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why random internal error Error, (in evala/Factors...

Asked by: nm 11173
allvalues
Yesterday at 10:00 AM
2  0

in Maple 2025 on Linux, I see random Error, (in evala/Factors) the modular inverse does not exist from call to allvalues().

Sometimes it happens and sometimes not. Any explanation of this?

 

It seems Maple uses random number generatror to decide when to generate an internal error as I am not able to see a pattern.

> 

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 1868. The version installed in this computer is 1866 created 2025, May 6, 10:52 hours Pacific Time, found in the directory /home/me/maple/toolbox/2025/Physics Updates/lib/`

> 

SupportTools:-Version();

`The Customer Support Updates version in the MapleCloud is 17 and is the same as the version installed in this computer, created May 5, 2025, 12:37 hours Eastern Time.`

> 

restart;
> 

kernelopts('assertlevel'=2):
> 

sol:=[1/3*exp(RootOf(-5*I*Pi-ln(256/(x+1)^6/(exp(_Z)^81+9)*(exp(_Z)^81+3)^3)+162*_Z))^81+2];
allvalues(sol);

[(1/3)*(exp(RootOf(-(5*I)*Pi-ln(256*((exp(_Z))^81+3)^3/((x+1)^6*((exp(_Z))^81+9)))+162*_Z)))^81+2]

Error, (in evala/Factors) the modular inverse does not exist

> 

allvalues(sol);

`[Length of output exceeds limit of 100000]`

> 

allvalues(sol);

`[Length of output exceeds limit of 100000]`

> 

allvalues(sol);

`[Length of output exceeds limit of 100000]`

> 

allvalues(sol);

Error, (in evala/Factors) the modular inverse does not exist

> 

allvalues(sol);

`[Length of output exceeds limit of 100000]`

> 

allvalues(sol);

`[Length of output exceeds limit of 100000]`

> 

allvalues(sol);

Error, (in evala/Factors) the modular inverse does not exist

> 

allvalues(sol);

`[Length of output exceeds limit of 100000]`

> 

allvalues(sol);

`[Length of output exceeds limit of 100000]`

> 

 


 

Download why_fail_sometimes_may_11_2025_V2.mw

Update was able to produce this also in Maple 2024.2 on windows

> 

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 1868. 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\`

> 

restart;
> 

kernelopts('assertlevel'=2):
sol:=[1/3*exp(RootOf(-5*I*Pi-ln(256/(x+1)^6/(exp(_Z)^81+9)*(exp(_Z)^81+3)^3)+162*_Z))^81+2];
allvalues(sol);

[(1/3)*(exp(RootOf(-(5*I)*Pi-ln(256*((exp(_Z))^81+3)^3/((x+1)^6*((exp(_Z))^81+9)))+162*_Z)))^81+2]

`[Length of output exceeds limit of 100000]`

> 

allvalues(sol);

`[Length of output exceeds limit of 100000]`

> 

allvalues(sol);

`[Length of output exceeds limit of 100000]`

> 

allvalues(sol);

`[Length of output exceeds limit of 100000]`

> 

allvalues(sol);

`[Length of output exceeds limit of 100000]`

> 

allvalues(sol);

`[Length of output exceeds limit of 100000]`

> 

allvalues(sol);

Error, (in evala/Factors) the modular inverse does not exist

> 

allvalues(sol);

`[Length of output exceeds limit of 100000]`

> 

allvalues(sol);

Error, (in evala/Factors) the modular inverse does not exist

> 

allvalues(sol);

`[Length of output exceeds limit of 100000]`

> 

allvalues(sol);

`[Length of output exceeds limit of 100000]`

> 

allvalues(sol);

`[Length of output exceeds limit of 100000]`

> 

allvalues(sol);

`[Length of output exceeds limit of 100000]`

> 

allvalues(sol);

`[Length of output exceeds limit of 100000]`

> 

allvalues(sol);

`[Length of output exceeds limit of 100000]`

> 

allvalues(sol);

Error, (in evala/Factors) the modular inverse does not exist

> 

 


 

Download modular_inverse_maple_2024_2.mw

 

Automating Parameter Selection for Optimal Non-Zer...

Asked by: salim-barzani 1390
solve incomplete-question
May 09 2025
0  0

I would like to automatically select a set of parameters that gives me a "good" solution, ideally, one where not all parameters are zero. The parameters A[0], A[1], A[2], B[1], and B[2] are essential and must always be included. The other parameters are optional and can be selected in various combinations (e.g., one, two, or more at a time).

Currently, I manually add or remove these optional parameters, which is time-consuming. I’m looking for a way to automate the selection process to find the best combination of parameters that yields a valid and meaningful (non-zero) solution.

How can I approach this systematically?

params.mw

> 

restart
> 

with(PDEtools)
> 

with(LinearAlgebra)
> 

NULL
> 

with(SolveTools)
> 

with(LargeExpressions)
> 

undeclare(prime)

`There is no more prime differentiation variable; all derivatives will be displayed as indexed functions`

