart;
ode:=diff(y(x), x) = (y(x)^3 + 2*x*y(x)^2 + x^2*y(x) + x^3)/(x*(y(x) + x)^2);
sol:=[dsolve(ode,y(x),[homogeneous])];

No problem here for odetest. it can verify any of the above 3 solutions with no error generated.

odetest(sol[1],ode)

          0

Lets compare using dAlembert type

restart;
ode:=diff(y(x), x) = (y(x)^3 + 2*x*y(x)^2 + x^2*y(x) + x^3)/(x*(y(x) + x)^2);
sol:=[dsolve(ode,y(x),[dAlembert])]: #solution too complicated to show here
odetest(sol[1],ode)

It looks like odetest does not know how to handle the form of the solution as returned by dsolve for this case. The problem is that each solution is actually made up of two parts, not just y(x) as normally is the case. One part defines something called X(T_) and the next part which is the solution y(x) uses this X(T) in it. 

Did I do something wrong, or is there a way around this, or is this by design?

Maple 2020.2

a^(5/2)*s^2*(D(f))(eta)^2*sqrt(nu)/(R*sqrt(a)*sqrt(nu)+eta*nu) = a^(5/2)*s^2*(D(P(s, eta*sqrt(nu)/sqrt(a))))(eta)/sqrt(nu)

Is it possible to rearrange the above equation for D(P)(eta)

Hi, i'm new on this site. I want to know how to set an output un-scientific number but we can set the number of digit "after comma" as we want? 

The best i can do is using this:

printf("%f\n",something)

So, for example i want to calculate 

123456789/123

It gives me:

1003713.732000 (only gives 6 digits after comma)

I don't want the output looks like this:

But, for example i want the result has 9 digits after comma and gives me:

1003713.731707317

How to do this? Please help me. Thanks.

One of the most interesting help page about the use of the Physics package is Physics,Examples. This page received some additions recently. It is also an excellent example of the File -> Export -> LaTeX capabilities under development.

Below you see the sections and subsections of this page. At the bottom, you have links to the updated PhysicsExample.mw worksheet, together with PhysicsExamples.PDF.

The PDF file has 74 pages and is obtained by going File -> Export -> LaTeX (FEL) on this worksheet to get a .tex version of it using an experimental version of Maple under development. The .tex file that results from FEL (used to get the PDF using TexShop on a Mac) has no manual editing. This illustrates new automatic line-breaking, equation labels, colours, plots, and the new LaTeX translation of sophisticated mathematical physics notation used in the Physics package (command Latex in the Maplesoft Physics Updates, to be renamed as latex in the upcoming Maple release). 

In brief, this LaTeX project aims at writing entire course lessons or scientific papers directly in the Maple worksheet that combines what-you-see-is-what-you-get editing capabilities with the Maple computational engine to produce mathematical results. And from there get a LaTeX version of the work in two clicks, optionally hiding all the input (View -> Show/Hide -> Input).

PhysicsExamples.mw   PhysicsExamples.pdf

PS: MANY THANKS to all of you who provided so-valuable feedback on the new Latex here in Mapleprimes.

Edgardo S. Cheb-Terrab
Physics, Differential Equations and Mathematical Functions, Maplesoft

Hello everyone,

I should solve the diffusivity equation using Maple. The equation and BSc are as follow: 

pde := W*diff(C(z, t), z $ 2) - diff(C(z, t), t $ 1) = 0

bc[1] := C(x, 0) = 0;
bc[2] := D[1](f)(0, t) = VMK*D[1](f)(t)/ZRTWA;
bc[3] := C(infinity, t) = 0;

The equation should be solved using Laplace method. Can anyone please help me ?

I will appreciate your insightful comments.

using the Physics package version:

Physics:-Version();                                                                                                                                                   
  The "Physics Updates" version in the MapleCloud is 899 and is the same as the version installed in this computer, created 2021, January 2, 19:51 hours Pacific Time.

I end up with:

Latex:-Settings(useimaginaryunit=i,
      usecolor = false,
      powersoftrigonometricfunctions= computernotation,
      leavespaceafterfunctionname = true,
      cacheresults = false
);

resluting in an error:

Error, module does not export `ModuleApply`

Maybe some changes in the interface in the latest version?

thanks

Simulations.mw

If you are interested in experimenting with simple antenna arrays, this worksheet may prove useful.  I have provided a few examples of arrays that repeat in the x, y and z directions, but it will be very easy to tweak this tool if you are more interested in circular or triangular arrays.

This is one of the example arrays:

Antenna_arrays.mw

antenna_arrays.pdf

Hello there, 

First of all, happy new year to you and those around you!

One question: would you teach me how to replace the 'Zs/Z_AB' expression in the last term of the expression 'eq_5_m5'?

In other words, I wanted to see the 'desired' expression, but the 'subs()' command repalced the first occurance of the 'Zs/Z_AB' expression. 

(Perhaps, this applet behind of this edit box does not like the Microsoft Edge browser)

Maple Worksheet - Error

Failed to load the worksheet /maplenet/convert/Q20210103.mw .
 

Download Q20210103.mw

Maple Worksheet - Error

Failed to load the worksheet /maplenet/convert/Q20210103.mw .

Download Q20210103.mw

here is my try

for ploting points of data ( d(n(, sum(n))

new.mw

Hello. I have certain requirements for drawings. Please tell me, is it possible to implement them when plotting in Maple? Thanks.
Drawing width 15 cm
Be sure to frame and mesh. The thickness of the frame and serifs on the axes is 0.5 pt. Mesh thickness 0.25 pt. The length of the serifs is 1.2 mm.
The thickness of the graph itself is 1 pt
Axis names 10 pt

Is there a similar function as (cylinderplot) to plot convex or concave toroidal shell segments?

This type of shell is as follows.

Recently, I encountered warnings and errors when size of my list is big. Maple says use array instead of list because of ... . When the list is just a list of numbers or a list of lists of the same size, I can rewrite it as an array, but how about a list like the following?

[seq([[0,0],0],i=1..10)]

This is just an example. So the elements of this list are lists containing a vector (a point in the plane) and a number (a property of this point). One idea is to use two arrays, a two dimensional array for recording the vectors, and one 1-dimensional array for recording the numbers and keep in mind that the i-th number of the second array is related to the i-th vector (row) in the first array. But is there any possibility to have this data recorded similar to when we are using lists, i.e. similar to the above code?

How can I get the follow graph of paraboloidal surfaces (ξ=1,η=2) with the coordinate vectors ξ⁰ , η⁰ , φ⁰ as shown in the picture.

Realation between cartesian coordinates and paraboloidal :

x=1/2 (ξ² - η²), y=ξ η cos(φ), z=ξ η sin(φ)

I wrote the following code:

Student:-VectorCalculus

S1 := PositionVector([1/2*(-eta^2 + 1), eta*cos(phi), eta*sin(phi)], cartesian[x, y, z]):

LH := PlotPositionVector(S1, eta = -2 .. 0, phi = 0 .. 2*Pi, coordcurve = [eta = -2, tangent = true, binormal = true, vectornum = 1], scaling = constrained)

S2 := PositionVector([1/2*(xi^2 - 4), 2*xi*cos(phi), 2*xi*sin(phi)], cartesian[x, y, z]):

LG := PlotPositionVector(S2, xi = -1 .. 1, phi = 0 .. 2*Pi, coordcurve = [xi = 1, tangent = true, vectornum = 1], scaling = constrained)

And I got the two paraboloidal surfaces with the vectors separently.How can I get only one graph with these two surfaces as shown in the picture (with ξ=1, η=2) ?