May be someone can come up with a way to simplify this ode solution? I used the option useInt but the solution can be written in much simpler way than Maple gives.  Below is worksheet showing Maple's 2024 solution and my hand solution.

(having trouble uploading worksheet, will try again).

Download simpler_solution.mw

I keep losing the edits I do. I post screen shot. Click submit, then find all my changes are lost. Will try one more time and give up:

This is Maple solution

This is implified version

Both versions are verified correct by odetest. The question is there is a way to obtain the simpler form from Maple.

Hi,

I need your insights on two technical questions regarding my BoxPlot:

1) How to adjust the color of the text (Title and caption)

2) How to remove only the y-axis

Thank you

S5StatBoxPlotBtest.mw

I was wondering why Maple do not give this simpler solution to this ode. It solves it as exact. But if solved as separable, the solution is much simpler.

I solved this by hand and Maple verifies my solution. You can see the separable solution is much simpler. Any tricks to make Maple gives the simpler solution?

Download why_not_this_simpler_solution.mw

Hand solution

Maple 2024

it took me hrs to find this as my solution was failing verification and I did not know why.

What logic do you think Maple used to simplify this:

expr:=sqrt(1 + sin(x))/x;
simplify(expr)

To this

How could the above be simpler than

?

Compare to Mathematica

And this is what I expected. I am now scared to use simplify in Maple as I do not know what I will get back.

Is there a way to tell Maple not to do such strange "simplification"? I am doing this in code, and the code does not know what the expression is.

To see an example of the side effect of this, here is one, where if solution to an ode is simplified first, it no longer verifies by odetest without adding extra assumptions:

One does not expect that simplified solution no longer verfiies the ode.

Sure, I can do

          odetest(simplify(sol),ode) assuming real;

and now it gives 0. But the point is that the first one did not need assumptions.

Download simplify_with_odetest.mw

Maple 2024 on windows 10.

I am trying to tidy up cases where a proc returns multiple values. Have being trying Tabulate. I can get it to work when called after the results are returned. I would the procedure to do this but  keep acces to the name(s) assigned to the returned values.

A,B,C:= proc(...)  .....  return a, b, c    end proc. 

So basically display a tabulated of a, b, c.
 

Download 2024-03-18_Q_Format_Returned_Results_into_a_Table..mw

I am trying to get Maple to simplify the following trigonometric expressions (for "generic" parameters) as much as possible: 

sineExpr(3) := (
   sin(a[2] - b[1])*sin(a[3] - b[1]))/(
   sin(b[2] - b[1])*sin(b[3] - b[1]))*sin(a[1] - b[1]) + (
   sin(a[3] - b[2])*sin(a[1] - b[2]))/(
   sin(b[3] - b[2])*sin(b[1] - b[2]))*sin(a[2] - b[2]) + (
   sin(a[1] - b[3])*sin(a[2] - b[3]))/(
   sin(b[1] - b[3])*sin(b[2] - b[3]))*sin(a[3] - b[3]);
 = 
   


sineExpr(4) := (
   sin(a[2] - b[1])*sin(a[3] - b[1])*sin(a[4] - b[1]))/(
   sin(b[2] - b[1])*sin(b[3] - b[1])*sin(b[4] - b[1]))*
   sin(a[1] - b[1]) + (
   sin(a[3] - b[2])*sin(a[4] - b[2])*sin(a[1] - b[2]))/(
   sin(b[3] - b[2])*sin(b[4] - b[2])*sin(b[1] - b[2]))*
   sin(a[2] - b[2]) + (
   sin(a[4] - b[3])*sin(a[1] - b[3])*sin(a[2] - b[3]))/(
   sin(b[4] - b[3])*sin(b[1] - b[3])*sin(b[2] - b[3]))*
   sin(a[3] - b[3]) + (
   sin(a[1] - b[4])*sin(a[2] - b[4])*sin(a[3] - b[4]))/(
   sin(b[1] - b[4])*sin(b[2] - b[4])*sin(b[3] - b[4]))*
   sin(a[4] - b[4]);
 = 

So far, all of my attempts have failed: 
 

Download sinIdentity.mw

Note that because zero testing is frequently considerably easier, combine always succeeds in showing that the difference between the simplest possible and the original version is zero. 

combine(sin((a[1]+a[2]+a[3])-(b[1]+b[2]+b[3]))-sineExpr(3));
 = 
                               0

combine(sin((a[1]+a[2]+a[3]+a[4])-(b[1]+b[2]+b[3]+b[4]))-sineExpr(4));
 = 
                               0

However, I wonder if Maple can thoroughly simplify them without knowing those known “simplest possible” form beforehand. 
I also tried some other functions like rationalize, radnormal, and `convert/trig`, yet Maple appears to have not been capable of completely simplifying even the sub-simplest case 𝑚＝2. Is there any workaround? 

Of note, it can be demonstrated inductively that ∀m∈ℕ_₊ 

where none of the denominators is 0. Nevertheless, as mentioned above, is it possible to transform  and  (as well as , if possible) into potentially more elegant forms (Ideally,  is rewritten into ,  is rewritten into , and  is rewritten into .) without any such a priori knowledge? 
In Mma, these may be done using TrigReduce directly (cf. ); unfortunately, I cannot found a Maple equivalent to such functionality. 

 I am writing help pages for a package. The inital Overview should be at the top of the listing like in other Maple help directories. 

How to I do this? Mine is listing purely alphabetically.
 

Download Help_Edit_to_Database_2023.mw

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.