 (1)
> 

declare(u(x, t), quiet); declare(V(xi), quiet); declare(U(xi), quiet)
> 

NULL
> 

CoefficientNullity := [0 = k^3*(beta*s-w)*(A[0]+A[1]+A[2]+B[1]+B[2])*(-5*beta*s*A[0]^2*c[2]-10*beta*s*A[0]*A[1]*c[2]-10*beta*s*A[0]*A[2]*c[2]-10*beta*s*A[0]*B[1]*c[2]-10*beta*s*A[0]*B[2]*c[2]-5*beta*s*A[1]^2*c[2]-10*beta*s*A[1]*A[2]*c[2]-10*beta*s*A[1]*B[1]*c[2]-10*beta*s*A[1]*B[2]*c[2]-5*beta*s*A[2]^2*c[2]-10*beta*s*A[2]*B[1]*c[2]-10*beta*s*A[2]*B[2]*c[2]-5*beta*s*B[1]^2*c[2]-10*beta*s*B[1]*B[2]*c[2]-5*beta*s*B[2]^2*c[2]+3*beta*k*s*w+5*w*A[0]^2*c[2]+10*w*A[0]*A[1]*c[2]+10*w*A[0]*A[2]*c[2]+10*w*A[0]*B[1]*c[2]+10*w*A[0]*B[2]*c[2]+5*w*A[1]^2*c[2]+10*w*A[1]*A[2]*c[2]+10*w*A[1]*B[1]*c[2]+10*w*A[1]*B[2]*c[2]+5*w*A[2]^2*c[2]+10*w*A[2]*B[1]*c[2]+10*w*A[2]*B[2]*c[2]+5*w*B[1]^2*c[2]+10*w*B[1]*B[2]*c[2]+5*w*B[2]^2*c[2]+2*k*s^2-5*k*w^2), 0 = (beta*s-w)*(5*beta*k^3*s*A[0]^3*c[2]-15*beta*k^3*s*A[0]^2*A[1]*c[2]-45*beta*k^3*s*A[0]^2*A[2]*c[2]+45*beta*k^3*s*A[0]^2*B[1]*c[2]+45*beta*k^3*s*A[0]^2*B[2]*c[2]-45*beta*k^3*s*A[0]*A[1]^2*c[2]-150*beta*k^3*s*A[0]*A[1]*A[2]*c[2]+30*beta*k^3*s*A[0]*A[1]*B[1]*c[2]+30*beta*k^3*s*A[0]*A[1]*B[2]*c[2]-105*beta*k^3*s*A[0]*A[2]^2*c[2]-30*beta*k^3*s*A[0]*A[2]*B[1]*c[2]-30*beta*k^3*s*A[0]*A[2]*B[2]*c[2]+75*beta*k^3*s*A[0]*B[1]^2*c[2]+150*beta*k^3*s*A[0]*B[1]*B[2]*c[2]+75*beta*k^3*s*A[0]*B[2]^2*c[2]-25*beta*k^3*s*A[1]^3*c[2]-105*beta*k^3*s*A[1]^2*A[2]*c[2]-15*beta*k^3*s*A[1]^2*B[1]*c[2]-15*beta*k^3*s*A[1]^2*B[2]*c[2]-135*beta*k^3*s*A[1]*A[2]^2*c[2]-90*beta*k^3*s*A[1]*A[2]*B[1]*c[2]-90*beta*k^3*s*A[1]*A[2]*B[2]*c[2]+45*beta*k^3*s*A[1]*B[1]^2*c[2]+90*beta*k^3*s*A[1]*B[1]*B[2]*c[2]+45*beta*k^3*s*A[1]*B[2]^2*c[2]-55*beta*k^3*s*A[2]^3*c[2]-75*beta*k^3*s*A[2]^2*B[1]*c[2]-75*beta*k^3*s*A[2]^2*B[2]*c[2]+15*beta*k^3*s*A[2]*B[1]^2*c[2]+30*beta*k^3*s*A[2]*B[1]*B[2]*c[2]+15*beta*k^3*s*A[2]*B[2]^2*c[2]+35*beta*k^3*s*B[1]^3*c[2]+105*beta*k^3*s*B[1]^2*B[2]*c[2]+105*beta*k^3*s*B[1]*B[2]^2*c[2]+35*beta*k^3*s*B[2]^3*c[2]-3*beta*k^4*s*w*A[0]+3*beta*k^4*s*w*A[1]+9*beta*k^4*s*w*A[2]-9*beta*k^4*s*w*B[1]-9*beta*k^4*s*w*B[2]-5*k^3*w*A[0]^3*c[2]+15*k^3*w*A[0]^2*A[1]*c[2]+45*k^3*w*A[0]^2*A[2]*c[2]-45*k^3*w*A[0]^2*B[1]*c[2]-45*k^3*w*A[0]^2*B[2]*c[2]+45*k^3*w*A[0]*A[1]^2*c[2]+150*k^3*w*A[0]*A[1]*A[2]*c[2]-30*k^3*w*A[0]*A[1]*B[1]*c[2]-30*k^3*w*A[0]*A[1]*B[2]*c[2]+105*k^3*w*A[0]*A[2]^2*c[2]+30*k^3*w*A[0]*A[2]*B[1]*c[2]+30*k^3*w*A[0]*A[2]*B[2]*c[2]-75*k^3*w*A[0]*B[1]^2*c[2]-150*k^3*w*A[0]*B[1]*B[2]*c[2]-75*k^3*w*A[0]*B[2]^2*c[2]+25*k^3*w*A[1]^3*c[2]+105*k^3*w*A[1]^2*A[2]*c[2]+15*k^3*w*A[1]^2*B[1]*c[2]+15*k^3*w*A[1]^2*B[2]*c[2]+135*k^3*w*A[1]*A[2]^2*c[2]+90*k^3*w*A[1]*A[2]*B[1]*c[2]+90*k^3*w*A[1]*A[2]*B[2]*c[2]-45*k^3*w*A[1]*B[1]^2*c[2]-90*k^3*w*A[1]*B[1]*B[2]*c[2]-45*k^3*w*A[1]*B[2]^2*c[2]+55*k^3*w*A[2]^3*c[2]+75*k^3*w*A[2]^2*B[1]*c[2]+75*k^3*w*A[2]^2*B[2]*c[2]-15*k^3*w*A[2]*B[1]^2*c[2]-30*k^3*w*A[2]*B[1]*B[2]*c[2]-15*k^3*w*A[2]*B[2]^2*c[2]-35*k^3*w*B[1]^3*c[2]-105*k^3*w*B[1]^2*B[2]*c[2]-105*k^3*w*B[1]*B[2]^2*c[2]-35*k^3*w*B[2]^3*c[2]+40*beta^2*k^2*s^2*A[1]+80*beta^2*k^2*s^2*A[2]-40*beta^2*k^2*s^2*B[1]-40*beta^2*k^2*s^2*B[2]-2*k^4*s^2*A[0]+2*k^4*s^2*A[1]+6*k^4*s^2*A[2]-6*k^4*s^2*B[1]-6*k^4*s^2*B[2]+5*k^4*w^2*A[0]-5*k^4*w^2*A[1]-15*k^4*w^2*A[2]+15*k^4*w^2*B[1]+15*k^4*w^2*B[2]-80*beta*k^2*s*w*A[1]-160*beta*k^2*s*w*A[2]+80*beta*k^2*s*w*B[1]+80*beta*k^2*s*w*B[2]+40*k^2*s^2*A[1]+80*k^2*s^2*A[2]-40*k^2*s^2*B[1]-40*k^2*s^2*B[2]-160*beta*s*w*A[1]-320*beta*s*w*A[2]+160*beta*s*w*B[1]+160*beta*s*w*B[2]+160*s^2*A[1]+320*s^2*A[2]-160*s^2*B[1]-160*s^2*B[2]), 0 = (beta*s-w)*(25*beta*k^3*s*A[0]^3*c[2]+75*beta*k^3*s*A[0]^2*A[1]*c[2]+15*beta*k^3*s*A[0]^2*A[2]*c[2]+15*beta*k^3*s*A[0]^2*B[1]*c[2]+15*beta*k^3*s*A[0]^2*B[2]*c[2]+15*beta*k^3*s*A[0]*A[1]^2*c[2]-210*beta*k^3*s*A[0]*A[1]*A[2]*c[2]+150*beta*k^3*s*A[0]*A[1]*B[1]*c[2]+150*beta*k^3*s*A[0]*A[1]*B[2]*c[2]-285*beta*k^3*s*A[0]*A[2]^2*c[2]+150*beta*k^3*s*A[0]*A[2]*B[1]*c[2]+150*beta*k^3*s*A[0]*A[2]*B[2]*c[2]-105*beta*k^3*s*A[0]*B[1]^2*c[2]-210*beta*k^3*s*A[0]*B[1]*B[2]*c[2]-105*beta*k^3*s*A[0]*B[2]^2*c[2]-35*beta*k^3*s*A[1]^3*c[2]-285*beta*k^3*s*A[1]^2*A[2]*c[2]+75*beta*k^3*s*A[1]^2*B[1]*c[2]+75*beta*k^3*s*A[1]^2*B[2]*c[2]-525*beta*k^3*s*A[1]*A[2]^2*c[2]+30*beta*k^3*s*A[1]*A[2]*B[1]*c[2]+30*beta*k^3*s*A[1]*A[2]*B[2]*c[2]+15*beta*k^3*s*A[1]*B[1]^2*c[2]+30*beta*k^3*s*A[1]*B[1]*B[2]*c[2]+15*beta*k^3*s*A[1]*B[2]^2*c[2]-275*beta*k^3*s*A[2]^3*c[2]-105*beta*k^3*s*A[2]^2*B[1]*c[2]-105*beta*k^3*s*A[2]^2*B[2]*c[2]+75*beta*k^3*s*A[2]*B[1]^2*c[2]+150*beta*k^3*s*A[2]*B[1]*B[2]*c[2]+75*beta*k^3*s*A[2]*B[2]^2*c[2]-95*beta*k^3*s*B[1]^3*c[2]-285*beta*k^3*s*B[1]^2*B[2]*c[2]-285*beta*k^3*s*B[1]*B[2]^2*c[2]-95*beta*k^3*s*B[2]^3*c[2]-15*beta*k^4*s*w*A[0]-15*beta*k^4*s*w*A[1]-3*beta*k^4*s*w*A[2]-3*beta*k^4*s*w*B[1]-3*beta*k^4*s*w*B[2]-25*k^3*w*A[0]^3*c[2]-75*k^3*w*A[0]^2*A[1]*c[2]-15*k^3*w*A[0]^2*A[2]*c[2]-15*k^3*w*A[0]^2*B[1]*c[2]-15*k^3*w*A[0]^2*B[2]*c[2]-15*k^3*w*A[0]*A[1]^2*c[2]+210*k^3*w*A[0]*A[1]*A[2]*c[2]-150*k^3*w*A[0]*A[1]*B[1]*c[2]-150*k^3*w*A[0]*A[1]*B[2]*c[2]+285*k^3*w*A[0]*A[2]^2*c[2]-150*k^3*w*A[0]*A[2]*B[1]*c[2]-150*k^3*w*A[0]*A[2]*B[2]*c[2]+105*k^3*w*A[0]*B[1]^2*c[2]+210*k^3*w*A[0]*B[1]*B[2]*c[2]+105*k^3*w*A[0]*B[2]^2*c[2]+35*k^3*w*A[1]^3*c[2]+285*k^3*w*A[1]^2*A[2]*c[2]-75*k^3*w*A[1]^2*B[1]*c[2]-75*k^3*w*A[1]^2*B[2]*c[2]+525*k^3*w*A[1]*A[2]^2*c[2]-30*k^3*w*A[1]*A[2]*B[1]*c[2]-30*k^3*w*A[1]*A[2]*B[2]*c[2]-15*k^3*w*A[1]*B[1]^2*c[2]-30*k^3*w*A[1]*B[1]*B[2]*c[2]-15*k^3*w*A[1]*B[2]^2*c[2]+275*k^3*w*A[2]^3*c[2]+105*k^3*w*A[2]^2*B[1]*c[2]+105*k^3*w*A[2]^2*B[2]*c[2]-75*k^3*w*A[2]*B[1]^2*c[2]-150*k^3*w*A[2]*B[1]*B[2]*c[2]-75*k^3*w*A[2]*B[2]^2*c[2]+95*k^3*w*B[1]^3*c[2]+285*k^3*w*B[1]^2*B[2]*c[2]+285*k^3*w*B[1]*B[2]^2*c[2]+95*k^3*w*B[2]^3*c[2]+120*beta^2*k^2*s^2*A[1]+560*beta^2*k^2*s^2*A[2]+200*beta^2*k^2*s^2*B[1]+200*beta^2*k^2*s^2*B[2]-10*k^4*s^2*A[0]-10*k^4*s^2*A[1]-2*k^4*s^2*A[2]-2*k^4*s^2*B[1]-2*k^4*s^2*B[2]+25*k^4*w^2*A[0]+25*k^4*w^2*A[1]+5*k^4*w^2*A[2]+5*k^4*w^2*B[1]+5*k^4*w^2*B[2]-240*beta*k^2*s*w*A[1]-1120*beta*k^2*s*w*A[2]-400*beta*k^2*s*w*B[1]-400*beta*k^2*s*w*B[2]+120*k^2*s^2*A[1]+560*k^2*s^2*A[2]+200*k^2*s^2*B[1]+200*k^2*s^2*B[2]-2400*beta*s*w*A[1]-9920*beta*s*w*A[2]-2720*beta*s*w*B[1]-2720*beta*s*w*B[2]+2400*s^2*A[1]+9920*s^2*A[2]+2720*s^2*B[1]+2720*s^2*B[2]), 0 = (beta*s-w)*(-25*beta*k^3*s*A[0]^3*c[2]+75*beta*k^3*s*A[0]^2*A[1]*c[2]+165*beta*k^3*s*A[0]^2*A[2]*c[2]-165*beta*k^3*s*A[0]^2*B[1]*c[2]-165*beta*k^3*s*A[0]^2*B[2]*c[2]+165*beta*k^3*s*A[0]*A[1]^2*c[2]+150*beta*k^3*s*A[0]*A[1]*A[2]*c[2]-150*beta*k^3*s*A[0]*A[1]*B[1]*c[2]-150*beta*k^3*s*A[0]*A[1]*B[2]*c[2]-315*beta*k^3*s*A[0]*A[2]^2*c[2]+150*beta*k^3*s*A[0]*A[2]*B[1]*c[2]+150*beta*k^3*s*A[0]*A[2]*B[2]*c[2]-75*beta*k^3*s*A[0]*B[1]^2*c[2]-150*beta*k^3*s*A[0]*B[1]*B[2]*c[2]-75*beta*k^3*s*A[0]*B[2]^2*c[2]+25*beta*k^3*s*A[1]^3*c[2]-315*beta*k^3*s*A[1]^2*A[2]*c[2]+75*beta*k^3*s*A[1]^2*B[1]*c[2]+75*beta*k^3*s*A[1]^2*B[2]*c[2]-1125*beta*k^3*s*A[1]*A[2]^2*c[2]+330*beta*k^3*s*A[1]*A[2]*B[1]*c[2]+330*beta*k^3*s*A[1]*A[2]*B[2]*c[2]-165*beta*k^3*s*A[1]*B[1]^2*c[2]-330*beta*k^3*s*A[1]*B[1]*B[2]*c[2]-165*beta*k^3*s*A[1]*B[2]^2*c[2]-825*beta*k^3*s*A[2]^3*c[2]+75*beta*k^3*s*A[2]^2*B[1]*c[2]+75*beta*k^3*s*A[2]^2*B[2]*c[2]-75*beta*k^3*s*A[2]*B[1]^2*c[2]-150*beta*k^3*s*A[2]*B[1]*B[2]*c[2]-75*beta*k^3*s*A[2]*B[2]^2*c[2]+105*beta*k^3*s*B[1]^3*c[2]+315*beta*k^3*s*B[1]^2*B[2]*c[2]+315*beta*k^3*s*B[1]*B[2]^2*c[2]+105*beta*k^3*s*B[2]^3*c[2]+15*beta*k^4*s*w*A[0]-15*beta*k^4*s*w*A[1]-33*beta*k^4*s*w*A[2]+33*beta*k^4*s*w*B[1]+33*beta*k^4*s*w*B[2]+25*k^3*w*A[0]^3*c[2]-75*k^3*w*A[0]^2*A[1]*c[2]-165*k^3*w*A[0]^2*A[2]*c[2]+165*k^3*w*A[0]^2*B[1]*c[2]+165*k^3*w*A[0]^2*B[2]*c[2]-165*k^3*w*A[0]*A[1]^2*c[2]-150*k^3*w*A[0]*A[1]*A[2]*c[2]+150*k^3*w*A[0]*A[1]*B[1]*c[2]+150*k^3*w*A[0]*A[1]*B[2]*c[2]+315*k^3*w*A[0]*A[2]^2*c[2]-150*k^3*w*A[0]*A[2]*B[1]*c[2]-150*k^3*w*A[0]*A[2]*B[2]*c[2]+75*k^3*w*A[0]*B[1]^2*c[2]+150*k^3*w*A[0]*B[1]*B[2]*c[2]+75*k^3*w*A[0]*B[2]^2*c[2]-25*k^3*w*A[1]^3*c[2]+315*k^3*w*A[1]^2*A[2]*c[2]-75*k^3*w*A[1]^2*B[1]*c[2]-75*k^3*w*A[1]^2*B[2]*c[2]+1125*k^3*w*A[1]*A[2]^2*c[2]-330*k^3*w*A[1]*A[2]*B[1]*c[2]-330*k^3*w*A[1]*A[2]*B[2]*c[2]+165*k^3*w*A[1]*B[1]^2*c[2]+330*k^3*w*A[1]*B[1]*B[2]*c[2]+165*k^3*w*A[1]*B[2]^2*c[2]+825*k^3*w*A[2]^3*c[2]-75*k^3*w*A[2]^2*B[1]*c[2]-75*k^3*w*A[2]^2*B[2]*c[2]+75*k^3*w*A[2]*B[1]^2*c[2]+150*k^3*w*A[2]*B[1]*B[2]*c[2]+75*k^3*w*A[2]*B[2]^2*c[2]-105*k^3*w*B[1]^3*c[2]-315*k^3*w*B[1]^2*B[2]*c[2]-315*k^3*w*B[1]*B[2]^2*c[2]-105*k^3*w*B[2]^3*c[2]+1120*beta^2*k^2*s^2*A[2]-320*beta^2*k^2*s^2*B[1]-320*beta^2*k^2*s^2*B[2]+10*k^4*s^2*A[0]-10*k^4*s^2*A[1]-22*k^4*s^2*A[2]+22*k^4*s^2*B[1]+22*k^4*s^2*B[2]-25*k^4*w^2*A[0]+25*k^4*w^2*A[1]+55*k^4*w^2*A[2]-55*k^4*w^2*B[1]-55*k^4*w^2*B[2]-2240*beta*k^2*s*w*A[2]+640*beta*k^2*s*w*B[1]+640*beta*k^2*s*w*B[2]+1120*k^2*s^2*A[2]-320*k^2*s^2*B[1]-320*k^2*s^2*B[2]-9600*beta*s*w*A[1]-65920*beta*s*w*A[2]+14720*beta*s*w*B[1]+14720*beta*s*w*B[2]+9600*s^2*A[1]+65920*s^2*A[2]-14720*s^2*B[1]-14720*s^2*B[2]), 0 = (beta*s-w)*(25*beta*k^3*s*A[0]^3*c[2]+75*beta*k^3*s*A[0]^2*A[1]*c[2]-45*beta*k^3*s*A[0]^2*A[2]*c[2]-45*beta*k^3*s*A[0]^2*B[1]*c[2]-45*beta*k^3*s*A[0]^2*B[2]*c[2]-45*beta*k^3*s*A[0]*A[1]^2*c[2]-330*beta*k^3*s*A[0]*A[1]*A[2]*c[2]+150*beta*k^3*s*A[0]*A[1]*B[1]*c[2]+150*beta*k^3*s*A[0]*A[1]*B[2]*c[2]-45*beta*k^3*s*A[0]*A[2]^2*c[2]+150*beta*k^3*s*A[0]*A[2]*B[1]*c[2]+150*beta*k^3*s*A[0]*A[2]*B[2]*c[2]-165*beta*k^3*s*A[0]*B[1]^2*c[2]-330*beta*k^3*s*A[0]*B[1]*B[2]*c[2]-165*beta*k^3*s*A[0]*B[2]^2*c[2]-55*beta*k^3*s*A[1]^3*c[2]-45*beta*k^3*s*A[1]^2*A[2]*c[2]+75*beta*k^3*s*A[1]^2*B[1]*c[2]+75*beta*k^3*s*A[1]^2*B[2]*c[2]+675*beta*k^3*s*A[1]*A[2]^2*c[2]-90*beta*k^3*s*A[1]*A[2]*B[1]*c[2]-90*beta*k^3*s*A[1]*A[2]*B[2]*c[2]-45*beta*k^3*s*A[1]*B[1]^2*c[2]-90*beta*k^3*s*A[1]*B[1]*B[2]*c[2]-45*beta*k^3*s*A[1]*B[2]^2*c[2]+825*beta*k^3*s*A[2]^3*c[2]-165*beta*k^3*s*A[2]^2*B[1]*c[2]-165*beta*k^3*s*A[2]^2*B[2]*c[2]+75*beta*k^3*s*A[2]*B[1]^2*c[2]+150*beta*k^3*s*A[2]*B[1]*B[2]*c[2]+75*beta*k^3*s*A[2]*B[2]^2*c[2]-15*beta*k^3*s*B[1]^3*c[2]-45*beta*k^3*s*B[1]^2*B[2]*c[2]-45*beta*k^3*s*B[1]*B[2]^2*c[2]-15*beta*k^3*s*B[2]^3*c[2]-15*beta*k^4*s*w*A[0]-15*beta*k^4*s*w*A[1]+9*beta*k^4*s*w*A[2]+9*beta*k^4*s*w*B[1]+9*beta*k^4*s*w*B[2]-25*k^3*w*A[0]^3*c[2]-75*k^3*w*A[0]^2*A[1]*c[2]+45*k^3*w*A[0]^2*A[2]*c[2]+45*k^3*w*A[0]^2*B[1]*c[2]+45*k^3*w*A[0]^2*B[2]*c[2]+45*k^3*w*A[0]*A[1]^2*c[2]+330*k^3*w*A[0]*A[1]*A[2]*c[2]-150*k^3*w*A[0]*A[1]*B[1]*c[2]-150*k^3*w*A[0]*A[1]*B[2]*c[2]+45*k^3*w*A[0]*A[2]^2*c[2]-150*k^3*w*A[0]*A[2]*B[1]*c[2]-150*k^3*w*A[0]*A[2]*B[2]*c[2]+165*k^3*w*A[0]*B[1]^2*c[2]+330*k^3*w*A[0]*B[1]*B[2]*c[2]+165*k^3*w*A[0]*B[2]^2*c[2]+55*k^3*w*A[1]^3*c[2]+45*k^3*w*A[1]^2*A[2]*c[2]-75*k^3*w*A[1]^2*B[1]*c[2]-75*k^3*w*A[1]^2*B[2]*c[2]-675*k^3*w*A[1]*A[2]^2*c[2]+90*k^3*w*A[1]*A[2]*B[1]*c[2]+90*k^3*w*A[1]*A[2]*B[2]*c[2]+45*k^3*w*A[1]*B[1]^2*c[2]+90*k^3*w*A[1]*B[1]*B[2]*c[2]+45*k^3*w*A[1]*B[2]^2*c[2]-825*k^3*w*A[2]^3*c[2]+165*k^3*w*A[2]^2*B[1]*c[2]+165*k^3*w*A[2]^2*B[2]*c[2]-75*k^3*w*A[2]*B[1]^2*c[2]-150*k^3*w*A[2]*B[1]*B[2]*c[2]-75*k^3*w*A[2]*B[2]^2*c[2]+15*k^3*w*B[1]^3*c[2]+45*k^3*w*B[1]^2*B[2]*c[2]+45*k^3*w*B[1]*B[2]^2*c[2]+15*k^3*w*B[2]^3*c[2]+160*beta^2*k^2*s^2*A[1]-80*beta^2*k^2*s^2*A[2]-10*k^4*s^2*A[0]-10*k^4*s^2*A[1]+6*k^4*s^2*A[2]+6*k^4*s^2*B[1]+6*k^4*s^2*B[2]+25*k^4*w^2*A[0]+25*k^4*w^2*A[1]-15*k^4*w^2*A[2]-15*k^4*w^2*B[1]-15*k^4*w^2*B[2]-320*beta*k^2*s*w*A[1]+160*beta*k^2*s*w*A[2]+160*k^2*s^2*A[1]-80*k^2*s^2*A[2]+8000*beta*s*w*A[1]+100160*beta*s*w*A[2]+20160*beta*s*w*B[1]+20160*beta*s*w*B[2]-8000*s^2*A[1]-100160*s^2*A[2]-20160*s^2*B[1]-20160*s^2*B[2]), 0 = (beta*s-w)*(-25*beta*k^3*s*A[0]^3*c[2]+75*beta*k^3*s*A[0]^2*A[1]*c[2]+105*beta*k^3*s*A[0]^2*A[2]*c[2]-105*beta*k^3*s*A[0]^2*B[1]*c[2]-105*beta*k^3*s*A[0]^2*B[2]*c[2]+105*beta*k^3*s*A[0]*A[1]^2*c[2]-210*beta*k^3*s*A[0]*A[1]*A[2]*c[2]-150*beta*k^3*s*A[0]*A[1]*B[1]*c[2]-150*beta*k^3*s*A[0]*A[1]*B[2]*c[2]-315*beta*k^3*s*A[0]*A[2]^2*c[2]+150*beta*k^3*s*A[0]*A[2]*B[1]*c[2]+150*beta*k^3*s*A[0]*A[2]*B[2]*c[2]+105*beta*k^3*s*A[0]*B[1]^2*c[2]+210*beta*k^3*s*A[0]*B[1]*B[2]*c[2]+105*beta*k^3*s*A[0]*B[2]^2*c[2]-35*beta*k^3*s*A[1]^3*c[2]-315*beta*k^3*s*A[1]^2*A[2]*c[2]+75*beta*k^3*s*A[1]^2*B[1]*c[2]+75*beta*k^3*s*A[1]^2*B[2]*c[2]+315*beta*k^3*s*A[1]*A[2]^2*c[2]+210*beta*k^3*s*A[1]*A[2]*B[1]*c[2]+210*beta*k^3*s*A[1]*A[2]*B[2]*c[2]-105*beta*k^3*s*A[1]*B[1]^2*c[2]-210*beta*k^3*s*A[1]*B[1]*B[2]*c[2]-105*beta*k^3*s*A[1]*B[2]^2*c[2]+1155*beta*k^3*s*A[2]^3*c[2]-105*beta*k^3*s*A[2]^2*B[1]*c[2]-105*beta*k^3*s*A[2]^2*B[2]*c[2]-75*beta*k^3*s*A[2]*B[1]^2*c[2]-150*beta*k^3*s*A[2]*B[1]*B[2]*c[2]-75*beta*k^3*s*A[2]*B[2]^2*c[2]+105*beta*k^3*s*B[1]^3*c[2]+315*beta*k^3*s*B[1]^2*B[2]*c[2]+315*beta*k^3*s*B[1]*B[2]^2*c[2]+105*beta*k^3*s*B[2]^3*c[2]+15*beta*k^4*s*w*A[0]-15*beta*k^4*s*w*A[1]-21*beta*k^4*s*w*A[2]+21*beta*k^4*s*w*B[1]+21*beta*k^4*s*w*B[2]+25*k^3*w*A[0]^3*c[2]-75*k^3*w*A[0]^2*A[1]*c[2]-105*k^3*w*A[0]^2*A[2]*c[2]+105*k^3*w*A[0]^2*B[1]*c[2]+105*k^3*w*A[0]^2*B[2]*c[2]-105*k^3*w*A[0]*A[1]^2*c[2]+210*k^3*w*A[0]*A[1]*A[2]*c[2]+150*k^3*w*A[0]*A[1]*B[1]*c[2]+150*k^3*w*A[0]*A[1]*B[2]*c[2]+315*k^3*w*A[0]*A[2]^2*c[2]-150*k^3*w*A[0]*A[2]*B[1]*c[2]-150*k^3*w*A[0]*A[2]*B[2]*c[2]-105*k^3*w*A[0]*B[1]^2*c[2]-210*k^3*w*A[0]*B[1]*B[2]*c[2]-105*k^3*w*A[0]*B[2]^2*c[2]+35*k^3*w*A[1]^3*c[2]+315*k^3*w*A[1]^2*A[2]*c[2]-75*k^3*w*A[1]^2*B[1]*c[2]-75*k^3*w*A[1]^2*B[2]*c[2]-315*k^3*w*A[1]*A[2]^2*c[2]-210*k^3*w*A[1]*A[2]*B[1]*c[2]-210*k^3*w*A[1]*A[2]*B[2]*c[2]+105*k^3*w*A[1]*B[1]^2*c[2]+210*k^3*w*A[1]*B[1]*B[2]*c[2]+105*k^3*w*A[1]*B[2]^2*c[2]-1155*k^3*w*A[2]^3*c[2]+105*k^3*w*A[2]^2*B[1]*c[2]+105*k^3*w*A[2]^2*B[2]*c[2]+75*k^3*w*A[2]*B[1]^2*c[2]+150*k^3*w*A[2]*B[1]*B[2]*c[2]+75*k^3*w*A[2]*B[2]^2*c[2]-105*k^3*w*B[1]^3*c[2]-315*k^3*w*B[1]^2*B[2]*c[2]-315*k^3*w*B[1]*B[2]^2*c[2]-105*k^3*w*B[2]^3*c[2]+120*beta^2*k^2*s^2*A[1]+960*beta^2*k^2*s^2*A[2]-280*beta^2*k^2*s^2*B[1]-280*beta^2*k^2*s^2*B[2]+10*k^4*s^2*A[0]-10*k^4*s^2*A[1]-14*k^4*s^2*A[2]+14*k^4*s^2*B[1]+14*k^4*s^2*B[2]-25*k^4*w^2*A[0]+25*k^4*w^2*A[1]+35*k^4*w^2*A[2]-35*k^4*w^2*B[1]-35*k^4*w^2*B[2]-240*beta*k^2*s*w*A[1]-1920*beta*k^2*s*w*A[2]+560*beta*k^2*s*w*B[1]+560*beta*k^2*s*w*B[2]+120*k^2*s^2*A[1]+960*k^2*s^2*A[2]-280*k^2*s^2*B[1]-280*k^2*s^2*B[2]+4320*beta*s*w*A[1]+168960*beta*s*w*A[2]-32480*beta*s*w*B[1]-32480*beta*s*w*B[2]-4320*s^2*A[1]-168960*s^2*A[2]+32480*s^2*B[1]+32480*s^2*B[2]), 0 = (beta*s-w)*(25*beta*k^3*s*A[0]^3*c[2]+75*beta*k^3*s*A[0]^2*A[1]*c[2]-105*beta*k^3*s*A[0]^2*A[2]*c[2]-105*beta*k^3*s*A[0]^2*B[1]*c[2]-105*beta*k^3*s*A[0]^2*B[2]*c[2]-105*beta*k^3*s*A[0]*A[1]^2*c[2]-210*beta*k^3*s*A[0]*A[1]*A[2]*c[2]+150*beta*k^3*s*A[0]*A[1]*B[1]*c[2]+150*beta*k^3*s*A[0]*A[1]*B[2]*c[2]+315*beta*k^3*s*A[0]*A[2]^2*c[2]+150*beta*k^3*s*A[0]*A[2]*B[1]*c[2]+150*beta*k^3*s*A[0]*A[2]*B[2]*c[2]-105*beta*k^3*s*A[0]*B[1]^2*c[2]-210*beta*k^3*s*A[0]*B[1]*B[2]*c[2]-105*beta*k^3*s*A[0]*B[2]^2*c[2]-35*beta*k^3*s*A[1]^3*c[2]+315*beta*k^3*s*A[1]^2*A[2]*c[2]+75*beta*k^3*s*A[1]^2*B[1]*c[2]+75*beta*k^3*s*A[1]^2*B[2]*c[2]+315*beta*k^3*s*A[1]*A[2]^2*c[2]-210*beta*k^3*s*A[1]*A[2]*B[1]*c[2]-210*beta*k^3*s*A[1]*A[2]*B[2]*c[2]-105*beta*k^3*s*A[1]*B[1]^2*c[2]-210*beta*k^3*s*A[1]*B[1]*B[2]*c[2]-105*beta*k^3*s*A[1]*B[2]^2*c[2]-1155*beta*k^3*s*A[2]^3*c[2]-105*beta*k^3*s*A[2]^2*B[1]*c[2]-105*beta*k^3*s*A[2]^2*B[2]*c[2]+75*beta*k^3*s*A[2]*B[1]^2*c[2]+150*beta*k^3*s*A[2]*B[1]*B[2]*c[2]+75*beta*k^3*s*A[2]*B[2]^2*c[2]+105*beta*k^3*s*B[1]^3*c[2]+315*beta*k^3*s*B[1]^2*B[2]*c[2]+315*beta*k^3*s*B[1]*B[2]^2*c[2]+105*beta*k^3*s*B[2]^3*c[2]-15*beta*k^4*s*w*A[0]-15*beta*k^4*s*w*A[1]+21*beta*k^4*s*w*A[2]+21*beta*k^4*s*w*B[1]+21*beta*k^4*s*w*B[2]-25*k^3*w*A[0]^3*c[2]-75*k^3*w*A[0]^2*A[1]*c[2]+105*k^3*w*A[0]^2*A[2]*c[2]+105*k^3*w*A[0]^2*B[1]*c[2]+105*k^3*w*A[0]^2*B[2]*c[2]+105*k^3*w*A[0]*A[1]^2*c[2]+210*k^3*w*A[0]*A[1]*A[2]*c[2]-150*k^3*w*A[0]*A[1]*B[1]*c[2]-150*k^3*w*A[0]*A[1]*B[2]*c[2]-315*k^3*w*A[0]*A[2]^2*c[2]-150*k^3*w*A[0]*A[2]*B[1]*c[2]-150*k^3*w*A[0]*A[2]*B[2]*c[2]+105*k^3*w*A[0]*B[1]^2*c[2]+210*k^3*w*A[0]*B[1]*B[2]*c[2]+105*k^3*w*A[0]*B[2]^2*c[2]+35*k^3*w*A[1]^3*c[2]-315*k^3*w*A[1]^2*A[2]*c[2]-75*k^3*w*A[1]^2*B[1]*c[2]-75*k^3*w*A[1]^2*B[2]*c[2]-315*k^3*w*A[1]*A[2]^2*c[2]+210*k^3*w*A[1]*A[2]*B[1]*c[2]+210*k^3*w*A[1]*A[2]*B[2]*c[2]+105*k^3*w*A[1]*B[1]^2*c[2]+210*k^3*w*A[1]*B[1]*B[2]*c[2]+105*k^3*w*A[1]*B[2]^2*c[2]+1155*k^3*w*A[2]^3*c[2]+105*k^3*w*A[2]^2*B[1]*c[2]+105*k^3*w*A[2]^2*B[2]*c[2]-75*k^3*w*A[2]*B[1]^2*c[2]-150*k^3*w*A[2]*B[1]*B[2]*c[2]-75*k^3*w*A[2]*B[2]^2*c[2]-105*k^3*w*B[1]^3*c[2]-315*k^3*w*B[1]^2*B[2]*c[2]-315*k^3*w*B[1]*B[2]^2*c[2]-105*k^3*w*B[2]^3*c[2]+120*beta^2*k^2*s^2*A[1]-960*beta^2*k^2*s^2*A[2]-280*beta^2*k^2*s^2*B[1]-280*beta^2*k^2*s^2*B[2]-10*k^4*s^2*A[0]-10*k^4*s^2*A[1]+14*k^4*s^2*A[2]+14*k^4*s^2*B[1]+14*k^4*s^2*B[2]+25*k^4*w^2*A[0]+25*k^4*w^2*A[1]-35*k^4*w^2*A[2]-35*k^4*w^2*B[1]-35*k^4*w^2*B[2]-240*beta*k^2*s*w*A[1]+1920*beta*k^2*s*w*A[2]+560*beta*k^2*s*w*B[1]+560*beta*k^2*s*w*B[2]+120*k^2*s^2*A[1]-960*k^2*s^2*A[2]-280*k^2*s^2*B[1]-280*k^2*s^2*B[2]+4320*beta*s*w*A[1]-168960*beta*s*w*A[2]-32480*beta*s*w*B[1]-32480*beta*s*w*B[2]-4320*s^2*A[1]+168960*s^2*A[2]+32480*s^2*B[1]+32480*s^2*B[2]), 0 = (beta*s-w)*(-25*beta*k^3*s*A[0]^3*c[2]+75*beta*k^3*s*A[0]^2*A[1]*c[2]+45*beta*k^3*s*A[0]^2*A[2]*c[2]-45*beta*k^3*s*A[0]^2*B[1]*c[2]-45*beta*k^3*s*A[0]^2*B[2]*c[2]+45*beta*k^3*s*A[0]*A[1]^2*c[2]-330*beta*k^3*s*A[0]*A[1]*A[2]*c[2]-150*beta*k^3*s*A[0]*A[1]*B[1]*c[2]-150*beta*k^3*s*A[0]*A[1]*B[2]*c[2]+45*beta*k^3*s*A[0]*A[2]^2*c[2]+150*beta*k^3*s*A[0]*A[2]*B[1]*c[2]+150*beta*k^3*s*A[0]*A[2]*B[2]*c[2]+165*beta*k^3*s*A[0]*B[1]^2*c[2]+330*beta*k^3*s*A[0]*B[1]*B[2]*c[2]+165*beta*k^3*s*A[0]*B[2]^2*c[2]-55*beta*k^3*s*A[1]^3*c[2]+45*beta*k^3*s*A[1]^2*A[2]*c[2]+75*beta*k^3*s*A[1]^2*B[1]*c[2]+75*beta*k^3*s*A[1]^2*B[2]*c[2]+675*beta*k^3*s*A[1]*A[2]^2*c[2]+90*beta*k^3*s*A[1]*A[2]*B[1]*c[2]+90*beta*k^3*s*A[1]*A[2]*B[2]*c[2]-45*beta*k^3*s*A[1]*B[1]^2*c[2]-90*beta*k^3*s*A[1]*B[1]*B[2]*c[2]-45*beta*k^3*s*A[1]*B[2]^2*c[2]-825*beta*k^3*s*A[2]^3*c[2]-165*beta*k^3*s*A[2]^2*B[1]*c[2]-165*beta*k^3*s*A[2]^2*B[2]*c[2]-75*beta*k^3*s*A[2]*B[1]^2*c[2]-150*beta*k^3*s*A[2]*B[1]*B[2]*c[2]-75*beta*k^3*s*A[2]*B[2]^2*c[2]-15*beta*k^3*s*B[1]^3*c[2]-45*beta*k^3*s*B[1]^2*B[2]*c[2]-45*beta*k^3*s*B[1]*B[2]^2*c[2]-15*beta*k^3*s*B[2]^3*c[2]+15*beta*k^4*s*w*A[0]-15*beta*k^4*s*w*A[1]-9*beta*k^4*s*w*A[2]+9*beta*k^4*s*w*B[1]+9*beta*k^4*s*w*B[2]+25*k^3*w*A[0]^3*c[2]-75*k^3*w*A[0]^2*A[1]*c[2]-45*k^3*w*A[0]^2*A[2]*c[2]+45*k^3*w*A[0]^2*B[1]*c[2]+45*k^3*w*A[0]^2*B[2]*c[2]-45*k^3*w*A[0]*A[1]^2*c[2]+330*k^3*w*A[0]*A[1]*A[2]*c[2]+150*k^3*w*A[0]*A[1]*B[1]*c[2]+150*k^3*w*A[0]*A[1]*B[2]*c[2]-45*k^3*w*A[0]*A[2]^2*c[2]-150*k^3*w*A[0]*A[2]*B[1]*c[2]-150*k^3*w*A[0]*A[2]*B[2]*c[2]-165*k^3*w*A[0]*B[1]^2*c[2]-330*k^3*w*A[0]*B[1]*B[2]*c[2]-165*k^3*w*A[0]*B[2]^2*c[2]+55*k^3*w*A[1]^3*c[2]-45*k^3*w*A[1]^2*A[2]*c[2]-75*k^3*w*A[1]^2*B[1]*c[2]-75*k^3*w*A[1]^2*B[2]*c[2]-675*k^3*w*A[1]*A[2]^2*c[2]-90*k^3*w*A[1]*A[2]*B[1]*c[2]-90*k^3*w*A[1]*A[2]*B[2]*c[2]+45*k^3*w*A[1]*B[1]^2*c[2]+90*k^3*w*A[1]*B[1]*B[2]*c[2]+45*k^3*w*A[1]*B[2]^2*c[2]+825*k^3*w*A[2]^3*c[2]+165*k^3*w*A[2]^2*B[1]*c[2]+165*k^3*w*A[2]^2*B[2]*c[2]+75*k^3*w*A[2]*B[1]^2*c[2]+150*k^3*w*A[2]*B[1]*B[2]*c[2]+75*k^3*w*A[2]*B[2]^2*c[2]+15*k^3*w*B[1]^3*c[2]+45*k^3*w*B[1]^2*B[2]*c[2]+45*k^3*w*B[1]*B[2]^2*c[2]+15*k^3*w*B[2]^3*c[2]+160*beta^2*k^2*s^2*A[1]+80*beta^2*k^2*s^2*A[2]+10*k^4*s^2*A[0]-10*k^4*s^2*A[1]-6*k^4*s^2*A[2]+6*k^4*s^2*B[1]+6*k^4*s^2*B[2]-25*k^4*w^2*A[0]+25*k^4*w^2*A[1]+15*k^4*w^2*A[2]-15*k^4*w^2*B[1]-15*k^4*w^2*B[2]-320*beta*k^2*s*w*A[1]-160*beta*k^2*s*w*A[2]+160*k^2*s^2*A[1]+80*k^2*s^2*A[2]+8000*beta*s*w*A[1]-100160*beta*s*w*A[2]+20160*beta*s*w*B[1]+20160*beta*s*w*B[2]-8000*s^2*A[1]+100160*s^2*A[2]-20160*s^2*B[1]-20160*s^2*B[2]), 