Maple 2022 Questions and Posts

These are Posts and Questions associated with the product, Maple 2022

Why the expression of lambda[1] is too large? One of the possible values of lambda[1] should be "sqrt(1/(4*omega^2 - 4))*a[-1]". 

JCN.mw 

Hi,

I want to illustrate the notion of volume generated by a plane region, with the disks. Ideas to animate my rectangles? Thanks

IdeaVolume.mw

Hello MaplePrimes community,

We just created a Frequently Asked Question article that may address some Primes questions about updates to Physics in Maple 2022.2: 

Why does Maple 2022.2 throw an error executing Physics:-Version(latest)?

For searchability, the specific error in question is

Error, (in Physics:-Version) unable to determine the Physics Updates version, could you please report the problem to support [at] maplesoft [dot] com

 

  • Maplesoft will work to improve package updating in future versions of Maple.
  • In Maple 2022.2, the workaround is to install and/or update the Maplesoft Physics Updates using the MapleCloud toolbar.

How can we draw the pot function the same as in the attached figure (namely 'pot.png')? The values of V(x) may not be the same.

pot.mw

Hello

I am trying to calculate a definite integral of an absolute value function. I should get a positive result, but I end up getting a negative result. Why is this?

The line I am trying to run is this

ET2 := int(abs(1/(x - 2) + 0.5333 + 0.3333*x + 0.1333*x^2), x = -1 .. 1);

And the result I get is:
 ET2 := -0.056854377998556975271421429744140962019176108843917

What am I missing?

Encountered new exception using odetest which can't be cought. Is this new one? I do not have earlier version of Maple than 2022.2 to check. On windows 10.

btw, I could not update to latest Physics now, may be server problem.  Attached worksheet

interface(version);

`Standard Worksheet Interface, Maple 2022.2, Windows 10, October 23 2022 Build ID 1657361`

Physics:-Version(latest)

Error, (in Physics:-Version) unable to determine the Physics Updates version, could you please report the problem to support@maplesoft.com

Physics:-Version();

`The "Physics Updates" version in the MapleCloud is 1351. The version installed in this computer is 1348 created 2022, November 14, 15:59 hours Pacific Time, found in the directory C:\Users\Owner\maple\toolbox\2022\Physics Updates\lib\`

restart;

 

sol:=y(x) = -LambertW(x/sin(x)*exp(c[1]/sin(x)))+c[1]/sin(x);
ode:=exp(y(x))+cos(x)*y(x)+(exp(y(x))*x+sin(x))*diff(y(x),x) = 0;
odetest(sol,ode)

y(x) = -LambertW(x*exp(c[1]/sin(x))/sin(x))+c[1]/sin(x)

exp(y(x))+cos(x)*y(x)+(exp(y(x))*x+sin(x))*(diff(y(x), x)) = 0

Error, (in tools/map) too many levels of recursion

try
sol:=y(x) = -LambertW(x/sin(x)*exp(c[1]/sin(x)))+c[1]/sin(x);
ode:=exp(y(x))+cos(x)*y(x)+(exp(y(x))*x+sin(x))*diff(y(x),x) = 0;
odetest(sol,ode);
catch:
   print("error in odetest");
end try;

y(x) = -LambertW(x*exp(c[1]/sin(x))/sin(x))+c[1]/sin(x)

exp(y(x))+cos(x)*y(x)+(exp(y(x))*x+sin(x))*(diff(y(x), x)) = 0

Error, (in tools/map) too many levels of recursion

 

Download problem_odetest_nov_20_2022.mw

I do not know what to do now, since if I can't catch the exception, the program can't run anymore and just stops.

 About 6 years ago I aked  a question on testing types in a package. How to Test Input Typed to a Procedure to Determine what to do? - MaplePrimes.  @Carl Love supplied the very good code below. I never used the answer back then as I really didn't understand what to do with it. I have a somewhat of a better idea now and I really need to be able to use this in general..

 Basically the code checks that all the inputs are of the same type and order (which is what the original question specified).

 Q1:- I now need to check  a mixed input type

         A:: a 2 list , B a 3 list   

          or 

           A:: a 2 Vector, and B a 3 Vector.

         etc

       I tried modifying the ModuleApply part of the code at the end, but that either causes errors or kernal looses connection.

Q2:-  What is a good way to handle different numbers of inputs to procedures (exported) here eg Proc1(a), Proc2(a,b), ....,                   ProcN(a1,...,aN)

Q3:-    Would the package exports of the module be the procedures inside the Mydispatch? Or does all of MyModule sit inside                the  package module?

