nm

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These are questions asked by nm

This happens in Maple 2025, but when I checked Maple 2024.2, same thing happen.

To reproduce, I typed ?coeff in the worksheet. Now the help page for coeff comes up OK. On the right, there are some links below "see also". 

Clicking on the one that says PolynomialTools[CoefficientVector] and now an EMPTY page opens up.

Also, typing ?PolynomialTools in worksheet, opens the help page for Overview of the PolynomialTools Package. Now clicking on CoefficientList link, opens an EMPTY page. Same when clicking on CoefficientVector, an EMPTY page !

Have not checked all the links in the help page, but why are some commands have empty help pages?

 

 

The series to ode using 'series' option (if it exists) should always be series(...), i.e. with big O at end. but sometimes Maple forgets to add this. Here is an example

interface(version);

`Standard Worksheet Interface, Maple 2025.0, Linux, March 24 2025 Build ID 1909157`

Physics:-Version();

`The "Physics Updates" version in the MapleCloud is 1862 and is the same as the version installed in this computer, created 2025, April 25, 10:33 hours Pacific Time.`

SupportTools:-Version();

`The Customer Support Updates version in the MapleCloud is 15 and is the same as the version installed in this computer, created April 27, 2025, 23:18 hours Eastern Time.`

restart;

ode:=diff(y(x),x)+y(x)=1+x;
IC:=y(0)=0;
sol:=dsolve([ode,IC],y(x),'series')

diff(y(x), x)+y(x) = 1+x

y(0) = 0

y(x) = x

lprint(sol); # notice solution is not series, it should be

y(x) = x

#above solution should be
y(x) = series(x+O(x^6),x,6)

y(x) = series(x+O(x^6),x,6)

#this example below is correct
ode:=diff(y(x),x)+y(x)=1+x;
IC:=y(0)=1;
sol:=dsolve([ode,IC],y(x),'series')

diff(y(x), x)+y(x) = 1+x

y(0) = 1

y(x) = series(1+(1/2)*x^2-(1/6)*x^3+(1/24)*x^4-(1/120)*x^5+O(x^6),x,6)

lprint(sol); #solution is series

y(x) = series(1+1/2*x^2-1/6*x^3+1/24*x^4-1/120*x^5+O(x^6),x,6)

 

 

Download bug_report_dsolve_series_april_28_2025.mw

These two expressions are the same, just pulled minus sign out

But look what happens when integrating them. the anti derivative of one is much more complicated than the other and contains complex numbers and logs. And no matter what I tried, I could not convert the complicated one to look same as the simpler result. Also could not verify the complicated one by back differentiating.

integrand_1:=x^2*(-arctan(x) + x)*exp(-arctan(x) + x)/(x^2 + 1);

x^2*(-arctan(x)+x)*exp(-arctan(x)+x)/(x^2+1)

integrand_2:=evala(integrand_1);

-x^2*(arctan(x)-x)*exp(-arctan(x)+x)/(x^2+1)

simplify(integrand_1 - integrand_2)

0

anti_1:=int(integrand_1,x);

(-arctan(x)+x)*exp(-arctan(x)+x)-exp(-arctan(x)+x)

anti_2:=int(integrand_2,x);

-(1-x+((1/2)*I)*ln(1-I*x)-((1/2)*I)*ln(1+x*I))*(1-I*x)^(-(1/2)*I)*(1+x*I)^((1/2)*I)*exp(x)

simplify(diff(anti_1,x)-integrand_1);

0

simplify(diff(anti_2,x)-integrand_2);

Error, (in simpl/simpl/ReIm/sum) too many levels of recursion

simplify(anti_1 - anti_2)

Error, (in simpl/simpl/ReIm/sum) too many levels of recursion

simplify(anti_2);

(1/2)*(I*ln(1+x*I)-I*ln(1-I*x)+2*x-2)*(1-I*x)^(-(1/2)*I)*(1+x*I)^((1/2)*I)*exp(x)

simplify(anti_2,ln);

(1/2)*(I*ln(1+x*I)-I*ln(1-I*x)+2*x-2)*(1-I*x)^(-(1/2)*I)*(1+x*I)^((1/2)*I)*exp(x)

 

 

Download int_strange_result_april_27_2025.mw

I would have expected same anti derivative to show.  To check, I used another software, and that one gave same anti-derivative for both integrands.