0 = (beta*s-w)*(-25*beta*k^3*s*A[0]^3*c[2]-75*beta*k^3*s*A[0]^2*A[1]*c[2]+165*beta*k^3*s*A[0]^2*A[2]*c[2]+165*beta*k^3*s*A[0]^2*B[1]*c[2]+165*beta*k^3*s*A[0]^2*B[2]*c[2]+165*beta*k^3*s*A[0]*A[1]^2*c[2]-150*beta*k^3*s*A[0]*A[1]*A[2]*c[2]-150*beta*k^3*s*A[0]*A[1]*B[1]*c[2]-150*beta*k^3*s*A[0]*A[1]*B[2]*c[2]-315*beta*k^3*s*A[0]*A[2]^2*c[2]-150*beta*k^3*s*A[0]*A[2]*B[1]*c[2]-150*beta*k^3*s*A[0]*A[2]*B[2]*c[2]-75*beta*k^3*s*A[0]*B[1]^2*c[2]-150*beta*k^3*s*A[0]*B[1]*B[2]*c[2]-75*beta*k^3*s*A[0]*B[2]^2*c[2]-25*beta*k^3*s*A[1]^3*c[2]-315*beta*k^3*s*A[1]^2*A[2]*c[2]-75*beta*k^3*s*A[1]^2*B[1]*c[2]-75*beta*k^3*s*A[1]^2*B[2]*c[2]+1125*beta*k^3*s*A[1]*A[2]^2*c[2]+330*beta*k^3*s*A[1]*A[2]*B[1]*c[2]+330*beta*k^3*s*A[1]*A[2]*B[2]*c[2]+165*beta*k^3*s*A[1]*B[1]^2*c[2]+330*beta*k^3*s*A[1]*B[1]*B[2]*c[2]+165*beta*k^3*s*A[1]*B[2]^2*c[2]-825*beta*k^3*s*A[2]^3*c[2]-75*beta*k^3*s*A[2]^2*B[1]*c[2]-75*beta*k^3*s*A[2]^2*B[2]*c[2]-75*beta*k^3*s*A[2]*B[1]^2*c[2]-150*beta*k^3*s*A[2]*B[1]*B[2]*c[2]-75*beta*k^3*s*A[2]*B[2]^2*c[2]-105*beta*k^3*s*B[1]^3*c[2]-315*beta*k^3*s*B[1]^2*B[2]*c[2]-315*beta*k^3*s*B[1]*B[2]^2*c[2]-105*beta*k^3*s*B[2]^3*c[2]+15*beta*k^4*s*w*A[0]+15*beta*k^4*s*w*A[1]-33*beta*k^4*s*w*A[2]-33*beta*k^4*s*w*B[1]-33*beta*k^4*s*w*B[2]+25*k^3*w*A[0]^3*c[2]+75*k^3*w*A[0]^2*A[1]*c[2]-165*k^3*w*A[0]^2*A[2]*c[2]-165*k^3*w*A[0]^2*B[1]*c[2]-165*k^3*w*A[0]^2*B[2]*c[2]-165*k^3*w*A[0]*A[1]^2*c[2]+150*k^3*w*A[0]*A[1]*A[2]*c[2]+150*k^3*w*A[0]*A[1]*B[1]*c[2]+150*k^3*w*A[0]*A[1]*B[2]*c[2]+315*k^3*w*A[0]*A[2]^2*c[2]+150*k^3*w*A[0]*A[2]*B[1]*c[2]+150*k^3*w*A[0]*A[2]*B[2]*c[2]+75*k^3*w*A[0]*B[1]^2*c[2]+150*k^3*w*A[0]*B[1]*B[2]*c[2]+75*k^3*w*A[0]*B[2]^2*c[2]+25*k^3*w*A[1]^3*c[2]+315*k^3*w*A[1]^2*A[2]*c[2]+75*k^3*w*A[1]^2*B[1]*c[2]+75*k^3*w*A[1]^2*B[2]*c[2]-1125*k^3*w*A[1]*A[2]^2*c[2]-330*k^3*w*A[1]*A[2]*B[1]*c[2]-330*k^3*w*A[1]*A[2]*B[2]*c[2]-165*k^3*w*A[1]*B[1]^2*c[2]-330*k^3*w*A[1]*B[1]*B[2]*c[2]-165*k^3*w*A[1]*B[2]^2*c[2]+825*k^3*w*A[2]^3*c[2]+75*k^3*w*A[2]^2*B[1]*c[2]+75*k^3*w*A[2]^2*B[2]*c[2]+75*k^3*w*A[2]*B[1]^2*c[2]+150*k^3*w*A[2]*B[1]*B[2]*c[2]+75*k^3*w*A[2]*B[2]^2*c[2]+105*k^3*w*B[1]^3*c[2]+315*k^3*w*B[1]^2*B[2]*c[2]+315*k^3*w*B[1]*B[2]^2*c[2]+105*k^3*w*B[2]^3*c[2]+1120*beta^2*k^2*s^2*A[2]+320*beta^2*k^2*s^2*B[1]+320*beta^2*k^2*s^2*B[2]+10*k^4*s^2*A[0]+10*k^4*s^2*A[1]-22*k^4*s^2*A[2]-22*k^4*s^2*B[1]-22*k^4*s^2*B[2]-25*k^4*w^2*A[0]-25*k^4*w^2*A[1]+55*k^4*w^2*A[2]+55*k^4*w^2*B[1]+55*k^4*w^2*B[2]-2240*beta*k^2*s*w*A[2]-640*beta*k^2*s*w*B[1]-640*beta*k^2*s*w*B[2]+1120*k^2*s^2*A[2]+320*k^2*s^2*B[1]+320*k^2*s^2*B[2]+9600*beta*s*w*A[1]-65920*beta*s*w*A[2]-14720*beta*s*w*B[1]-14720*beta*s*w*B[2]-9600*s^2*A[1]+65920*s^2*A[2]+14720*s^2*B[1]+14720*s^2*B[2]), 0 = (beta*s-w)*(-25*beta*k^3*s*A[0]^3*c[2]+75*beta*k^3*s*A[0]^2*A[1]*c[2]-15*beta*k^3*s*A[0]^2*A[2]*c[2]+15*beta*k^3*s*A[0]^2*B[1]*c[2]+15*beta*k^3*s*A[0]^2*B[2]*c[2]-15*beta*k^3*s*A[0]*A[1]^2*c[2]-210*beta*k^3*s*A[0]*A[1]*A[2]*c[2]-150*beta*k^3*s*A[0]*A[1]*B[1]*c[2]-150*beta*k^3*s*A[0]*A[1]*B[2]*c[2]+285*beta*k^3*s*A[0]*A[2]^2*c[2]+150*beta*k^3*s*A[0]*A[2]*B[1]*c[2]+150*beta*k^3*s*A[0]*A[2]*B[2]*c[2]+105*beta*k^3*s*A[0]*B[1]^2*c[2]+210*beta*k^3*s*A[0]*B[1]*B[2]*c[2]+105*beta*k^3*s*A[0]*B[2]^2*c[2]-35*beta*k^3*s*A[1]^3*c[2]+285*beta*k^3*s*A[1]^2*A[2]*c[2]+75*beta*k^3*s*A[1]^2*B[1]*c[2]+75*beta*k^3*s*A[1]^2*B[2]*c[2]-525*beta*k^3*s*A[1]*A[2]^2*c[2]-30*beta*k^3*s*A[1]*A[2]*B[1]*c[2]-30*beta*k^3*s*A[1]*A[2]*B[2]*c[2]+15*beta*k^3*s*A[1]*B[1]^2*c[2]+30*beta*k^3*s*A[1]*B[1]*B[2]*c[2]+15*beta*k^3*s*A[1]*B[2]^2*c[2]+275*beta*k^3*s*A[2]^3*c[2]-105*beta*k^3*s*A[2]^2*B[1]*c[2]-105*beta*k^3*s*A[2]^2*B[2]*c[2]-75*beta*k^3*s*A[2]*B[1]^2*c[2]-150*beta*k^3*s*A[2]*B[1]*B[2]*c[2]-75*beta*k^3*s*A[2]*B[2]^2*c[2]-95*beta*k^3*s*B[1]^3*c[2]-285*beta*k^3*s*B[1]^2*B[2]*c[2]-285*beta*k^3*s*B[1]*B[2]^2*c[2]-95*beta*k^3*s*B[2]^3*c[2]+15*beta*k^4*s*w*A[0]-15*beta*k^4*s*w*A[1]+3*beta*k^4*s*w*A[2]-3*beta*k^4*s*w*B[1]-3*beta*k^4*s*w*B[2]+25*k^3*w*A[0]^3*c[2]-75*k^3*w*A[0]^2*A[1]*c[2]+15*k^3*w*A[0]^2*A[2]*c[2]-15*k^3*w*A[0]^2*B[1]*c[2]-15*k^3*w*A[0]^2*B[2]*c[2]+15*k^3*w*A[0]*A[1]^2*c[2]+210*k^3*w*A[0]*A[1]*A[2]*c[2]+150*k^3*w*A[0]*A[1]*B[1]*c[2]+150*k^3*w*A[0]*A[1]*B[2]*c[2]-285*k^3*w*A[0]*A[2]^2*c[2]-150*k^3*w*A[0]*A[2]*B[1]*c[2]-150*k^3*w*A[0]*A[2]*B[2]*c[2]-105*k^3*w*A[0]*B[1]^2*c[2]-210*k^3*w*A[0]*B[1]*B[2]*c[2]-105*k^3*w*A[0]*B[2]^2*c[2]+35*k^3*w*A[1]^3*c[2]-285*k^3*w*A[1]^2*A[2]*c[2]-75*k^3*w*A[1]^2*B[1]*c[2]-75*k^3*w*A[1]^2*B[2]*c[2]+525*k^3*w*A[1]*A[2]^2*c[2]+30*k^3*w*A[1]*A[2]*B[1]*c[2]+30*k^3*w*A[1]*A[2]*B[2]*c[2]-15*k^3*w*A[1]*B[1]^2*c[2]-30*k^3*w*A[1]*B[1]*B[2]*c[2]-15*k^3*w*A[1]*B[2]^2*c[2]-275*k^3*w*A[2]^3*c[2]+105*k^3*w*A[2]^2*B[1]*c[2]+105*k^3*w*A[2]^2*B[2]*c[2]+75*k^3*w*A[2]*B[1]^2*c[2]+150*k^3*w*A[2]*B[1]*B[2]*c[2]+75*k^3*w*A[2]*B[2]^2*c[2]+95*k^3*w*B[1]^3*c[2]+285*k^3*w*B[1]^2*B[2]*c[2]+285*k^3*w*B[1]*B[2]^2*c[2]+95*k^3*w*B[2]^3*c[2]+120*beta^2*k^2*s^2*A[1]-560*beta^2*k^2*s^2*A[2]+200*beta^2*k^2*s^2*B[1]+200*beta^2*k^2*s^2*B[2]+10*k^4*s^2*A[0]-10*k^4*s^2*A[1]+2*k^4*s^2*A[2]-2*k^4*s^2*B[1]-2*k^4*s^2*B[2]-25*k^4*w^2*A[0]+25*k^4*w^2*A[1]-5*k^4*w^2*A[2]+5*k^4*w^2*B[1]+5*k^4*w^2*B[2]-240*beta*k^2*s*w*A[1]+1120*beta*k^2*s*w*A[2]-400*beta*k^2*s*w*B[1]-400*beta*k^2*s*w*B[2]+120*k^2*s^2*A[1]-560*k^2*s^2*A[2]+200*k^2*s^2*B[1]+200*k^2*s^2*B[2]-2400*beta*s*w*A[1]+9920*beta*s*w*A[2]-2720*beta*s*w*B[1]-2720*beta*s*w*B[2]+2400*s^2*A[1]-9920*s^2*A[2]+2720*s^2*B[1]+2720*s^2*B[2]), 0 = (beta*s-w)*(-5*beta*k^3*s*A[0]^3*c[2]-15*beta*k^3*s*A[0]^2*A[1]*c[2]+45*beta*k^3*s*A[0]^2*A[2]*c[2]+45*beta*k^3*s*A[0]^2*B[1]*c[2]+45*beta*k^3*s*A[0]^2*B[2]*c[2]+45*beta*k^3*s*A[0]*A[1]^2*c[2]-150*beta*k^3*s*A[0]*A[1]*A[2]*c[2]-30*beta*k^3*s*A[0]*A[1]*B[1]*c[2]-30*beta*k^3*s*A[0]*A[1]*B[2]*c[2]+105*beta*k^3*s*A[0]*A[2]^2*c[2]-30*beta*k^3*s*A[0]*A[2]*B[1]*c[2]-30*beta*k^3*s*A[0]*A[2]*B[2]*c[2]-75*beta*k^3*s*A[0]*B[1]^2*c[2]-150*beta*k^3*s*A[0]*B[1]*B[2]*c[2]-75*beta*k^3*s*A[0]*B[2]^2*c[2]-25*beta*k^3*s*A[1]^3*c[2]+105*beta*k^3*s*A[1]^2*A[2]*c[2]-15*beta*k^3*s*A[1]^2*B[1]*c[2]-15*beta*k^3*s*A[1]^2*B[2]*c[2]-135*beta*k^3*s*A[1]*A[2]^2*c[2]+90*beta*k^3*s*A[1]*A[2]*B[1]*c[2]+90*beta*k^3*s*A[1]*A[2]*B[2]*c[2]+45*beta*k^3*s*A[1]*B[1]^2*c[2]+90*beta*k^3*s*A[1]*B[1]*B[2]*c[2]+45*beta*k^3*s*A[1]*B[2]^2*c[2]+55*beta*k^3*s*A[2]^3*c[2]-75*beta*k^3*s*A[2]^2*B[1]*c[2]-75*beta*k^3*s*A[2]^2*B[2]*c[2]-15*beta*k^3*s*A[2]*B[1]^2*c[2]-30*beta*k^3*s*A[2]*B[1]*B[2]*c[2]-15*beta*k^3*s*A[2]*B[2]^2*c[2]+35*beta*k^3*s*B[1]^3*c[2]+105*beta*k^3*s*B[1]^2*B[2]*c[2]+105*beta*k^3*s*B[1]*B[2]^2*c[2]+35*beta*k^3*s*B[2]^3*c[2]+3*beta*k^4*s*w*A[0]+3*beta*k^4*s*w*A[1]-9*beta*k^4*s*w*A[2]-9*beta*k^4*s*w*B[1]-9*beta*k^4*s*w*B[2]+5*k^3*w*A[0]^3*c[2]+15*k^3*w*A[0]^2*A[1]*c[2]-45*k^3*w*A[0]^2*A[2]*c[2]-45*k^3*w*A[0]^2*B[1]*c[2]-45*k^3*w*A[0]^2*B[2]*c[2]-45*k^3*w*A[0]*A[1]^2*c[2]+150*k^3*w*A[0]*A[1]*A[2]*c[2]+30*k^3*w*A[0]*A[1]*B[1]*c[2]+30*k^3*w*A[0]*A[1]*B[2]*c[2]-105*k^3*w*A[0]*A[2]^2*c[2]+30*k^3*w*A[0]*A[2]*B[1]*c[2]+30*k^3*w*A[0]*A[2]*B[2]*c[2]+75*k^3*w*A[0]*B[1]^2*c[2]+150*k^3*w*A[0]*B[1]*B[2]*c[2]+75*k^3*w*A[0]*B[2]^2*c[2]+25*k^3*w*A[1]^3*c[2]-105*k^3*w*A[1]^2*A[2]*c[2]+15*k^3*w*A[1]^2*B[1]*c[2]+15*k^3*w*A[1]^2*B[2]*c[2]+135*k^3*w*A[1]*A[2]^2*c[2]-90*k^3*w*A[1]*A[2]*B[1]*c[2]-90*k^3*w*A[1]*A[2]*B[2]*c[2]-45*k^3*w*A[1]*B[1]^2*c[2]-90*k^3*w*A[1]*B[1]*B[2]*c[2]-45*k^3*w*A[1]*B[2]^2*c[2]-55*k^3*w*A[2]^3*c[2]+75*k^3*w*A[2]^2*B[1]*c[2]+75*k^3*w*A[2]^2*B[2]*c[2]+15*k^3*w*A[2]*B[1]^2*c[2]+30*k^3*w*A[2]*B[1]*B[2]*c[2]+15*k^3*w*A[2]*B[2]^2*c[2]-35*k^3*w*B[1]^3*c[2]-105*k^3*w*B[1]^2*B[2]*c[2]-105*k^3*w*B[1]*B[2]^2*c[2]-35*k^3*w*B[2]^3*c[2]+40*beta^2*k^2*s^2*A[1]-80*beta^2*k^2*s^2*A[2]-40*beta^2*k^2*s^2*B[1]-40*beta^2*k^2*s^2*B[2]+2*k^4*s^2*A[0]+2*k^4*s^2*A[1]-6*k^4*s^2*A[2]-6*k^4*s^2*B[1]-6*k^4*s^2*B[2]-5*k^4*w^2*A[0]-5*k^4*w^2*A[1]+15*k^4*w^2*A[2]+15*k^4*w^2*B[1]+15*k^4*w^2*B[2]-80*beta*k^2*s*w*A[1]+160*beta*k^2*s*w*A[2]+80*beta*k^2*s*w*B[1]+80*beta*k^2*s*w*B[2]+40*k^2*s^2*A[1]-80*k^2*s^2*A[2]-40*k^2*s^2*B[1]-40*k^2*s^2*B[2]-160*beta*s*w*A[1]+320*beta*s*w*A[2]+160*beta*s*w*B[1]+160*beta*s*w*B[2]+160*s^2*A[1]-320*s^2*A[2]-160*s^2*B[1]-160*s^2*B[2]), 0 = k^3*(beta*s-w)*(A[0]-A[1]+A[2]-B[1]-B[2])*(-5*beta*s*A[0]^2*c[2]+10*beta*s*A[0]*A[1]*c[2]-10*beta*s*A[0]*A[2]*c[2]+10*beta*s*A[0]*B[1]*c[2]+10*beta*s*A[0]*B[2]*c[2]-5*beta*s*A[1]^2*c[2]+10*beta*s*A[1]*A[2]*c[2]-10*beta*s*A[1]*B[1]*c[2]-10*beta*s*A[1]*B[2]*c[2]-5*beta*s*A[2]^2*c[2]+10*beta*s*A[2]*B[1]*c[2]+10*beta*s*A[2]*B[2]*c[2]-5*beta*s*B[1]^2*c[2]-10*beta*s*B[1]*B[2]*c[2]-5*beta*s*B[2]^2*c[2]+3*beta*k*s*w+5*w*A[0]^2*c[2]-10*w*A[0]*A[1]*c[2]+10*w*A[0]*A[2]*c[2]-10*w*A[0]*B[1]*c[2]-10*w*A[0]*B[2]*c[2]+5*w*A[1]^2*c[2]-10*w*A[1]*A[2]*c[2]+10*w*A[1]*B[1]*c[2]+10*w*A[1]*B[2]*c[2]+5*w*A[2]^2*c[2]-10*w*A[2]*B[1]*c[2]-10*w*A[2]*B[2]*c[2]+5*w*B[1]^2*c[2]+10*w*B[1]*B[2]*c[2]+5*w*B[2]^2*c[2]+2*k*s^2-5*k*w^2)]
> 