  I have three different packages I would like to apply this to in general.

restart

 

MyModule:= module()
uses TT= TypeTools;
global _T1, _T2L, _T2V, _T3L, _T3V, _MyType;
local
     MyTypes:= {_T1, _T2L, _T2V, _T3L, _T3V},
     AllMyTypes:= MyTypes union {_MyType},

     ModuleLoad:= proc()
     local
          g, #iterator over module globals
          e
     ;
          #op([2,6], ...) of a module is its globals.
          for g in op([2,6], thismodule) do
               e:= eval(g);
               if g <> e and e in AllMyTypes then
                    error "The name %1 must be globally available.", g
               end if
          end do;
          TT:-AddType(_T1, algebraic);
          TT:-AddType(_T2V, 'Vector(2, algebraic)');
          TT:-AddType(_T2L, [algebraic $ 2]);
          TT:-AddType(_T3V, 'Vector(3, algebraic)');
          TT:-AddType(_T3L, [algebraic $ 3]);
          TT:-AddType(_MyType, MyTypes)
     end proc,

     ModuleUnload:= proc()
     local T;
          for T in AllMyTypes do TT:-RemoveType(T) end do
     end proc,

     MyDispatch:= overload([
          proc(A::_T1, B, C)
          option overload;
          local r:= "A, B, C are T1."; #unnecessary; just an example.
               #statements to process this type
          end proc,

          proc(A::_T2L, B, C)
          option overload;
          local r:= "A, B, C are T2L.";
               #
          end proc,

          proc(A::_T2V, B, C)
          option overload;
          local r:= "A, B, C are T2V.";
               #
          end proc,

          proc(A::_T3L, B, C)
          option overload;
          local r:= "A, B, C are T3L.";
               #         
          end proc,

          proc(A, B, C)
          local r:= "A, B, C are T3V.";
               #
          end proc,
#
#I added this
#
          proc(A, B)
          local r:= "A, B, are mixed.";
               #
          end proc
     ]),
#
# I have have  added  'Or'(....(A::_T2L,B::_T3L)
#
     ModuleApply:= proc(
          A::'Or'(And(
               _MyType,
               satisfies(A-> andmap(T-> A::T implies B::T and C::T, MyTypes) )
          ),

          (A::_T2L,B::_T3L)),
          B::_MyType, C::_MyType
     )
          MyDispatch(args)
     end proc
;
     ModuleLoad()    
end module:
 

#Example usage:
#

x:=[9,4];
y:=[5,7];
z:=[1,9];                                 
MyModule(x,y,z);

[9, 4]

[5, 7]

[1, 9]

"A, B, C are T2L."

x:=[9,4];
y:=[5,6,7];
z:=p;                                 
MyModule(x,y);  #Looses kernel connection

[9, 4]

[5, 6, 7]

p

Download Q_19-11-22_Module_Test_Types.mw

Why is the Maple giving this error. See attched file. Further, how can we eq. of the form "A+B`*sqrt(C) = 0" by eliminating the common denominator.

CM_TW.mw

Dears

Can you give me advice on how to improve the calculation time for Binomial-Beta mcmc Metropolis-Hastings algorithm?

The calculation time for 50 000 samples for my laptop (Dell XPS 9710) takes approx 22 sec.
At the same time, in MathCAD Prime 8.0, the same amount of samples is calculated (using the same procedure) in approx 0.3 s.

======

======

I will be appreciated any help

wzelik

 

dchange gives the error when I try to convert pde into ode. Why?

restarts

with(PDEtools)

pde1 := diff(u(x, t), t)-(diff(u(x, t), `$`(x, 2), t))+3*u(x, t)^2*(diff(u(x, t), x))-2*(diff(u(x, t), x))*(diff(u(x, t), `$`(x, 2)))-u(x, t)*(diff(u(x, t), `$`(x, 3))) = 0

diff(u(x, t), t)-(diff(diff(diff(u(x, t), t), x), x))+3*u(x, t)^2*(diff(u(x, t), x))-2*(diff(u(x, t), x))*(diff(diff(u(x, t), x), x))-u(x, t)*(diff(diff(diff(u(x, t), x), x), x)) = 0

(1)

trans1 := {seq(var[i] = tau[i], i = 2), FN = Y(zz), var[1] = (zz-(sum(lambda[i]*tau[i], i = 2)))/lambda[1]}

{FN = Y(zz), var[1] = (-lambda[2]*tau[2]+zz)/lambda[1], var[2] = tau[2]}

(2)

ode1 := dchange(trans1, pde, [Y(zz), zz, seq(tau[i], i = 2)])

Error, (in dchange/info) the number of new and old independent variables must be the same. Found {zz, tau[2]} as new, while {FN, var[1], var[2]} as old

 

op(lhs(pde1))

diff(u(x, t), t), -(diff(diff(diff(u(x, t), t), x), x)), 3*u(x, t)^2*(diff(u(x, t), x)), -2*(diff(u(x, t), x))*(diff(diff(u(x, t), x), x)), -u(x, t)*(diff(diff(diff(u(x, t), x), x), x))

(3)

 

Download P_O.mw

I think I mentioned this before long time ago and never got any satisfactory answer. So I thought I will try again.

