Maple 2019 Questions and Posts

These are Posts and Questions associated with the product, Maple 2019

Hi,

I'm trying to plot:

y = x(x^4 - 10*x^2 + 39)/30

I keep getting a what looks like a straight line. it should be a curved line.

I got it to work on :

y = x(x^4 - 10*x^2 + 39)/30

https://www.mathway.com/Algebra

Hello,

I am Seonhwa Kim, a mathematical researcher in Korea. Recently, I have extensively used Maple to compute character varieties of 3-manifolds. Several months ago, I obtained some strange results in Maple which implies a contradiction in theory.  I have been struggling with these issues since it is usually about enormous polynomial systems.  Eventually, I could figure out that the issues are caused by a defect in Maple and were able to construct a minimal working example to produce wrong computations in Maple.  I am writing this post to report them.

 

This is mainly about the PolynomialIdeal package.  Along with the documentation in Maple, If an ideal J is radical, PrimeDecomposition and PrimaryDecomposition should have the same result.  But, as we see the following, the result of PrimeDecomposition and PrimaryDecomposition are different although J is a radical ideal.


The problem seems to be that the PrimaryDecomposition command in Maple sometimes produces incorrect results.

We can compute the primary decomposition of J by hand.  It should be <x> and  <y, x-1>.

I double-checked this by the other software;Macauley2, Singular, and Magma, for example, you can see it as follows.

 

 

 

Secondly, not only for PrimaryDecomposition but also PrimeDecomposition may produce an incorrect result.

Here is a minimal working example.

Maple tells us a compatible result of prime and primary decomposition of a radical ideal J.

But the first component of J,  < b-1, c-a+1 >, contains the third component < a, b-1, c+1 >.

It contradicts with the definition of Primary decomposition. So the correct answer should be  < b - 1, c - a +1 >, <a,b,c>.

 

I also checked that  Macaluey2, Singular and Magma. They all say that my hand computation is correct. as follows.


 

I have used Maple 2017 by the license of my institute (Korea Institute for Advanced Study).

When I noticed these defects, I thought it would be fixed in the newest Maple version.

So, I have tried my examples by Maple2019  free trial, but It also has the same problem. 

I guess this problem is not reported or recognized yet. 

 

I hope this problem will be fixed as soon as possible.

Thank you for attention.

 

Sincerely,

Seonhwa

I'd like to solve this ODE

But not sure how to write it in Maple. In Mathematica, this is what I do

ClearAll[F, x, y, t];
ode = D[F[x[t], y[t]], x[t]]*D[x[t], t] + D[F[x[t], y[t]], y[t]]*D[y[t], t] == 0;
DSolve[ode, F[x[t], y[t]], {x[t], y[t]}]

and it gives

In Maple, I tried

ode:=diff(F(x(t),y(t)),x(t))*diff(x(t),t)+diff(F(x(t),y(t)),y(t))*diff(y(t),t)=0

Error, invalid input: diff received x(t), which is not valid for its 2nd argument

ode:=D[1](F)(x(t),y(t))*diff(x(t),t)+D[2](F)(x(t),y(t))*diff(y(t),t)=0;
dsolve(ode,F(x(t),y(t)))

Error, (in dsolve) expected the indeterminate function as, say, F(x) where x is of type "name" - and also cannot be a procedure name. Received: [F(x(t), y(t))]

 

What is the correct way to write this in Maple?

 

 

I'm am pretty new to maple, coming from a mathcad background, so sorry in advance if this is a dumb question.  My original need was to plot text objects with sold backgrounds on top of other plotted objects.  I saw in other posts that Maple doesn't natively support this.  So instead I'm trying to create a composite plot of objects by plotting text objects over polygons or rectangles.  However I can't seem to make a given plotted object "cover" another plotted object.  

 

Below is a simple example.  The easy analogy is just that I want to plot these objects in “layer order”, with L1 being the top layer.  So I would like the polygon to opaquely obscure the “underlying” contour plot, and then in turn, the text object to behave as a “top-most layer” with the polygon acting as a background for the text. 