indets(CoefficientNullity)

{beta, k, s, w, A[0], A[1], A[2], B[1], B[2], c[2]}

 (2)
> 

sols := solve(CoefficientNullity, [beta, k, s, w, A[0], A[1], A[2], B[1], B[2], c[2]]); sols := `assuming`([eval(sols)], [b > 0]); whattype(sols); print(cat(`$`('_', 120))); `~`[print](sols)

[[beta = beta, k = 0, s = 0, w = w, A[0] = A[0], A[1] = A[1], A[2] = A[2], B[1] = B[1], B[2] = B[2], c[2] = c[2]], [beta = beta, k = 0, s = s, w = w, A[0] = A[0], A[1] = 0, A[2] = 0, B[1] = -B[2], B[2] = B[2], c[2] = c[2]], [beta = w/s, k = 0, s = s, w = w, A[0] = A[0], A[1] = A[1], A[2] = A[2], B[1] = B[1], B[2] = B[2], c[2] = c[2]], [beta = beta, k = 0, s = beta*w, w = w, A[0] = A[0], A[1] = A[1], A[2] = A[2], B[1] = B[1], B[2] = B[2], c[2] = c[2]]]

  

list

  

________________________________________________________________________________________________________________________

  

[beta = beta, k = 0, s = 0, w = w, A[0] = A[0], A[1] = A[1], A[2] = A[2], B[1] = B[1], B[2] = B[2], c[2] = c[2]]

  

[beta = beta, k = 0, s = s, w = w, A[0] = A[0], A[1] = 0, A[2] = 0, B[1] = -B[2], B[2] = B[2], c[2] = c[2]]

  

[beta = w/s, k = 0, s = s, w = w, A[0] = A[0], A[1] = A[1], A[2] = A[2], B[1] = B[1], B[2] = B[2], c[2] = c[2]]

  

[beta = beta, k = 0, s = beta*w, w = w, A[0] = A[0], A[1] = A[1], A[2] = A[2], B[1] = B[1], B[2] = B[2], c[2] = c[2]]

 (3)

Download params.mw

how to fix the problem in final output?...

Asked by: AHSAN 160
ode dsolve numeric
May 08 2025
1  2

Hi everyone, I am trying to plot graphs for dp/dx versus x from my ordinary differential equation numerically. My file is working, but the outcome is straight lines, which means I am doing something wrong. Could anyone  please have a look on my file.

Help-dpdx.mw

the expected  results should be  look like this

Error, (in content/gcd) too many levels of recursi...

Asked by: nm 11173
ode differential-equations odetest
May 07 2025
0  0

I do not remember seeing this before or reporting. Just in case, here is how to reproduce it. This happens also in Maple 2024.2

The problem with these errors is that they can not be cought using try/catch.