I never been able to figure why/how dsolve decides when to integrate the intermediate result vs. keeping the integral inert, even though it can integrate it.

It must use some rule internal to decide this, and this is what I am trying to find out.

Here is a very simple separable ode. So this is just really an integration problem.

restart;
ode:=diff(y(x),x)=(b*y(x)+sqrt(y(x)^2+b^2-1) )/(b^2-1);
dsolve(ode)

The first thing that comes to mind, is that Maple could not integrate it, that is why it gave inert integral. but it can integrate it but the result is a little long

int((b^2 - 1)/(b*y + sqrt(y^2 + b^2 - 1)),y)

So it could have generated the above implicit solution instead. Now notice what happens when I make very small change the ode.

restart;
ode:=diff(y(x),x)=(y(x)+sqrt(y(x)^2+b^2-1) )/(b^2-1);
dsolve(ode)

In the above I changed b*y to just y and guess what, now maple will integrate it and give an implicit solution instead of an inert integral

In both cases, Maple is able to do the integration. But in first case, it returned an inert integral and in the second it did not.

my question is why?  Does it have a rule where if the size of the integral is larger than some limit, it does not solve it? Did it say,

     "I think this result is too complicated to the user, so I will keep the integral inert instead"

If so, what are the rules it uses to decide when to do the integration and when to keep it inert? Is it based on leafcount? number of terms? something else?

infolevel does not give a hint on this, as all what it says is that it is separable.

Any one has an ideas on this?

It appears that using 2D math can generate hidden characters that make code not run. 

It seems like a lot of people think that using 1D math is a no-brainer, as if it had all the advantages and no disadvantages.

I am trying to write code for an object. I was using 2D math, because the automatic formatting of the code (italics, bold) makes it much easier to see and understand the code. Then again, I ran into an issue I face sometimes which is that code that looks absolutely perfect can't be parsed. 

I read that we can convert the code to 1D math and we will see hidden characters messing things up but that doesn't seem to be the case (or at least I can't seem to see the extra character). And in any case, it is just maddening and not a productive thing to have to do.

Is 1D math really the best user experience that is available? Is there really a tradeoff between legibility and useability in Maple 2022?

This ode from textbook, and the solution is given in back of book and I verified it is correct.

odetest gives zero also when asked to verify the solution.

but when asked to verify both the solution and the initial conditions, instead of returning [0,0] as expected, it returns [the_ode,0]

Here is an example
 

interface(version);

`Standard Worksheet Interface, Maple 2022.2, Windows 10, October 23 2022 Build ID 1657361`

restart

ode:=diff(y(x), x) = 2*(2*y(x) - x)/(x + y(x));
ic:=y(0) = 2;
booksol:=(x-y(x))^2/( y(x)-2*x)^3 = 1/2;

diff(y(x), x) = 2*(2*y(x)-x)/(x+y(x))

y(0) = 2

(x-y(x))^2/(y(x)-2*x)^3 = 1/2

#this returns zero, so maple agree the book solution is correct
odetest(booksol,ode)

0

#when adding ic, when does it not give [0,0] ?
odetest(booksol,[ode,ic])

[diff(y(x), x)-2*(2*y(x)-x)/(x+y(x)), 0]

 


How shoulld one interpret the above answer?

Download question_on_odetest_nov_14_2022.mw

Consider the following system of differential equations

sys := diff(y(x), x) = z(x)*f1(i), diff(z(x), x) = y(x)*f2(i)

where f1 and f2 are functions that depend on the current iteration. Ultimately, I'd like to index into an array that has the length of the number of iterations, to obtain a value that will be part of the differential equations. It's an array of random numbers, but I'd rather not have to generate them on the fly while dsolve is working.

I've been investigating the use of Events for this, but the documentation is quite atrocious and outdated (and I only know this because, for example, when I try to use certain arguments to dsolve some error messages show that the arguments have changed name)

I've read the documentation on events, and as far as I can tell after an hour or two, I am doing exactly what is in the documentation but not getting the expected result.

Here is a worksheet illustrating the issue: dsolve_events.mw

Basically there is a very simply system of two differential equations and I would simply like to see an event triggered when the dependent variable is above 2. 

This event has no useful interpretation, it was just my attempt at trying to get something to trigger (I have tried multiple things). As far as I can tell from the docs I am using an event specification of form 

[0, c(t,y(x)) < 0]: discrete event with a conditional trigger

ie, [0,2-x<0]

and when that is triggered I set i(x) to something like i(x)+1 (but even something as simple as assigning it to some constant like 7, given that the initial value i(0)=0, would allow me to check when the event is being triggered), where i(x) is defined as a discrete variable (my ultimate goal is to trigger the event on every iteration and have i be the iteration counter. I want to use this iteration counter in the equations)

I run the dsolve command, assign the result to a variable and then call, for example p(3). I would expect to see the event triggered and i(3) not equal to the initial value i(0). But the value of i(x) doesn't change.

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