 

L1 := textplot([2, 2, "Polygon"], color = white);

L2 := polygon([[0, 0], [3, 4], [3, 1]], color = red);

L3 := contourplot(x^2 + y^2, x = 1 .. 2, y = 1 .. 2);

display(L3, L2, L1); 

I have the following simple dsolve code:

ode := diff(y(x), x, x) + (n*pi)^2*y(x) = A^3*sin(n*pi*x)^3;
dsol1 := dsolve({ode, y(0) = 0, y(1) = 0}, y(x));

 

How to declare that n is an integer here?

 

Thanks!

 

I need to take the inverse of a tensor which I have denoted as e[~mu,nu] which is defined by a rather larger Matrix. I had computed this matrix using Mathematica and then simply transferred the resulting matrix by using the calling sequence 

with(MmaTranslator):

which worked swell for transferring said matrix in to Maple. Then using the Physics package I was able to define it as a tensor, with a contravariant and covariant index, respectively. Now, when trying to transfer the inverse of said matrix into Maple to define as a new tensor which I intend to call f[mu,~nu], I get an error saying that the number of free indices on the left hand side does not coincide with the number of free indices on the right hand side. Since, this "new" tensor will really just be the inverse of the matrix which I used to define e[~mu,nu], I was wondering if there was any way in which I can simply compute the inverse of the matrix defining e[~mu,nu] in Maple and then let it be equivalent to f[mu,~nu], afterwhich I would then define it as a new tensor itself. 

 

Research_project.mw

Any help would be greatly appreciated.

Hi 

I have a matrix consisting of components which are all definite integrals like the following example: 

L is a paramter I would like to keep as a symbol for now. How do I get maple to write out the result of the definite integral of such an expression? 

 

Best regards, 

Brian

When I try to find the trace of the product of Dirac Gamma matrices with variable indices, I get a different answer than in textbook. The product is Dgamma[~mu]Dgamma[~nu]Dgamma[~rho]Dgamma[~sigma]Dgamma[~5]. The answer I get using Maple is 0. The textbook answer is -4*i*epsilon[~mu,~nu,~rho,~sigma](Levi-Civita symbol). I verified this using Maple with using 1,2,3,4 and 2,1,3,4 for mu,nu,rho,sigma. I think I'm probably the one doing something wrong. Maple 2019 on Mac with Physics package default standard setup.

Hi,

 

I have two functions that I took the inetgral of their product (1.3 and 1). Then i multiplied the resulting naswer with the variable and integrates again however the inetgral did not evaluate (3,4, and 5). 

I was able to calculate both inegrals using tables of integrals, MATLAB & Mathematica were able to evaluate.

any insights on why this may happening?

Integrals_Sheet2.mw

Hi,

 

I am trying to use Maple to evaluate the recursion series as below, but I am getting an error when I try to call c: Error, (in depends) too many levels of recursion

Recursion.mw

 


 

 

b := proc (k) options operator, arrow; (-1)^k*GAMMA(1+(1/2)*k)^2/factorial(k) end proc

proc (k) options operator, arrow; (-1)^k*GAMMA(1+(1/2)*k)^2/factorial(k) end proc

(1)

c := proc (k) options operator, arrow; piecewise(k = 0, b(0)^N, 1 <= k, (sum((q*(N+1)-k)*b(q)*c(k-q), q = 1 .. k))/(k*b(0))) end proc

proc (k) options operator, arrow; piecewise(k = 0, b(0)^N, 1 <= k, (sum((q*(N+1)-k)*b(q)*c(k-q), q = 1 .. k))/(k*b(0))) end proc

(2)

b(2)^N

(1/2)^N

(3)

c(1)

Error, (in depends) too many levels of recursion

 

 