I was testing a solution which most likely wrong, but I get 

                 Error, (in content/gcd) too many levels of recursion

> 

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 1866 and is the same as the version installed in this computer, created 2025, May 6, 10:52 hours Pacific Time.`

> 

SupportTools:-Version();

`The Customer Support Updates version in the MapleCloud is 17 and is the same as the version installed in this computer, created May 5, 2025, 12:37 hours Eastern Time.`

> 

restart;
> 

sol:=ln((1/9*u(x)*6^(1/3)/surd((-9*A^2+2*A*x^(3/2))/(-288*A*x^(9/2)-5832*A^3*x^(3/2)+16*x^6+1944*A^2*x^3+6561*A^4),3)+1)^(1/3)/(1/81*u(x)^2*6^(2/3)/surd((-9*A^2+2*A*x^(3/2))/(-288*A*x^(9/2)-5832*A^3*x^(3/2)+16*x^6+1944*A^2*x^3+6561*A^4),3)^2-1/9*u(x)*6^(1/3)/surd((-9*A^2+2*A*x^(3/2))/(-288*A*x^(9/2)-5832*A^3*x^(3/2)+16*x^6+1944*A^2*x^3+6561*A^4),3)+1)^(1/6))+1/3*3^(1/2)*arctan(1/3*(2/9*u(x)*6^(1/3)/surd((-9*A^2+2*A*x^(3/2))/(-288*A*x^(9/2)-5832*A^3*x^(3/2)+16*x^6+1944*A^2*x^3+6561*A^4),3)-1)*3^(1/2)) = Int(3/2*(-32*x^(15/2)-6480*A^2*x^(9/2)-65610*A^4*x^(3/2)+720*A*x^6+29160*A^3*x^3+59049*A^5)/surd(-A*(-2*x^(3/2)+9*A)/(-288*A*x^(9/2)-5832*A^3*x^(3/2)+16*x^6+1944*A^2*x^3+6561*A^4),3)/(-128*x^11-54432*A^2*x^8-1837080*A^4*x^5+4782969*A^7*x^(1/2)-7440174*A^6*x^2+4960116*A^5*x^(7/2)+408240*A^3*x^(13/2)+4032*A*x^(19/2))*A*6^(1/3),x)+2*_C1;
ode:=diff(u(x),x) = -1/18/x^(1/2)*(-576*A*x^(9/2)-11664*A^3*x^(3/2)+32*x^6+3888*A^2*x^3+13122*A^4)/(-2*x^(3/2)+9*A)^3*u(x)^3-1/18/x^(1/2)*(1944*A*x^(5/2)-216*x^4-4374*A^2*x)/(-2*x^(3/2)+9*A)^3*u(x)-1/18/x^(1/2)*(486*A*x^(3/2)-2187*A^2)/(-2*x^(3/2)+9*A)^3;

ln(((1/9)*u(x)*6^(1/3)/surd((-9*A^2+2*A*x^(3/2))/(-288*A*x^(9/2)-5832*A^3*x^(3/2)+16*x^6+1944*A^2*x^3+6561*A^4), 3)+1)^(1/3)/((1/81)*u(x)^2*6^(2/3)/surd((-9*A^2+2*A*x^(3/2))/(-288*A*x^(9/2)-5832*A^3*x^(3/2)+16*x^6+1944*A^2*x^3+6561*A^4), 3)^2-(1/9)*u(x)*6^(1/3)/surd((-9*A^2+2*A*x^(3/2))/(-288*A*x^(9/2)-5832*A^3*x^(3/2)+16*x^6+1944*A^2*x^3+6561*A^4), 3)+1)^(1/6))+(1/3)*3^(1/2)*arctan((1/3)*((2/9)*u(x)*6^(1/3)/surd((-9*A^2+2*A*x^(3/2))/(-288*A*x^(9/2)-5832*A^3*x^(3/2)+16*x^6+1944*A^2*x^3+6561*A^4), 3)-1)*3^(1/2)) = Int((3/2)*(-32*x^(15/2)-6480*A^2*x^(9/2)-65610*A^4*x^(3/2)+720*A*x^6+29160*A^3*x^3+59049*A^5)*A*6^(1/3)/(surd(-A*(-2*x^(3/2)+9*A)/(-288*A*x^(9/2)-5832*A^3*x^(3/2)+16*x^6+1944*A^2*x^3+6561*A^4), 3)*(-128*x^11-54432*A^2*x^8-1837080*A^4*x^5+4782969*A^7*x^(1/2)-7440174*A^6*x^2+4960116*A^5*x^(7/2)+408240*A^3*x^(13/2)+4032*A*x^(19/2))), x)+2*_C1

diff(u(x), x) = -(1/18)*(-576*A*x^(9/2)-11664*A^3*x^(3/2)+32*x^6+3888*A^2*x^3+13122*A^4)*u(x)^3/(x^(1/2)*(-2*x^(3/2)+9*A)^3)-(1/18)*(1944*A*x^(5/2)-216*x^4-4374*A^2*x)*u(x)/(x^(1/2)*(-2*x^(3/2)+9*A)^3)-(1/18)*(486*A*x^(3/2)-2187*A^2)/(x^(1/2)*(-2*x^(3/2)+9*A)^3)

> 

try
    odetest(sol,ode);
catch:
    print("cought error ok");
end try;

Error, (in content/gcd) too many levels of recursion

 

 

Download content_gce_odetest_error_may_7_2025.mw

How to find what changed in SupportTools after eac...

Asked by: nm 11173
update supporttools
May 06 2025
4  1

I asked similar question 5 years ago about Physics update but it was not possible to find this information

How-To-Find-What-Changed-In-Physics

I'd like to ask now again same about  SupportTools. Can one find out what update is actually included in new version?

Even if it is just 2-3 lines. It will be good if users had an idea what was fixed or improved in the new version.

Any update to software should inlcude such information. Not asking for details, just general information will be nice. Right now one does an update and have no idea at all what the new update fixed or improved which is not good.

May be such information can be displayed on screen after a user updates?

Can we plot this gain function in 3D from pde?...

Asked by: janhardo 620
pde differential-equations plotting
May 05 2025
3  3

Yes , i can ..a procedure for thiis?

> 

restart; with(plots); printf("Step 1: Declare l and b as free variables for the 3D plot.\n"); l := 'l'; b := 'b'; printf("Step 2: Set fixed values for remaining parameters.\n"); a := 1; c := 1; d := .2; f := 1; epsilon := 1; printf("Step 3: Define the 3D gain function G(l,b) with fixed a,c,d and variable l,b.\n"); G := proc (l, b) options operator, arrow; 2*Im(sqrt(-a^2*f*d-a*b+(1/2)*l^2-3*a+(1/2)*sqrt(-48*a^3*f*d+4*epsilon*l^3*c-24*a*epsilon*l*c+l^4+4*l^2*c^2-48*a^2*b-12*a*l^2+36*a^2))) end proc; printf("Step 4: Create a 3D surface plot of G(l,b).\n"); gainPlot := plot3d(G(l, b), l = -6 .. 4, b = .1 .. 1.2, labels = ["Wave number l", "Parameter b", "Gain G(l,b)"], title = "3D MI Gain Spectrum over (l, b)", shading = zhue, axes = boxed, grid = [60, 60]); printf("Step 5: Display the 3D surface plot.\n"); gainPlot

Step 1: Declare l and b as free variables for the 3D plot.
Step 2: Set fixed values for remaining parameters.
Step 3: Define the 3D gain function G(l,b) with fixed a,c,d and variable l,b.
Step 4: Create a 3D surface plot of G(l,b).
Step 5: Display the 3D surface plot.

  

 
 

 

Download can_we_plotthisin_3Dshapemprimes5-5-2025.mw

How generate systems of equation and solve?...

Asked by: SSMB 100
coefficients conjugate duplicate-question
May 05 2025
2  3

in here How we can seperate the coefficent of conjugate this conjugate sign how remove from my equation ?

> 

restart
> 

with(PDEtools)
> 

with(LinearAlgebra)
> 

NULL
> 

with(SolveTools)
> 

undeclare(prime)

`There is no more prime differentiation variable; all derivatives will be displayed as indexed functions`

 (1)
> 

declare(u(x, t)); declare(U(xi)); declare(V(xi)); declare(P(x, t)); declare(q(x, t))

u(x, t)*`will now be displayed as`*u

  

U(xi)*`will now be displayed as`*U

  

V(xi)*`will now be displayed as`*V

  

P(x, t)*`will now be displayed as`*P

  

q(x, t)*`will now be displayed as`*q

 (2)
> 

pde := I*(diff(u(x, t), t))+diff(u(x, t), `$`(x, 2))+abs(u(x, t))^2*u(x, t) = 0

I*(diff(u(x, t), t))+diff(diff(u(x, t), x), x)+abs(u(x, t))^2*u(x, t) = 0

 (3)
> 

S := u(x, t) = (sqrt(a)+P(x, t))*exp(I*a*t)

u(x, t) = (a^(1/2)+P(x, t))*exp(I*a*t)

 (4)
> 

S1 := conjugate(u(x, t)) = (sqrt(a)+conjugate(P(x, t)))*exp(-I*a*t)

conjugate(u(x, t)) = (a^(1/2)+conjugate(P(x, t)))*exp(-I*a*t)

 (5)
> 

Q := abs(u(x, t))^2 = u(x, t)*conjugate(u(x, t))

abs(u(x, t))^2 = u(x, t)*conjugate(u(x, t))

 (6)
> 

F1 := expand(simplify(subs({S, S1}, rhs(Q))))

a+a^(1/2)*P(x, t)+a^(1/2)*conjugate(P(x, t))+abs(P(x, t))^2

 (7)
> 

F2 := abs(u(x, t))^2 = remove(has, F1, abs(P(x, t))^2)

abs(u(x, t))^2 = a+a^(1/2)*P(x, t)+a^(1/2)*conjugate(P(x, t))

 (8)
> 

FF := collect(F2, sqrt(a))

abs(u(x, t))^2 = a+(P(x, t)+conjugate(P(x, t)))*a^(1/2)

 (9)
> 

F3 := abs(u(x, t))^2*u(x, t) = (a+(P(x, t)+conjugate(P(x, t)))*sqrt(a))*rhs(S)

abs(u(x, t))^2*u(x, t) = (a+(P(x, t)+conjugate(P(x, t)))*a^(1/2))*(a^(1/2)+P(x, t))*exp(I*a*t)

 (10)
> 

F4 := remove(has, F3, P(x, t)*conjugate(P(x, t)))

abs(u(x, t))^2*u(x, t) = (a+(P(x, t)+conjugate(P(x, t)))*a^(1/2))*(a^(1/2)+P(x, t))*exp(I*a*t)

 (11)
> 

expand(%)

abs(u(x, t))^2*u(x, t) = exp(I*a*t)*a^(3/2)+2*exp(I*a*t)*a*P(x, t)+exp(I*a*t)*a^(1/2)*P(x, t)^2+exp(I*a*t)*a*conjugate(P(x, t))+exp(I*a*t)*a^(1/2)*conjugate(P(x, t))*P(x, t)

 (12)
> 

pde_linear, pde_nonlinear := selectremove(proc (term) options operator, arrow; not has((eval(term, P(x, t) = T*P(x, t)))/T, T) end proc, expand(%))

() = (), abs(u(x, t))^2*u(x, t) = exp(I*a*t)*a^(3/2)+2*exp(I*a*t)*a*P(x, t)+exp(I*a*t)*a^(1/2)*P(x, t)^2+exp(I*a*t)*a*conjugate(P(x, t))+exp(I*a*t)*a^(1/2)*conjugate(P(x, t))*P(x, t)

 (13)
> 

F6 := abs(u(x, t))^2*u(x, t) = exp(I*a*t)*a^(3/2)+2*exp(I*a*t)*a*P(x, t)+exp(I*a*t)*a*conjugate(P(x, t))

abs(u(x, t))^2*u(x, t) = exp(a*t*I)*a^(3/2)+2*exp(a*t*I)*a*P(x, t)+exp(a*t*I)*a*conjugate(P(x, t))

 (14)
> 

subs({F6, S}, pde)

I*(diff((a^(1/2)+P(x, t))*exp(a*t*I), t))+diff(diff((a^(1/2)+P(x, t))*exp(a*t*I), x), x)+exp(a*t*I)*a^(3/2)+2*exp(a*t*I)*a*P(x, t)+exp(a*t*I)*a*conjugate(P(x, t)) = 0

 (15)
> 

eval(%)

I*((diff(P(x, t), t))*exp(a*t*I)+I*(a^(1/2)+P(x, t))*a*exp(a*t*I))+(diff(diff(P(x, t), x), x))*exp(a*t*I)+exp(a*t*I)*a^(3/2)+2*exp(a*t*I)*a*P(x, t)+exp(a*t*I)*a*conjugate(P(x, t)) = 0

 (16)
> 

expand(%)

I*(diff(P(x, t), t))*exp(a*t*I)+exp(a*t*I)*a*P(x, t)+(diff(diff(P(x, t), x), x))*exp(a*t*I)+exp(a*t*I)*a*conjugate(P(x, t)) = 0

 (17)
> 

expand(%/exp(I*a*t))

I*(diff(P(x, t), t))+a*P(x, t)+diff(diff(P(x, t), x), x)+a*conjugate(P(x, t)) = 0

 (18)
> 

PP := collect(%, a)

(P(x, t)+conjugate(P(x, t)))*a+I*(diff(P(x, t), t))+diff(diff(P(x, t), x), x) = 0

 (19)
> 

U1 := P(x, t) = r[1]*exp(I*(l*x-m*t))+r[2]*exp(-I*(l*x-m*t))

P(x, t) = r[1]*exp(I*(l*x-m*t))+r[2]*exp(-I*(l*x-m*t))

 (20)
> 

eval(subs(U1, PP))

(r[1]*exp(I*(l*x-m*t))+r[2]*exp(-I*(l*x-m*t))+conjugate(r[1]*exp(I*(l*x-m*t))+r[2]*exp(-I*(l*x-m*t))))*a+I*(-I*r[1]*m*exp(I*(l*x-m*t))+I*r[2]*m*exp(-I*(l*x-m*t)))-r[1]*l^2*exp(I*(l*x-m*t))-r[2]*l^2*exp(-I*(l*x-m*t)) = 0

