## Compare Maple 2019 with Maple 16: True or False?...

Asked by:

In this paper (see the footnote on the page), the authors pointed out:

We use -v16 as it is faster than the -v2019 for real root isolation on our benchmarks.

Since I don't have Maple 16 at present, I cannot confirm such an assertion personally. However, I'd like to ascertain if old Maple 16 (released in 2012) is still faster in that specialized realm now (i.e., in 2023). Is there any benchmark test that supports this claim (or tells an opposite story instead?)?

Note. Here I just try to justify the authors' statement (which has caused confusion). Incidentally, will this library be a part of Maple in some future version? (I find that some recent papers provide new "powerful"—in accordance with their "Experiment" sections—Maple packages to tackle difficult problems efficaciously, but such functionalities are not built into the Maple kernel as yet. (In fact, if Maple is a single integrated all-in-one technical platform, then I will no longer need to change tools and formats at each stage. :) ))

## How do you transform vector expression ?...

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How do you transform vector expression (*) into [M,A] – 3[M,B] = 7[M,C] using Maple command?

Thank you for your help !

## How to solve PDE in Maple...

Asked by:

Good day everyone, please I'm soliciting help on how to solve PDE in Maple. I know how to solve ODE but I don't know how to go about PDE. The problem I want to solve is attached as an attachment. If epsilon is zero, then the problem reduces to ODE which can easily be solved, but epsilon is not supposed to be zero. please I need your help, thank you in anticipation.

PDE.pdf

## How to find coefficients of a complex expressions?...

Asked by:

ans:=6 *a[0]+2 *k^2 *b[1]*x^2 *y+k^2 *b[1] *y *lambda+6* k^2 *b[2]* x^3 *y-c *b[1] *x* y-2* c* b[2] *x^2 *y-c *b[2] *y *lambda+(6 *b[2]^2 *x^4 *lambda)/(lambda^2 *sigma+mu^2)+(6 *b[2]^2 *x^2 *lambda^2)/(lambda^2 *sigma+mu^2)+(6 *b[1]^2 *lambda* x^2)/(lambda^2 *sigma+mu^2)-12 *a[0] *b[2] *x *y-12* (a[1] . x)* b[2] *x* y-12* (a[2] . (x^2)) *b[2] *x* y+(6 *b[1]^2 *lambda^2)/(lambda^2 *sigma+mu^2)+k^2 *(a[1] . (-2 *x* (mu* y-x^2-lambda)-mu *x* y))+2 *k^2* (a[2] . ((mu* y-x^2-lambda)^2+x* (-2 *x (mu* y-x^2-lambda)-mu *x* y)))+c (a[1] . (mu *y-x^2-lambda))+2 *c (a[2] . (x *(mu *y-x^2-lambda)))+5* k^2 *b[2] *x *y *lambda-(c *b[2] *lambda^2 *mu)/(lambda^2 *sigma+mu^2)+(12 *b[1] *lambda *b[2] *x^3)/(lambda^2 *sigma+mu^2)+(12 *b[1] *lambda^2 *b[2] *x)/(lambda^2 *sigma+mu^2)-(12 *b[1]^2 *lambda *mu* y)/(lambda^2 *sigma+mu^2)+(k^2 *b[1] *lambda^2 *mu)/(lambda^2* sigma+mu^2)-12 *a[0] *b[1] *y-12* (a[1] . x) *b[1] *y-12* (a[2] . (x^2)) b[1] *y-6 *a[0]^2-12 *a[0] *(a[1] . x)-12 *a[0]* (a[2] . (x^2))-6* (a[1] . x)^2-12* (a[1] . x) *(a[2] . (x^2))-6* (a[2] . (x^2))^2-(2 *k^(2)* b[1] *lambda* mu^2 *y)/(lambda^2 *sigma+mu^2)+(k^2 *b[1] *lambda *mu *x^2)/(lambda^2 *sigma+mu^2)+(6* k^2 *b[2] *lambda *mu *x^3)/(lambda^2 *sigma+mu^2)+(6* k^2 *b[2] *lambda^2 *mu *x)/(lambda^2 *sigma+mu^2)+(2* c *b[2] *lambda *mu^2* y)/(lambda^2 *sigma+mu^2)-(c *b[2] *lambda* mu* x^2)/(lambda^2 *sigma+mu^2)-(12 *b[2]^2 *x^2 *lambda* mu* y)/(lambda^2 *sigma+mu^2)-(12* k^2 *b[2] *lambda* mu^2 *x *y)/(lambda^2 *sigma+mu^2)-(24 *b[1] *lambda *b[2] *x *mu* y)/(lambda^2 *sigma+mu^2)+6* (a[1] . x)+6* (a[2] . (x^2))+6 *b[2] *x *y+6 *b[1] *y;

P1 := coeff(coeff(ans, x, 4), y, 0);

Error, unable to compute coeff

Sometime, answer is coming sometine not.

2. Also, if one wants to substitute the value of x^2=t^2+5, in x^3 then why it is giving the ans.

Thank you very much!