The questions I have: Why Maple gives such different result for same integrand? And how could one convert the one with the logs and complex numbers to the first one?

Maple 2025

FYI;

 

You might have to try the command more than one time to see the above crash. Here is the worksheet

restart;

interface(version);

`Standard Worksheet Interface, Maple 2025.0, Linux, March 24 2025 Build ID 1909157`

Physics:-Version();

`The "Physics Updates" version in the MapleCloud is 1862 and is the same as the version installed in this computer, created 2025, April 25, 10:33 hours Pacific Time.`

SupportTools:-Version();

`The Customer Support Updates version in the MapleCloud is 13 and is the same as the version installed in this computer, created April 22, 2025, 15:14 hours Eastern Time.`

restart;

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

x^2-2*x*y(x)+5*y(x)^2 = (x^2+2*x*y(x)+y(x)^2)*(diff(y(x), x))

sol:=y(x) = (-1/2*exp(RootOf(-exp(_Z)^2*ln(x*(exp(_Z)-2))+2*_C7*exp(_Z)^2+_Z*exp(_Z)^2+4*exp(_Z)*ln(x*(exp(_Z)-2))-8*_C7*exp(_Z)-4*exp(_Z)*_Z-2*exp(_Z)-4*ln(x*(exp(_Z)-2))+8*_C7+4*_Z+6))^2+3*exp(RootOf(-exp(_Z)^2*ln(x*(exp(_Z)-2))+2*_C7*exp(_Z)^2+_Z*exp(_Z)^2+4*exp(_Z)*ln(x*(exp(_Z)-2))-8*_C7*exp(_Z)-4*exp(_Z)*_Z-2*exp(_Z)-4*ln(x*(exp(_Z)-2))+8*_C7+4*_Z+6))-6+2*(exp(RootOf(-exp(_Z)^2*ln(x*(exp(_Z)-2))+2*_C7*exp(_Z)^2+_Z*exp(_Z)^2+4*exp(_Z)*ln(x*(exp(_Z)-2))-8*_C7*exp(_Z)-4*exp(_Z)*_Z-2*exp(_Z)-4*ln(x*(exp(_Z)-2))+8*_C7+4*_Z+6))^2-6*exp(RootOf(-exp(_Z)^2*ln(x*(exp(_Z)-2))+2*_C7*exp(_Z)^2+_Z*exp(_Z)^2+4*exp(_Z)*ln(x*(exp(_Z)-2))-8*_C7*exp(_Z)-4*exp(_Z)*_Z-2*exp(_Z)-4*ln(x*(exp(_Z)-2))+8*_C7+4*_Z+6))+9)^(1/2))/(1/2*exp(RootOf(-exp(_Z)^2*ln(x*(exp(_Z)-2))+2*_C7*exp(_Z)^2+_Z*exp(_Z)^2+4*exp(_Z)*ln(x*(exp(_Z)-2))-8*_C7*exp(_Z)-4*exp(_Z)*_Z-2*exp(_Z)-4*ln(x*(exp(_Z)-2))+8*_C7+4*_Z+6))^2-3*exp(RootOf(-exp(_Z)^2*ln(x*(exp(_Z)-2))+2*_C7*exp(_Z)^2+_Z*exp(_Z)^2+4*exp(_Z)*ln(x*(exp(_Z)-2))-8*_C7*exp(_Z)-4*exp(_Z)*_Z-2*exp(_Z)-4*ln(x*(exp(_Z)-2))+8*_C7+4*_Z+6)))*x:

odetest(sol,ode);

 

Download crash_maple_2025_april_27_2025.mw

Hopefully a fix could be found for this.