 (21)
> 

simplify((r[1]*exp(I*(l*x-m*t))+r[2]*exp(-I*(l*x-m*t))+conjugate(r[1]*exp(I*(l*x-m*t))+r[2]*exp(-I*(l*x-m*t))))*a+I*(-I*r[1]*m*exp(I*(l*x-m*t))+I*r[2]*m*exp(-I*(l*x-m*t)))-r[1]*l^2*exp(I*(l*x-m*t))-r[2]*l^2*exp(-I*(l*x-m*t)) = 0)

conjugate(r[1]*exp(I*(l*x-m*t))+r[2]*exp(-I*(l*x-m*t)))*a+r[2]*(-l^2+a-m)*exp(-I*(l*x-m*t))+r[1]*exp(I*(l*x-m*t))*(-l^2+a+m) = 0

 (22)
> 

J := eval(%)

conjugate(r[1]*exp(I*(l*x-m*t))+r[2]*exp(-I*(l*x-m*t)))*a+r[2]*(-l^2+a-m)*exp(-I*(l*x-m*t))+r[1]*exp(I*(l*x-m*t))*(-l^2+a+m) = 0

 (23)
> 

expand(%)

a*conjugate(r[1])*exp(I*conjugate(m)*conjugate(t))/exp(I*conjugate(l)*conjugate(x))+a*conjugate(r[2])*exp(I*conjugate(l)*conjugate(x))/exp(I*conjugate(m)*conjugate(t))-r[2]*exp(I*m*t)*l^2/exp(I*l*x)+r[2]*exp(I*m*t)*a/exp(I*l*x)-r[2]*exp(I*m*t)*m/exp(I*l*x)-r[1]*exp(I*l*x)*l^2/exp(I*m*t)+r[1]*exp(I*l*x)*a/exp(I*m*t)+r[1]*exp(I*l*x)*m/exp(I*m*t) = 0

 (24)
> 

indets(%)

{a, l, m, t, x, r[1], r[2], exp(I*l*x), exp(I*m*t), exp(I*conjugate(l)*conjugate(x)), exp(I*conjugate(m)*conjugate(t)), conjugate(l), conjugate(m), conjugate(t), conjugate(x), conjugate(r[1]), conjugate(r[2])}

 (25)
> 

subs({exp(-I*(l*x-m*t)) = Y, exp(I*(l*x-m*t)) = X}, J)

conjugate(X*r[1]+Y*r[2])*a+r[2]*(-l^2+a-m)*Y+r[1]*X*(-l^2+a+m) = 0

 (26)
> 

collect(%, {X, Y})

conjugate(X*r[1]+Y*r[2])*a+r[2]*(-l^2+a-m)*Y+r[1]*X*(-l^2+a+m) = 0

 (27)

Download conjugate.mw

Clarifying and Solving a New ODE with Exponential ...

Asked by: salim-barzani 1390
ode
May 03 2025
1  10

I am currently working with an ordinary differential equation (ODE) that I find difficult to express and solve accurately. In this ODE, the symbol f represents an exponential function rather than a typical variable, which adds to the confusion. Although I have followed the format used in related research papers, the results I obtain are not satisfactory.

Since this type of ODE is new and somewhat unfamiliar to me, I would greatly appreciate your guidance in:

  1. Properly formulating the ODE.

  2. Understanding the role of f in the context of exponential functions.

  3. Finding the correct and complete solutions.

  4. Learning how to clearly present each solution step by step.

Thank you in advance for your support.

AA.mw

How to find KKT Condition and range?...

Asked by: Andiguys 65
optimization condition
May 03 2025
0  3

Syntax to find KKT Condition, only one constrain is there? Need help
KKT_Condition.mw

Symbolic Factoring of Multiplicative Terms in Alge...

Asked by: salim-barzani 1390
factorization coefficients duplicate-question
May 02 2025
1  14

Manually factoring each equation in this system one by one is time-consuming and inefficient. Is there a way to automate the factoring of expressions into two multiplicative terms—some of which may be single-term factors—using code?

> 

restart
> 

with(PDEtools)
> 

NULL
> 

with(SolveTools)
> 

undeclare(prime)

`There is no more prime differentiation variable; all derivatives will be displayed as indexed functions`

 (1)
> 

G1 := 5*lambda^2*alpha[1]^4*alpha[0]*a[4]+lambda^2*alpha[1]^4*a[3]-10*lambda*alpha[1]^2*alpha[0]^3*a[4]+lambda*k^2*a[1]*alpha[1]^2-6*lambda*alpha[1]^2*alpha[0]^2*a[3]+alpha[0]^5*a[4]-k^2*a[1]*alpha[0]^2-3*lambda*alpha[1]^2*alpha[0]*a[2]+alpha[0]^4*a[3]+lambda*w*alpha[1]^2+alpha[0]^3*a[2]-w*alpha[0]^2+((lambda^2*a[4]*alpha[1]^5-10*lambda*a[4]*alpha[0]^2*alpha[1]^3-4*lambda*a[3]*alpha[0]*alpha[1]^3+5*a[4]*alpha[0]^4*alpha[1]-2*k^2*a[1]*alpha[0]*alpha[1]-lambda*a[2]*alpha[1]^3+4*a[3]*alpha[0]^3*alpha[1]+3*a[2]*alpha[0]^2*alpha[1]-2*w*alpha[0]*alpha[1])*(diff(G(xi), xi))+lambda^2*beta[0]*a[5]*alpha[1]^2-4*mu*lambda*alpha[1]^4*a[3]+5*lambda^2*beta[0]*alpha[1]^4*a[4]-3*lambda*beta[0]*alpha[1]^2*a[2]-lambda*beta[0]*a[5]*alpha[0]^2-(1/2)*lambda*a[1]*alpha[0]*beta[0]-2*k^2*a[1]*alpha[0]*beta[0]+12*mu*alpha[1]^2*alpha[0]^2*a[3]+6*mu*alpha[1]^2*alpha[0]*a[2]-2*mu*k^2*a[1]*alpha[1]^2-(1/2)*mu*lambda*alpha[1]^2*a[1]+20*mu*alpha[1]^2*alpha[0]^3*a[4]-20*mu*lambda*alpha[1]^4*alpha[0]*a[4]-2*mu*lambda*alpha[1]^2*a[5]*alpha[0]-30*lambda*beta[0]*alpha[1]^2*alpha[0]^2*a[4]-12*lambda*beta[0]*alpha[1]^2*alpha[0]*a[3]-2*w*alpha[0]*beta[0]+5*beta[0]*alpha[0]^4*a[4]+4*beta[0]*alpha[0]^3*a[3]+3*beta[0]*alpha[0]^2*a[2]-2*mu*w*alpha[1]^2)/G(xi)+((1/4)*(3*(-(2*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*lambda+4*mu^2))*alpha[1]^2*a[1]+6*mu*beta[0]*alpha[1]^2*a[2]+3*mu*beta[0]*a[5]*alpha[0]^2-6*lambda*beta[0]^2*alpha[1]^2*a[3]-2*lambda*beta[0]^2*a[5]*alpha[0]+(6*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*alpha[1]^2*alpha[0]^2*a[3]+(3*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*alpha[1]^2*alpha[0]*a[2]-12*mu^2*alpha[1]^2*a[5]*alpha[0]+3*mu*a[1]*alpha[0]*beta[0]*(1/2)+10*beta[0]^2*alpha[0]^3*a[4]+6*beta[0]^2*alpha[0]^2*a[3]+3*beta[0]^2*alpha[0]*a[2]-k^2*a[1]*beta[0]^2+(10*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*alpha[1]^2*alpha[0]^3*a[4]-(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda)*k^2*a[1]*alpha[1]^2+(5*(-(2*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*lambda+4*mu^2))*alpha[1]^4*alpha[0]*a[4]+(4*(-(2*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*lambda+4*mu^2))*alpha[1]^2*a[5]*alpha[0]+(1/2)*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda)*alpha[1]^2*lambda*a[1]-9*mu^2*alpha[1]^2*a[1]*(1/4)-(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda)*w*alpha[1]^2+(-(2*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*lambda+4*mu^2)*alpha[1]^4*a[3]-(1/4)*lambda*beta[0]^2*a[1]-30*lambda*beta[0]^2*alpha[1]^2*alpha[0]*a[4]+24*mu*beta[0]*alpha[1]^2*alpha[0]*a[3]+60*mu*beta[0]*alpha[1]^2*alpha[0]^2*a[4]+(4*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*alpha[1]^2*lambda*a[5]*alpha[0]-20*mu*lambda*beta[0]*alpha[1]^4*a[4]-7*mu*lambda*beta[0]*a[5]*alpha[1]^2+(2*mu*alpha[1]^3*a[2]-2*w*alpha[1]*beta[0]-4*lambda*beta[0]*alpha[1]^3*a[3]+8*mu*alpha[1]^3*alpha[0]*a[3]+mu*alpha[1]*a[5]*alpha[0]^2+(1/2)*mu*alpha[1]*alpha[0]*a[1]+20*mu*alpha[1]^3*alpha[0]^2*a[4]-4*mu*lambda*alpha[1]^5*a[4]-mu*lambda*alpha[1]^3*a[5]+20*beta[0]*alpha[1]*alpha[0]^3*a[4]+12*beta[0]*alpha[1]*alpha[0]^2*a[3]+6*beta[0]*alpha[1]*alpha[0]*a[2]-2*k^2*a[1]*alpha[1]*beta[0]-(1/2)*lambda*beta[0]*alpha[1]*a[1]-20*lambda*beta[0]*alpha[1]^3*alpha[0]*a[4]-2*lambda*beta[0]*a[5]*alpha[1]*alpha[0])*(diff(G(xi), xi))-w*beta[0]^2)/G(xi)^2+(((lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda)*alpha[1]^3*a[2]+(-(2*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*lambda+4*mu^2)*alpha[1]^5*a[4]+(2*(-(2*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*lambda+4*mu^2))*alpha[1]^3*a[5]+3*beta[0]^2*alpha[1]*a[2]+3*mu*beta[0]*alpha[1]*a[1]*(1/2)+8*mu*beta[0]*alpha[1]^3*a[3]-2*lambda*beta[0]^2*a[5]*alpha[1]+(4*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*alpha[1]^3*alpha[0]*a[3]+(2*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*alpha[1]*a[5]*alpha[0]^2+(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda)*alpha[1]*alpha[0]*a[1]+(10*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*alpha[1]^3*alpha[0]^2*a[4]+(2*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*alpha[1]^3*lambda*a[5]+30*beta[0]^2*alpha[1]*alpha[0]^2*a[4]+12*beta[0]^2*alpha[1]*alpha[0]*a[3]-6*mu^2*alpha[1]^3*a[5]-10*lambda*beta[0]^2*alpha[1]^3*a[4]+40*mu*beta[0]*alpha[1]^3*alpha[0]*a[4]+8*mu*beta[0]*a[5]*alpha[1]*alpha[0])*(diff(G(xi), xi))+(4*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*mu*alpha[1]^4*a[3]+(5*(-(2*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*lambda+4*mu^2))*beta[0]*alpha[1]^4*a[4]+(6*(-(2*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*lambda+4*mu^2))*beta[0]*a[5]*alpha[1]^2-10*lambda*beta[0]^3*alpha[1]^2*a[4]+(2*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*mu*alpha[1]^2*a[1]+(3*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*beta[0]*alpha[1]^2*a[2]+(2*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*beta[0]*a[5]*alpha[0]^2+(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda)*a[1]*alpha[0]*beta[0]+12*mu*beta[0]^2*alpha[1]^2*a[3]+6*mu*beta[0]^2*a[5]*alpha[0]+(20*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*mu*alpha[1]^4*alpha[0]*a[4]+(10*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*mu*alpha[1]^2*a[5]*alpha[0]+beta[0]^3*a[2]-14*mu^2*beta[0]*a[5]*alpha[1]^2+(30*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*beta[0]*alpha[1]^2*alpha[0]^2*a[4]+(5*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*beta[0]*lambda*a[5]*alpha[1]^2+(12*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*beta[0]*alpha[1]^2*alpha[0]*a[3]+60*mu*beta[0]^2*alpha[1]^2*alpha[0]*a[4]+mu*beta[0]^2*a[1]-lambda*beta[0]^3*a[5]+10*beta[0]^3*alpha[0]^2*a[4]+4*beta[0]^3*alpha[0]*a[3])/G(xi)^3+((4*beta[0]^3*alpha[1]*a[3]+(1/2)*(3*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*beta[0]*alpha[1]*a[1]+(4*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*beta[0]*alpha[1]^3*a[3]+7*mu*beta[0]^2*a[5]*alpha[1]+(4*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*mu*alpha[1]^5*a[4]+(5*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*mu*alpha[1]^3*a[5]+20*beta[0]^3*alpha[1]*alpha[0]*a[4]+20*mu*beta[0]^2*alpha[1]^3*a[4]+(20*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*beta[0]*alpha[1]^3*alpha[0]*a[4]+(8*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*beta[0]*a[5]*alpha[1]*alpha[0])*(diff(G(xi), xi))+20*mu*beta[0]^3*alpha[1]^2*a[4]+(6*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*beta[0]^2*alpha[1]^2*a[3]+(4*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*beta[0]^2*a[5]*alpha[0]+5*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda)^2*alpha[1]^4*alpha[0]*a[4]+4*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda)^2*alpha[1]^2*a[5]*alpha[0]+(17*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*mu*beta[0]*a[5]*alpha[1]^2+(20*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*mu*beta[0]*alpha[1]^4*a[4]+beta[0]^4*a[3]+(30*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*beta[0]^2*alpha[1]^2*alpha[0]*a[4]+(1/4)*(3*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*beta[0]^2*a[1]+3*mu*beta[0]^3*a[5]+5*beta[0]^4*alpha[0]*a[4]+(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda)^2*alpha[1]^4*a[3]+3*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda)^2*alpha[1]^2*a[1]*(1/4))/G(xi)^4+(((lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda)^2*alpha[1]^5*a[4]+2*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda)^2*alpha[1]^3*a[5]+5*beta[0]^4*alpha[1]*a[4]+(6*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*beta[0]^2*a[5]*alpha[1]+(10*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*beta[0]^2*alpha[1]^3*a[4])*(diff(G(xi), xi))+(2*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*beta[0]^3*a[5]+(10*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*beta[0]^3*alpha[1]^2*a[4]+5*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda)^2*beta[0]*alpha[1]^4*a[4]+6*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda)^2*beta[0]*a[5]*alpha[1]^2+beta[0]^5*a[4])/G(xi)^5 = 0
> 

indets(G1)