F := proc (s, kmax, N) options operator, arrow; sum(c(k)*s^k, k = 0 .. kmax) end proc

proc (s, kmax, N) options operator, arrow; sum(c(k)*s^k, k = 0 .. kmax) end proc

(4)

powcreate(c(k) = (sum((q*(N+1)-k)*b(q)*c(k-q), q = 1 .. k))/(k*b(0)), c(0) = b(0)^N)

Error, (in depends) too many levels of recursion

 

c := rsolve({c(0) = b(0)^N, c(k) = (sum((q*(N+1)-k)*b(q)*c(k-q), q = 1 .. k))/(k*b(0))}, c(k), makeproc)

Error, (in depends) too many levels of recursion

 

c := proc (k) if k = 0 then return b(0)^N else return (sum((q*(N+1)-k)*b(q)*c(k-q), q = 1 .. k))/(k*b(0)) end if end proc

proc (k) if k = 0 then return b(0)^N else return (sum((q*(N+1)-k)*b(q)*c(k-q), q = 1 .. k))/(k*b(0)) end if end proc

(5)

c(1)

Error, (in _factorial) too many levels of recursion

 

F := proc (s, kmax, N) options operator, arrow; sum(c(k)*s^k, k = 0 .. kmax) end proc

proc (s, kmax, N) options operator, arrow; sum(c(k)*s^k, k = 0 .. kmax) end proc

(6)

F(1, 2, 2)

Error, (in unknown) too many levels of recursion

 

NULL


 

Download Recursion.mw

I'm using MAPLE 2019 and I'm sometimes surprised by its behaviour.  For example, I appear to have an example where it evaluates the integral of each of two terms but not their sum...  What's going on?  Please see the attached.

restart

g0 := exp(r*cos(theta))/Pi

exp(r*cos(theta))/Pi

(1)

G0 := `assuming`([int(g0, theta = 0 .. Pi)], [r > 0])

BesselI(0, r)

(2)

g1 := exp(r*cos(theta))*cos(theta)/Pi

exp(r*cos(theta))*cos(theta)/Pi

(3)

G1 := `assuming`([int(g1, theta = 0 .. Pi)], [r > 0])

BesselI(1, r)

(4)

g := g0+g1

exp(r*cos(theta))/Pi+exp(r*cos(theta))*cos(theta)/Pi

(5)

G := `assuming`([int(g, theta = 0 .. Pi)], [r > 0])

int(exp(r*cos(theta))/Pi+exp(r*cos(theta))*cos(theta)/Pi, theta = 0 .. Pi)

(6)

``


 

Download Maplesumint.mw

Hello, I'm using free 15 day trial Maple 2019.2 on my Macbook (Macos 10.15.3).

I can't work Maple. I enter some inputs (2+3) and press enter. It works. But when I write plot, version(), f, sin.. or something else it didn't works. And no response. When I click enter, nothind happen. What is the problem? Please help me.. 

   I download one  file about  all 5 connected graphs with graph6  (total 21 graphs). format from http://users.cecs.anu.edu.au/~bdm/data/graphs.html,and I want to import it in Maple. Since platform restrictions , I can not attach the file .   Please download it by yourself,very thanks to you ! 

   I put the file  in the installation path of  Maple in my computer:D:\\ Program Files\Maple 2019. (my computer system is Window 10 )  And I import it like following: 

  But it  only imports the graph of  the first row in the file. How to import all graphs in a file of graph6 format one time?

 

I received an (automated) email, which called attention to an update.

Where can I find the update?

Thank you, Jan Drösler

 

Hi there,

I have been using Maple for a while now.

I installed Maple on my Desktop PC, but I am experencing horrendous loading times, and just in general, a slow client. When I look in Task Manager I can see Java Platform SE Binary run at 0% CPU or close to 0% CPU. It uses about 600 MB of ram. I think this is the issue. On my laptop it runs much higher, and I experience no issues. My Desktop PC is significantly better than my laptop. I am running a i7-7700k with a RTX 2080, so there shouldn't be any hardware worries. 

Does anyone know what is causing this? Simple math like 1+1 takes time to execute. It is very slow.

Hope someone knows what to do.

Thanks,

Kritix.

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