THis ode looks complicated

ode := (2*x^(5/2) - 3*y(x)^(5/3))/(2*x^(5/2)*y(x)^(2/3)) + ((-2*x^(5/2) + 3*y(x)^(5/3))*diff(y(x), x))/(3*x^(3/2)*y(x)^(5/3)) = 0;

But is actually a simple first order linear ode:

RHS:=solve(ode,diff(y(x),x));
new_ode:=diff(y(x),x)=RHS;

Whose solution is 

But Maple gives this very complicated answer as shown below. When asking it to solve as linear ode, it now gives the much simpler solution.  

Maple complicated solutions are all verified OK. But the question is, why did it not give this simple solution?

Attached worksheet.  All on Maple 2024

Download why_missed_simple_solution_march_17_2024.mw

In Maple 2022

restart;

res := t^3 - 3*t^2*sqrt(t^2*(12*sqrt(2)*ln(t) + 9*ln(t)^2 + 8)^(1/3))*ln(t)/(12*sqrt(2)*ln(t) + 9*ln(t)^2 + 8)^(2/3) - 2*t^2*sqrt(t^2*(12*sqrt(2)*ln(t) + 9*ln(t)^2 + 8)^(1/3))*sqrt(2)/(12*sqrt(2)*ln(t) + 9*ln(t)^2 + 8)^(2/3);
plot(res,t=-5..1)

gives

The same exact code in Maple 2024 gives

Worksheet is below. 

Both on same PC. Windows 10.

Will report to Maplesoft, but thought to check also here is others have seen such problem before.

Btw, Maple 2022 plot is the correct one.

Download wrong_plot_V_2024_march_15_2024.mw

Maple's coulditbe  is useful. But unfortunately it does not return back to the user the conditions under which the proposition was found true. This could make it much more useful. It seems in way similar to Mathematica' Reduce but Reduce returns the conditions.

Is there a way to find the conditions which makes it true? 

I use coulditbe alot. I use it to verify that the result of odetest (I call it the residue) is zero or not. Maytimes, odetest does not return zero. And using simplify, or evalb or is to check if the residue is zero, all fail. But many times, coulditbe returns true, meaning the residue is zero. But I do not know under what conditions. In Mathematica's Reduce, it tells me the conditions. 

Here is one of hundreds of examples I have

restart;
ode:=(t^3+y(t)^2*sqrt(t^2+y(t)^2))-(t*y(t)*sqrt(t^2+y(t)^2))*diff(y(t),t)=0;
ic:=y(1)=1;
sol:=dsolve([ode,ic]);
the_residue:=odetest(sol,[ode,ic]);

You see, odetest says it could not verify the solution (the first entry above) but it did verify the solution against the initial conditions. 

Using simplify, evalb and is all also could not verify it

simplify(the_residue[1]);
evalb(the_residue[1]=0);
is(the_residue[1]=0);

Now coulditbe does:

_EnvTry:='hard':
coulditbe(the_residue[1]=0);

So the solution is correct, but I do not know under what conditions. Using Mathematica's Reduce I can find this:

So now back in Maple, I can do this

simplify(the_residue[1]) assuming t>exp(-2*sqrt(2)/3);

                      0

Actually in this example, just using assume t>0 also gives zero. But I am using Mathematica's result for illustration.

You might ask, why do I need to know for what values of the independent variable is the residue zero?

Because in some cases, the residue is zero only at single point! So it does not make sense to say the solution is verified to be correct only at one single point of the domain, right?

it needs to be some finite range at least. Here is an example of an ode whose solution is correct only at x=0

ode:=diff(y(x),x)=3*x*(y(x)-1)^(1/3);
ic:=y(3)=-7;
sol:=dsolve([ode,ic]);
the_residue:=odetest(sol,[ode,ic]);

And simplify, evalb, is all fail to verifiy this, but coulditbe says true

simplify(the_residue[1]);
evalb(the_residue[1]=0);
is(the_residue[1]=0);
_EnvTry:='hard':
coulditbe(the_residue[1]=0);

So now, we ask, is this solution then correct or not? It turns out to be zero but only at origin x=0

plot(abs(the_residue[1]),x=-1..1)

If I knew that residue is zero only at single point, then I would say this solution is not correct, right?

And that is why I need to know under what conditions coulditbe retruned true.

I tried infolevel[coulditbe]:=5 but nothing more was displayed on the screen.

Mathematica's Reduce confirms that when x=0 the residue is zero.

So my question is simply this: Can one obtain the conditions used by coulditbe to determine when result is true?

It will be useful if Maple could in future version return the value/range which makes it true.

I am trying to solve the following set of equations, I am able to find solutions for a simplified case (b=0) using the command solve but cannot seem to solve it for general b.

