MaplePrimes Questions

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I am trying to create a diagram in Maple using its plotting tools and simulate a simply connected domain and multiple paths between two points.

My first try is the following

with(plots); with(plottools)

 

 

curveDomainPts := [[-1, 0], [-.7, 1.2], [0, 1.5], [.7, 1.2], [1.2, 0], [.7, -1.2], [0, -1.4], [-.7, -1.2], [-1, 0]]; domain := polygon(curveDomainPts, color = "LightBlue", transparency = .4); z0 := [-.8, .6]; z := [.9, -.4]; curve1_pts := [[-.8, .6], [-.3, 1.0], [.4, .5], [.9, -.4]]; curve2_pts := [[-.8, .6], [-.7, 0.], [.2, -.6], [.9, -.4]]; curve1 := pointplot(curve1_pts, color = red, linestyle = dot, thickness = 2, connect = true); curve2 := pointplot(curve2_pts, color = green, linestyle = dot, thickness = 2, connect = true); pt1 := pointplot([z0], symbol = solidcircle, symbolsize = 15, color = black); pt2 := pointplot([z], symbol = solidcircle, symbolsize = 15, color = black); label1 := textplot([z0[1], z0[2]-.1, z__0], font = [Helvetica, Bold, 14]); label2 := textplot([z[1], z[2]-.1, "z"], font = [Helvetica, Bold, 14]); display(domain, curve1, curve2, pt1, pt2, label1, label2, scaling = constrained, axes = none, title = "Curved Domain with Arbitrary Paths")

 
 

NULL

I would like to ask if I could create something like that in Maple or should I use another software to draw it?

Download curved_domain.mw

Dear all
How can I compute the integral from a to b of   y^2 cot(y)

Thank you

With Maple 2015, but maybe for more recent versions too, I try to understant fow the simplification rules apply in the cas of the expression 

f := n -> (ln(x)^n)^(1/n)

Here n is assumed to be strictly positive and I consider only the cases "n is an integer" or "1/n is an integer".

All the questions are orange written in the attached file and resumed below:

  1. Why symplify(f(2)) simplifies f(2) whereas symplify(f(n)) doesn't simplifies f(n) for any integer n > 2?
     
  2. Why symplify(f(1/n)) simplifies f(1/n)?
     
  3. Why symplify(f(3)) with adhoc assumptions returns a simplified expression of some form whereas, for any integer n > 3,  symplify(f(n)) with (the same corresponding) adhoc assumptions returns a simplified expression of a complete different form than with n=3?

Can you please have a look to it and give me some clarifications?
Simplification_rules.mw

Thanks in advance

When using FunctionAdvisor(branch_cuts, f(x), plot="2D"); how do I enforce discontinuous lines be presented with option discont=true?

To save space, I've decided to show problems found so far in Maple 2025 in one worksheet.

Hoping someone will figure the cause. The big problem is that these internal errors can not be cought using try/catch. Which means there is no user workaround. If they can be cought, then it is not a big problem.

Some from odetest, some from int and some from simplify and some from symgen.

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 1861 and is the same as the version installed in this computer, created 2025, April 10, 15:58 hours Pacific Time.`

restart;

#18573
e:=(1/4*(RootOf(-100*_Z^4*exp(arctanh(1/3*(5*_Z^2-32*_Z+80)/(_Z^2-16))+arctanh(1/3*(5*_Z^2+32*_Z+80)/(_Z^2-16)))+x^(16/5)*_Z^4*exp(_C11)^16-68*x^(16/5)*_Z^2*exp(_C11)^16+256*x^(16/5)*exp(_C11)^16)^2+16)/RootOf(-100*_Z^4*exp(arctanh(1/3*(5*_Z^2-32*_Z+80)/(_Z^2-16))+arctanh(1/3*(5*_Z^2+32*_Z+80)/(_Z^2-16)))+x^(16/5)*_Z^4*exp(_C11)^16-68*x^(16/5)*_Z^2*exp(_C11)^16+256*x^(16/5)*exp(_C11)^16)-1/2*(1/4*(RootOf(-100*_Z^4*exp(arctanh(1/3*(5*_Z^2-32*_Z+80)/(_Z^2-16))+arctanh(1/3*(5*_Z^2+32*_Z+80)/(_Z^2-16)))+x^(16/5)*_Z^4*exp(_C11)^16-68*x^(16/5)*_Z^2*exp(_C11)^16+256*x^(16/5)*exp(_C11)^16)^2+16)^2/RootOf(-100*_Z^4*exp(arctanh(1/3*(5*_Z^2-32*_Z+80)/(_Z^2-16))+arctanh(1/3*(5*_Z^2+32*_Z+80)/(_Z^2-16)))+x^(16/5)*_Z^4*exp(_C11)^16-68*x^(16/5)*_Z^2*exp(_C11)^16+256*x^(16/5)*exp(_C11)^16)^2-16)^(1/2))*x:

try
    timelimit(60,simplify(e));
catch:
    print("OK, cought error");
end try;