{k, lambda, mu, w, xi, B[1], B[2], a[1], a[2], a[3], a[4], a[5], alpha[0], alpha[1], beta[0], G(xi), diff(G(xi), xi)}

 (2)

``

 (3)
> 

eq0 := 5*lambda^2*a[4]*alpha[0]*alpha[1]^4+lambda^2*a[3]*alpha[1]^4-10*lambda*a[4]*alpha[0]^3*alpha[1]^2+k^2*lambda*a[1]*alpha[1]^2-6*lambda*a[3]*alpha[0]^2*alpha[1]^2+a[4]*alpha[0]^5-k^2*a[1]*alpha[0]^2-3*lambda*a[2]*alpha[0]*alpha[1]^2+a[3]*alpha[0]^4+lambda*w*alpha[1]^2+a[2]*alpha[0]^3-w*alpha[0]^2 = 0
> 

``
> 

eq1 := lambda^2*a[4]*alpha[1]^5-10*lambda*a[4]*alpha[0]^2*alpha[1]^3-4*lambda*a[3]*alpha[0]*alpha[1]^3+5*a[4]*alpha[0]^4*alpha[1]-2*k^2*a[1]*alpha[0]*alpha[1]-lambda*a[2]*alpha[1]^3+4*a[3]*alpha[0]^3*alpha[1]+3*a[2]*alpha[0]^2*alpha[1]-2*w*alpha[0]*alpha[1] = 0
> 

eq2 := lambda^2*beta[0]*a[5]*alpha[1]^2+6*mu*alpha[1]^2*alpha[0]*a[2]-2*mu*k^2*a[1]*alpha[1]^2-(1/2)*mu*alpha[1]^2*lambda*a[1]+20*mu*alpha[1]^2*alpha[0]^3*a[4]+12*mu*alpha[1]^2*alpha[0]^2*a[3]-(1/2)*lambda*a[1]*alpha[0]*beta[0]-2*k^2*a[1]*alpha[0]*beta[0]-3*lambda*beta[0]*alpha[1]^2*a[2]-lambda*beta[0]*a[5]*alpha[0]^2+5*lambda^2*beta[0]*alpha[1]^4*a[4]-4*mu*lambda*alpha[1]^4*a[3]-2*mu*w*alpha[1]^2+5*beta[0]*alpha[0]^4*a[4]+4*beta[0]*alpha[0]^3*a[3]+3*beta[0]*alpha[0]^2*a[2]-2*w*alpha[0]*beta[0]-20*mu*lambda*alpha[1]^4*alpha[0]*a[4]-2*mu*alpha[1]^2*lambda*a[5]*alpha[0]-30*lambda*beta[0]*alpha[1]^2*alpha[0]^2*a[4]-12*lambda*beta[0]*alpha[1]^2*alpha[0]*a[3] = 0
> 

NULL
> 

eq3 := (1/4)*(3*(-(2*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*lambda+4*mu^2))*alpha[1]^2*a[1]-(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda)*k^2*a[1]*alpha[1]^2+(1/2)*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda)*alpha[1]^2*lambda*a[1]+(5*(-(2*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*lambda+4*mu^2))*alpha[1]^4*alpha[0]*a[4]+(10*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*alpha[1]^2*alpha[0]^3*a[4]+(6*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*alpha[1]^2*alpha[0]^2*a[3]-30*lambda*beta[0]^2*alpha[1]^2*alpha[0]*a[4]-20*mu*beta[0]*lambda*alpha[1]^4*a[4]+(4*(-(2*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*lambda+4*mu^2))*alpha[1]^2*a[5]*alpha[0]-12*mu^2*alpha[1]^2*a[5]*alpha[0]+(3*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*alpha[1]^2*alpha[0]*a[2]+(4*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*alpha[1]^2*lambda*a[5]*alpha[0]-7*mu*beta[0]*lambda*a[5]*alpha[1]^2+24*mu*beta[0]*alpha[1]^2*alpha[0]*a[3]-9*mu^2*alpha[1]^2*a[1]*(1/4)-w*beta[0]^2+3*beta[0]^2*alpha[0]*a[2]-(1/4)*lambda*beta[0]^2*a[1]-k^2*a[1]*beta[0]^2+10*beta[0]^2*alpha[0]^3*a[4]+6*beta[0]^2*alpha[0]^2*a[3]-(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda)*w*alpha[1]^2+3*mu*a[1]*alpha[0]*beta[0]*(1/2)+(-(2*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*lambda+4*mu^2)*alpha[1]^4*a[3]+3*mu*beta[0]*a[5]*alpha[0]^2-6*lambda*beta[0]^2*alpha[1]^2*a[3]-2*lambda*beta[0]^2*a[5]*alpha[0]+6*mu*beta[0]*alpha[1]^2*a[2]+60*mu*beta[0]*alpha[1]^2*alpha[0]^2*a[4] = 0
> 

eq4 := 2*mu*alpha[1]^3*a[2]-2*w*alpha[1]*beta[0]-20*lambda*beta[0]*alpha[1]^3*alpha[0]*a[4]-2*lambda*beta[0]*a[5]*alpha[1]*alpha[0]-2*k^2*a[1]*alpha[1]*beta[0]+20*beta[0]*alpha[1]*alpha[0]^3*a[4]+12*beta[0]*alpha[1]*alpha[0]^2*a[3]+6*beta[0]*alpha[1]*alpha[0]*a[2]+8*mu*alpha[1]^3*alpha[0]*a[3]+mu*alpha[1]*a[5]*alpha[0]^2+(1/2)*mu*alpha[1]*alpha[0]*a[1]-4*lambda*beta[0]*alpha[1]^3*a[3]-lambda*alpha[1]^3*mu*a[5]-(1/2)*lambda*beta[0]*alpha[1]*a[1]+20*mu*alpha[1]^3*alpha[0]^2*a[4]-4*mu*lambda*alpha[1]^5*a[4] = 0
> 

eq5 := -6*mu^2*alpha[1]^3*a[5]+(2*(-(2*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*lambda+4*mu^2))*alpha[1]^3*a[5]+(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda)*alpha[1]^3*a[2]+(-(2*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*lambda+4*mu^2)*alpha[1]^5*a[4]+3*beta[0]^2*alpha[1]*a[2]+40*mu*beta[0]*alpha[1]^3*alpha[0]*a[4]+8*mu*beta[0]*a[5]*alpha[1]*alpha[0]+30*beta[0]^2*alpha[1]*alpha[0]^2*a[4]+12*beta[0]^2*alpha[1]*alpha[0]*a[3]+(4*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*alpha[1]^3*alpha[0]*a[3]+(2*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*alpha[1]*a[5]*alpha[0]^2+(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda)*alpha[1]*alpha[0]*a[1]+8*mu*beta[0]*alpha[1]^3*a[3]+3*mu*beta[0]*alpha[1]*a[1]*(1/2)-10*lambda*beta[0]^2*alpha[1]^3*a[4]-2*lambda*beta[0]^2*a[5]*alpha[1]+(10*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*alpha[1]^3*alpha[0]^2*a[4]+(2*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*alpha[1]^3*lambda*a[5] = 0
> 

eq6 := -14*mu^2*beta[0]*a[5]*alpha[1]^2+beta[0]^3*a[2]+(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda)*a[1]*alpha[0]*beta[0]+12*mu*beta[0]^2*alpha[1]^2*a[3]+6*mu*beta[0]^2*a[5]*alpha[0]-10*lambda*beta[0]^3*alpha[1]^2*a[4]+(6*(-(2*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*lambda+4*mu^2))*beta[0]*a[5]*alpha[1]^2+(3*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*beta[0]*alpha[1]^2*a[2]+(2*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*beta[0]*a[5]*alpha[0]^2+(5*(-(2*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*lambda+4*mu^2))*beta[0]*alpha[1]^4*a[4]+(4*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*mu*alpha[1]^4*a[3]+(2*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*mu*alpha[1]^2*a[1]+10*beta[0]^3*alpha[0]^2*a[4]+4*beta[0]^3*alpha[0]*a[3]-lambda*beta[0]^3*a[5]+mu*beta[0]^2*a[1]+(20*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*mu*alpha[1]^4*alpha[0]*a[4]+(10*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*mu*alpha[1]^2*a[5]*alpha[0]+(30*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*beta[0]*alpha[1]^2*alpha[0]^2*a[4]+(5*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*beta[0]*lambda*a[5]*alpha[1]^2+(12*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*beta[0]*alpha[1]^2*alpha[0]*a[3]+60*mu*beta[0]^2*alpha[1]^2*alpha[0]*a[4] = 0
> 

eq7 := 4*beta[0]^3*alpha[1]*a[3]+(20*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*beta[0]*alpha[1]^3*alpha[0]*a[4]+(8*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*beta[0]*a[5]*alpha[1]*alpha[0]+20*beta[0]^3*alpha[1]*alpha[0]*a[4]+(4*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*beta[0]*alpha[1]^3*a[3]+(5*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*alpha[1]^3*mu*a[5]+(1/2)*(3*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*beta[0]*alpha[1]*a[1]+20*mu*beta[0]^2*alpha[1]^3*a[4]+7*mu*beta[0]^2*a[5]*alpha[1]+(4*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*mu*alpha[1]^5*a[4] = 0
> 

eq8 := 4*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda)^2*alpha[1]^2*a[5]*alpha[0]+5*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda)^2*alpha[1]^4*alpha[0]*a[4]+beta[0]^4*a[3]+(6*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*beta[0]^2*alpha[1]^2*a[3]+(4*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*beta[0]^2*a[5]*alpha[0]+20*mu*beta[0]^3*alpha[1]^2*a[4]+(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda)^2*alpha[1]^4*a[3]+3*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda)^2*alpha[1]^2*a[1]*(1/4)+5*beta[0]^4*alpha[0]*a[4]+3*mu*beta[0]^3*a[5]+(1/4)*(3*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*beta[0]^2*a[1]+(30*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*beta[0]^2*alpha[1]^2*alpha[0]*a[4]+(17*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*beta[0]*mu*a[5]*alpha[1]^2+(20*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*beta[0]*mu*alpha[1]^4*a[4] = 0
> 

eq9 := (10*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*beta[0]^2*alpha[1]^3*a[4]+(6*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*beta[0]^2*a[5]*alpha[1]+5*beta[0]^4*alpha[1]*a[4]+(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda)^2*alpha[1]^5*a[4]+2*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda)^2*alpha[1]^3*a[5] = 0
> 

eq10 := (2*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*beta[0]^3*a[5]+beta[0]^5*a[4]+5*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda)^2*beta[0]*alpha[1]^4*a[4]+6*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda)^2*beta[0]*a[5]*alpha[1]^2+(10*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*beta[0]^3*alpha[1]^2*a[4] = 0
 
> 

with(LargeExpressions)
> 

COEFFS := solve({eq0, eq1, eq10, eq2, eq3, eq4, eq5, eq6, eq7, eq8, eq9}, {w, a[1], a[2], alpha[0], alpha[1], beta[0]})

Download by_hand!.mw

Can Maple Handle Fuzzy Derivatives and Plotting in...

Asked by: salim-barzani 1390
derivative plotting
May 02 2025
1  1

This question is actually on behalf of a colleague who works with fuzzy mathematics. He typically computes things like fuzzy derivatives by hand, including for specific functions such as "function 14" (though I'm not familiar with the specific form of that function). He’s interested in whether Maple can symbolically and numerically handle tasks in fuzzy calculus — especially taking and plotting fuzzy derivatives.

I’m not experienced with fuzzy systems myself, but I’d like to recommend Maple to him if it supports these features. So my main questions are:

  1. Can Maple compute and plot fuzzy functions and their derivatives?

  2. Does Maple have built-in support or packages for fuzzy arithmetic or fuzzy calculus?

  3. If not natively, is there a workaround or external library that integrates with Maple to do this?

I’d really appreciate any insights or examples. It seems like a missed opportunity for my friend to be doing all this manually when such software might already handle it.

Thanks in advance!

 

Older posts missing images...

Asked by: Christopher2222 5950
image deleted incomplete-question
May 02 2025
1  1

What's with some of the older posts missing images?  Were they deleted by maplesoft to save space on mapleprimes servers?  (Storage is pretty cheap these days)

I actually replaced some images a while ago, maybe a few years back.  However I've come across the post again and the image is gone ... strange.  Maybe there's an AI at work here clearing out images. 

In some cases the images are just the output of Maple code plots.  That's ok to remove, I guess, but in others, people have used screenshots which contain code that have been removed where in some cases after they're removed make the entire thread useless.  It's not often but it occurs. 

Anyways, does mapleprimes sometimes clear out images?  Or is it an inadvertent effect when some maintenance is performed?

why some help pages are empty?...

Asked by: nm 11173
documentation
May 01 2025
3  1

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?

 

 

Slider Plot and Value Substitution Help...

Asked by: Andiguys 65
parameters explore plotting
April 29 2025
0  4

I need to create a slider plot for A10, A11, and A12 by varying the parameters theta, Pu, and a.
I have a syntax ready — could you suggest modifications to make it work correctly and generate the plot?

Additionally, is it possible to compute the values of A13 and A14 by substituting the obtained A10, A11, and A12 values for each combination of theta, Pu, and a from the slider plot?

Sheet attached: Slider_Q.mw

Compute integral exactly ...

Asked by: Zeineb 540
integration
April 27 2025
0  0

Dear all 
I have a double integral, i want to compute this integral and verify if the pproposed solution verify the proposed equation or not. 
I can modify the right hand side of my equation or the exact solution, so that my equation has an exact solution with simple form of right hand side. 

exact_solution.mw

Thank you for your help 

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