## How to plot with numeric solution from dsolve...

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 > for k to 10 do       sol_All := dsolve                  ( eval                    ( {bcs1, bcs2, ode3, ode4},                      [N= L[k],a=1,S=1]                    ),                    [f(eta), theta(eta)],                    numeric,                    output = listprocedure                  );       Y_sol || k := rhs(sol_All[5]);       YP_sol || k := -rhs(sol_All[6]); feta || k := rhs(sol_All[4]);       fpeta || k := rhs(sol_All[3])   end do:
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 > plot( [ seq((Y_sol||j)(eta), j = 1..16)],          eta = 0 .. 10,          labels = [eta, theta(eta)],          axes = boxed       ); plot( [ seq((YP_sol||j)(eta), j = 1..6)],          eta = 0 .. 8,          labels = [eta, thetaprime(eta)],          axes = boxed       );  plot( [ seq((feta||j)(eta), j = 1..6)],          eta = 0 .. 8,          labels = [eta, f(eta)],          axes = boxed       );   plot( [ seq((fpeta||j)(eta), j = 1..6)],          eta = 0 .. 8,          labels = [eta, fprime(eta)],          axes = boxed       );
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Download ishak.mw

Good day every one;

please im soliciting for a help on how to plot my Nusselt number and Skin friction.

The attached is plotting against the dependent variable (eta) but i want skin friction (f  ' ' ) against N or Pr not against eta

thank you for your help in aticipation

## How can i add "FourierSeries" package to maple 16...

Asked by:

Hi
when I use this package, maple makes error like bellow. what is the problem ? thank u

## Help IntegrationTools Change...

Asked by:

Hello everyone

Please help me about IntegrationTools:-Change does not transform x to u

IntegrationTools:-Change(int(3*x*sqrt(x+8), x))

I want to convert that primitive to a primitive like this: (2/3)*(Int(u^2*(u^2-8), u)) and Error, (in IntegrationTools:-Change) invalid boolean expression: 1

Please help me

Help_integrationTools.mw

## Combining algebraic expression...

Asked by:

Hi,

It might be a really silly question, but I am wondering is it possible to simplify expression like this

. Just by looking it we know that we can write it in the form of (a+b)^2+c^2. This is the basic exmaple I come up with. I have very lengthy expressions in maple, which can be factorize like this, but factor command will not work as it will try to factorize entire expression. So I am wondering is it doable in maple or I have to do it manually by collecting terms and check whether they can be factorize or not.

Thanks in Advance.

With Regards

sunit

## Exporting maple plot into MATLAB...

Asked by:

Hi every one

I'm having some plots in maple, but the layout is not pretty enough, I want export in to MATLAB. Does some one please have an idea on how I can go about it?.

I'm using Maple 16

Thank you in anticipation

## Solve a PDE with a known solution...

Asked by:

Can anyone help me to find a solution to  for the attached partial differential equation ?

I want to find a general solution to a partial differential equation by assuming that I know one solution, called , and trying to find another solution  by assuming that the general solution in the form of . I want to restrict the second solution to be in the form of  so that it satisfies the PDE, and is a function of  times . The latter makes error as the maple identifies that the function  depends on only one variable . Could you please help me to find a solution for  in the form ?

Also, I have trouble with defining the operator Do in the attached file.  When it operates on , maple gives D. It is not clear for me that whether this derivative is with respect to  or . I need is to define Do in a way so that the derivatives are correctly taken with respect to different separate variables.

Thank you for your help,

## Solve a system of partial differential equations w...

Asked by:

Can anyone help me to solve the attached system of PDEs with a given expression for the HINT such as

I am not able to set such an arbitray HINT function for system of PDEs.

SysPDE_HINT.mw

Thank you,

Ahmad

## How do I find the eigenvalues of a symbolic matrix...

Asked by:

I am currently working on a project that generates a set of matrices and I want to find their eigenvalues, but using the inbuilt Maple engine takes too long. The problem is that whenever I try to use the Matlab[eig] command I get the error:

Error, (in Matlab:-setvar) unable to store '-3.*Re(X)' when datatype=float[8]
I found out that solving symbolic matrices in MATLAB requires first defining symbols with the "sym" command but I've been unable to do that in Maple.

## How to get rid of 1.0 in numerical and symbolic ca...

Asked by:

Hi,

This might be a very silly question but it is troubling me a little bit and that's why I need to post it. During the combination of symbolic and numerical comutation this '1.0' is appearing as a coefficient for the variables whose coeffecient is just '1'. It's quite annoying as sometimes if I have to collect coefficient of a variable for an example exp(I*omega*t) then I have to write exp(1.I*omega*t), so chances of making mistake is higher. Please find the attached worksheet for this. In eq(4), you can easily see that for x[3](t) and x[1](t) this '1.0' appears in front of the variables.

I really appreciate  if someone can help me out of this.

With Regards

Sunitquestion.mw

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Download question.mw

## Convert expression to LaTeX...

Asked by:

How to convert expression below to LaTex:  $\lim _{x \rightarrow 2} \frac{2}{x+3}$

And How to convert expression below to LaTex:  $\int_{2}^{3} \frac{1}{x^{2}+2} d x$

file test: newLaTex.mw

## Incorrect definite integration of hyperbolic funct...

Asked by:

Hi Guys,

I am trying to intgrate a function involving hyperbolic functions in a range of 0 to 1 and it is giving me very large value of 10^94. However, on doing integration terms terms i can see that some large terms involving 10^191 cancel out with each other and I can have a fnite value of this integration. It would be really helpful if someone can help me out why it is happening with int function and how can I solve this case involving hyperbolic function. For reference maple file is attached. Thanks in advance and much appreciated.

With Regards

Sunit

question.mw

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