Is there a better way to attempt to find a solution?
solve.mw

Download solve.mw

In many special cases, generalized hypergeometric functions can be transformed into other (possibly less general) functions, but sometimes Maple fails to convert some of them to other functions when possible.
For instance, 

4*hypergeom([1, 1], [2, 3, 7/2], -(x/2)**2) - 
 35*hypergeom([1, 1], [2, 5/2, 3], -(x/2)**2) - 
 2*hypergeom([1, 1], [3, 3, 7/2], -(x/2)**2) + 
 10*hypergeom([1, 1], [5/2, 3, 3], -(x/2)**2): # which is, in fact, “360*((Ci(x) - ln(x) + 19/18 - gamma)/x**2 - sin(x)/x**3 + (cos(x) + 5/3)/x**4 - 8/3*sin(x)/x**5)” 
expand(%);
 = 



simplify(%);

Is it possible to obtain a non-hypergeometric form of it? E.g., 

. 

Here are more examples that `simplify/hypergeom` (as well as expand) is unable to deal with: 

1. hypergeom([1, 1, 3/2], [5/2, 5/2, 3, 3], -(x/2)**2):
2. hypergeom([1, 1], [5/2, 3, 3], -(x/2)**2):
3. hypergeom([1, 1], [3/2, 2, 2], -(x/2)**2):
4. hypergeom([3/2], [5/2, 5/2], -(x/2)**2):
5. … (to be continued) 

I have read something like How to simplify this hypergeometric function? - MaplePrimes, yet those tricks do not appear to work here. Is there any workaround? 

Edit. There seems to be a bug in `simplify/hypergeom`: 

'hypergeom([-1/3, 1/3, -1/2 - m, -m], [1/2, 1/3 - m, 2/3 - m], 1)':
simplify(`%`, hypergeom) assuming m::nonnegint;
 = 
                               -1
                               --
                               2 

simplify(eval(`%%`, m = 0), 'constant');
 = 
                               1

The expected result should be a piecewise function. 

Maple does not have full_simplify() command like with Mathematica.

So I figured why not make one? 

Here is a basic implementation. All what it does is blindly tries different simplifications methods I know about and learned from this forum then at the end sorts the result by leaf count and returns to the user the one with smallest leaf count.

I tried it on few inputs.

Advantage of full_simplify() is that user does not have to keep trying themselves. One disadvantage is that this can take longer time. timelimit can be added to this to make it not hang.

Can you see and make more improvement to this function?

May be we all together can make a better full_simplify() in Maple to use. Feel free to edit and change.

#version 1.0  
#increment version number each time when making changes.

full_simplify:=proc(e::anything)
   local result::list;
   local f:=proc(a,b)
      RETURN(MmaTranslator:-Mma:-LeafCount(a)<MmaTranslator:-Mma:-LeafCount(b))
   end proc;

   #add more methods as needed

   result:=[simplify(e),
            simplify(e,size),
            simplify(combine(e)),
            simplify(combine(e),size),
            radnormal(evala( combine(e) )),
            simplify(evala( combine(e) )),
            evala(radnormal( combine(e) )),
            simplify(radnormal( combine(e) )),
            evala(factor(e)),
            simplify(e,ln),
            simplify(e,power),
            simplify(e,RootOf),
            simplify(e,sqrt),
            simplify(e,trig),
            simplify(convert(e,trig)),
            simplify(convert(e,exp)),
            combine(e)
   ];   
   RETURN( sort(result,f)[1]);   

end proc:

worksheet below

Download full_simplify.mw

I just installed Maple 2024.0 and I discovered a problem in that the "Manage Style Sets" under the "Format" menu DOESN'T WORK!!! Type the following to understand how this feature works and see if you have the same problem:

>?workshhet,documenting,styles

Follow the instructions.  They are pretty simple.  Find a worksheet that has the styles you like and open it up and then save this Style Set in Maple 2024.0.  Then close it.  Open a new worksheet.  Go to "Format" and then click on "Managing Style Sets" and then click on the Style Set file name you saved previously and you will find that it does not set the style set you saved previously.  

Another problem you will find is that it doesn't save your Style Set file where it is supposed to save it.  It needs to be saved in a Maple 2024.0 created folder known as "data" and then in a folder under "data" called "stylesets".  I had to manually go find my Style Set file and copy and paste it there.  

Please check this out and see if I am wrong.  I use the "Format" "Manage Style Sets" option a lot when I download files from this blog and ".mw"  have fonts size 12 and they default to the nearly impossible to read font!  After I have applied the "Manage Style Sets" I can see what I have! But for some reason in Maple 2024.0 this feature was not tested or something has changed in Maple 2024.0 to break this feature!

AllGraphs is a new function in Maple 2024. Good things！

However, it seems that most of its functionalities are already provided by NonIsomorphicGraphs, and its speed even lags behind that of NonIsomorphicGraphs 

I'm curious about what truly sets this function apart from existing ones. It generates isomorphic graphs if nonisomorphic=falseBut I donot know what its application is. Supporting directed graphs is a new thing, but its speed is not well.

iterator := GraphTheory[AllGraphs](vertices = 6, edges =6..7, connected, nonisomorphic)
s:=[seq(p, p = iterator)]:
nops(s)

Note that this function is suitable for generating non-isomorphic connected graphs with 6 vertices and either 6 or 7 edges. It doesn't hold an advantage in terms of speed， andNonIsomorphicGraphs also provides an iteration option.