Just found new regression in Maple 2025. This internal error can not be cought and was not there in Maple 2024.2. This is new from the ones reprted earlier in Collection-Of-Problems-In-Maple-2025 

Here it is , using latest SupportTools

restart;

interface(version);

`Standard Worksheet Interface, Maple 2025.0, Linux, March 24 2025 Build ID 1909157`

Physics:-Version();

`The "Physics Updates" version in the MapleCloud is 1862 and is the same as the version installed in this computer, created 2025, April 25, 10:33 hours Pacific Time.`

SupportTools:-Version();

`The Customer Support Updates version in the MapleCloud is 13 and is the same as the version installed in this computer, created April 22, 2025, 15:14 hours Eastern Time.`

restart;

#17593
eq:=2*A[6]*exp(-2*t)*cos(t)+2*A[3]*exp(-2*t)*sin(t)-2*A[4]*exp(-2*t)*cos(t)-4*A[7]*exp(-t)*sin(2*t)+4*A[8]*exp(-t)*cos(2*t)-2*A[5]*exp(-2*t)*sin(t)+4*A[2]*exp(-t)+4*A[1]*t*exp(-t)+4*A[3]*exp(-2*t)*cos(t)+4*A[4]*exp(-2*t)*sin(t)+2*A[9]*exp(-t)*cos(2*t)-8*A[9]*t*exp(-t)*sin(2*t)+2*A[10]*exp(-t)*sin(2*t)+8*A[10]*t*exp(-t)*cos(2*t)-2*A[5]*exp(-2*t)*cos(t)+2*A[5]*t*exp(-2*t)*sin(t)-2*A[6]*exp(-2*t)*sin(t)-2*A[6]*t*exp(-2*t)*cos(t)+4*A[5]*t*exp(-2*t)*cos(t)+4*A[6]*t*exp(-2*t)*sin(t) = 3*t*exp(-t)*cos(2*t)-2*t*exp(-2*t)*cos(t):


trial_solution_constants:=[A[1], A[2], A[3], A[4], A[5], A[6], A[7], A[8], A[9], A[10]]:

try
     timelimit(30,[solve(identity(eq,t),trial_solution_constants) ]);
catch:
     print("OK cought error");
end try;

Error, (in type/trig) too many levels of recursion

 

 

Download regression_maple_2025_april_26_2025.mw

Here is the same code in Maple 2024.2 but using windows. No internal error and timeout was cought as expected.

restart;
interface(version);

`Standard Worksheet Interface, Maple 2024.2, Windows 10, October 29 2024 Build ID 1872373`

Physics:-Version();

`The "Physics Updates" version in the MapleCloud is 1862. The version installed in this computer is 1849 created 2025, March 12, 12:37 hours Pacific Time, found in the directory C:\Users\Owner\maple\toolbox\2024\Physics Updates\lib\`

#17593
eq:=2*A[6]*exp(-2*t)*cos(t)+2*A[3]*exp(-2*t)*sin(t)-2*A[4]*exp(-2*t)*cos(t)-4*A[7]*exp(-t)*sin(2*t)+4*A[8]*exp(-t)*cos(2*t)-2*A[5]*exp(-2*t)*sin(t)+4*A[2]*exp(-t)+4*A[1]*t*exp(-t)+4*A[3]*exp(-2*t)*cos(t)+4*A[4]*exp(-2*t)*sin(t)+2*A[9]*exp(-t)*cos(2*t)-8*A[9]*t*exp(-t)*sin(2*t)+2*A[10]*exp(-t)*sin(2*t)+8*A[10]*t*exp(-t)*cos(2*t)-2*A[5]*exp(-2*t)*cos(t)+2*A[5]*t*exp(-2*t)*sin(t)-2*A[6]*exp(-2*t)*sin(t)-2*A[6]*t*exp(-2*t)*cos(t)+4*A[5]*t*exp(-2*t)*cos(t)+4*A[6]*t*exp(-2*t)*sin(t) = 3*t*exp(-t)*cos(2*t)-2*t*exp(-2*t)*cos(t):


trial_solution_constants:=[A[1], A[2], A[3], A[4], A[5], A[6], A[7], A[8], A[9], A[10]]:

 

try
     timelimit(30,[solve(identity(eq,t),trial_solution_constants) ]);
catch:
     print("OK cought error");
end try;


Download no_problem_in_maple_2024_april_26_2025.mw

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