I have been trying Maple 2024 and found this strange result. 

Calling solve(identity...  on same input in Maple 2024 gives very large and complex output compare with Maple 2023.2.1.

This was causing problem, until I found that simplifying the solution now gives same output as Maple 2023.2.1

But why is this now needed in Maple 2024? i.e. why is calling simplify needed when in Maple 2023 the simpler solution was returned automatically?

I changed my code to call simplify now on result of solve(identity...  but I am just curious what happened to cause this?

Below are two worksheets, one from Maple 2024 and one from Maple 2023.2 and you see the huge difference in result.

Download solve_identity_march_11_2024_maple_2023.mw

Download solve_identity_march_11_2024.mw

Download QuestionSimplifyMultivariateRationalFunction.mw

 Hello,

  Doing simple calculations I found Maple 2024 and 2023 don't recognize Kronecker delta in the expression

Full worksheet attached. Is there any way to let Maple handle this?

Remaining questions:
1. Doing calculations using Int and value left the result unevaluated eq. (6) and eq. (7) while using int gives 0. Why?
2. Is there possibility to substitute indexed (i.e.) atomic variables like p__m? For example changing by command p__m to p__k.

Thank you in advance,

delta_kron-problem.mw

This code used to work OK in Maple 2023.2.1 on windows 10. Now it gives this new internal Maple error 

Error, (in property/ConvertRelation) numeric exception: division by zero

I think this is new problem in Maple 2024 as I have not seen it before. Will report it to Maplesoft. Mean while if someone has any workaround other than not using the `is` command will try it.

The following are two worksheets. One using 2023 shows it works OK (no error) and one in Maple 2024 with the new error

Download no_numeric_exception_march_7_2024_version_2023.mw
 

Download numeric_exception_march_7_2024_version_2024.mw

I was wondering if this is by design or not. Here is one example., This ode is solved by Maple 2023.2.1 on windows 10. The solution is in terms of DESol though. It takes less than one minute.

In Maple 2024 on same PC, dsolve hangs on it.

If this by design? Since DESol solution is not very useful actually. I was thinking that may be Maple is now trying to return a solution without DESol in it, and that is why it hangs or take long time. I stopped it after 5 minutes. 

Or should I report it to Maplesoft as possible bug?  

Below are 2 worksheets. One using Maple 2023 and one using 2024.

Download dsolve_march_7_2024_maple_2023.mw

Download dsolve_march_7_2024_maple_2024.mw

One may easily spot that the symbols “→” and “⇒” are missing here and here. 

These two PDF files were printed officially, so I think they can be considered examples of best practice for the export functionality. Does this mean that this functionality is still defective in the most recent release?

chatGPT version used by the new NaturalLanguage package seems to be using chatGPT 3?. I asked it and this what it said

NL:=NaturalLanguage;
NL:-Query("what is your name?");

"As an Artificial Intelligence, I don't have a personal name. However, If 
you're asking how to represent the question \"What is your name?\" in MathML, 
it's actually irrelevant as MathML is used for marking up mathematical notations, 
not regular text or questions. \n\nBut in English, it's as simple 
as just asking \"What is your name?

Then I asked it 

NL:-Query("what version of chatGPT are you?");

"As an AI developed by OpenAI, I don't have a specific version like software 
programs or applications. I get continuous updates and improvements over time. 
However, as of my current operation, I'm based on GPT-3 model.

some questions: It is possible to make it use chatGPT 3.5 or 4.0 with NL?

How is this free to use and without getting a key from openAI? After agreeing to terms fromn the options menu, can one continue to use it for free? I thought chatGPT requires some fee to use. But I could be wrong.  but this is nice to be able to use it this easily from Maple!

Btw, It is still not very good in math. Asked it to first this simple first order ode and got wrong answer

NL:-Query("what is the solution to the differential equation y'(x)+y(x)=sin(x)");

"Sorry, this query was too complicated. Please rephrase and/or try again."

So I tried

NL:-Query("solve the differential equation y'(x)+y(x)=sin(x)");

"The differential equation given is a first order linear 

   ordinary differential equation. 

  

  The general solution can be obtained through the following 

   steps:

  

  1. Identify the homogeneous part of the equation, which is 

   y'(x) + y(x) = 0. The solution of such a homogeneous 

   equation known as the "complementary function" is y_c = 

   e^(-x) * A. where A is an arbitrary constant which will be 

   determined by a specific condition or boundary value.

  

  2. Find a Particular Integral (solution specific to the 

   nonhomogeneous part of the differential equation) which in 

   this case is y_p = -cos(x)

  

  3. Combine the Complementary function and Particular Integral 

   to get a general solution, y(x) = e^(-x) * A - cos(x).

  

  Now let's express the solution in MathML:"


                            (-x)          
                     y x = e     A - cos x

 "Note: Here A is a to-be-determined constant. If the problem 

    was a boundary value or initial value problem, you would 

    substitute the given values into this general solution and 

    solve it for A."

The solution should be

dsolve(diff(y(x),x)+y(x)=sin(x))

                y(x) = -cos(x)/2 + sin(x)/2 + exp(-x)*c__1