 

Error, (in anonymous procedure called from depends) too many levels of recursion

restart;

#12178
ode:=diff(y(x),x) = lambda*arctan(x)^n*y(x)^2+beta*m*x^(m-1)-lambda*beta^2*x^(2*m)*arctan(x)^n:
try
    timelimit(60,DEtools:-symgen(ode));
catch:
    print("OK, cought error");
end try;

Error, (in simplify/exp/exp) too many levels of recursion

restart;

#12181
ode:=diff(x(y),y) = x(y)/(x(y)^(2*m)*arctan(x(y))^m*a*y^2+x(y)^n*arctan(x(y))^m*b*y+arctan(x(y))^m*c-n*y):
try
    timelimit(60,DEtools:-symgen(ode));
catch:
    print("OK, cought error");
end try;

Error, (in simplify/exp/exp) too many levels of recursion

restart;

#12187
ode:=diff(y(x),x)=lambda*arccot(x)^n*y(x)^2+beta*m*x^(m-1)-lambda*beta^2*x^(2*m)*arccot(x)^n:
try
    timelimit(60,DEtools:-symgen(ode));
catch:
    print("OK, cought error");
end try;

Error, (in simplify/exp/exp) too many levels of recursion

restart;

#12190
ode:=diff(x(y),y) = x(y)/(x(y)^(2*m)*arccot(x(y))^m*a*y^2+x(y)^n*arccot(x(y))^m*b*y+arccot(x(y))^m*c-n*y):
try
    timelimit(60,DEtools:-symgen(ode));
catch:
    print("OK, cought error");
end try;

Error, (in simplify/exp/exp) too many levels of recursion

restart;

#10708
e:=2/(ln(x)-exp(1/x))*x*diff(diff(u(x),x),x)-(-2/(ln(x)-exp(1/x))^2*x*(1/x+1/x^2*exp(1/x))+2/(ln(x)-exp(1/x))+8*x^3/(ln(x)-exp(1/x))^2)*diff(u(x),x)-4/(ln(x)-exp(1/x))^3*x^2*(-2*x^3+ln(x)-exp(1/x)-2*x)*u(x):
e:=evala(e):
try
    timelimit(60,int(e,x));
catch:
    print("OK, cought error");
end try;

Error, (in anonymous procedure called from property/ConvertRelation) too many levels of recursion

restart;

#6764
e:=1/2/x^(7/2)*2^(1/2)*Pi^(1/2)/(1/x)^(1/2)*cos(1/x)*(1+x):
try
    timelimit(60,int(e,x));
catch:
    print("OK, cought error");
end try;

Error, (in simplify/common_factors/do) too many levels of recursion

restart;

#19337

sol:=-y+Intat((_a*((_a^2+1)/_a^2)^(1/2)+_a^2+1)*exp(-1/2*(arctanh(1/(_a^2+1)^(1/2))*((_a^2+1)/_a^2)^(1/2)*_a^3+2*_C3*(_a^2+1)^(1/2)*_a^2+(_a^2+1)^(1/2)*((_a^2+1)/_a^2)^(1/2)*_a+(_a^2+1)^(1/2))/(_a^2+1)^(1/2)/_a^2)/((_a^2+1)/_a^2)^(1/2)/_a^5,_a = RootOf(x(y)-exp(-1/2*(arctanh(1/(_Z^2+1)^(1/2))*((_Z^2+1)/_Z^2)^(1/2)*_Z^3+2*_C3*(_Z^2+1)^(1/2)*_Z^2+(_Z^2+1)^(1/2)*((_Z^2+1)/_Z^2)^(1/2)*_Z+(_Z^2+1)^(1/2))/(_Z^2+1)^(1/2)/_Z^2)))+_C4 = 0:
ode:=-1/2/(diff(x(y),y)^2+1)^(1/2)*(diff(x(y),y)*(arctanh(1/(diff(x(y),y)^2+1)^(1/2))*diff(x(y),y)^2+(diff(x(y),y)^2+1)^(1/2))*((diff(x(y),y)^2+1)/diff(x(y),y)^2)^(1/2)+(diff(x(y),y)^2+1)^(1/2))/diff(x(y),y)^2 = ln(x(y))+_C3:
try
    timelimit(60,odetest(sol,ode));
catch:
    print("OK, cought error");
end try;
 

Error, (in unknown) too many levels of recursion

 

 

Download collection_of_problems_maple_2025.mw

Below is worksheet showing output in Maple 2024.2. It shows NO internal error is generated in any one. Either a result is returned, or it timedout as expected.

This shows all the above cases are regressions in Maple 2025.

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 1861. 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;

#18573
e:=(1/4*(RootOf(-100*_Z^4*exp(arctanh(1/3*(5*_Z^2-32*_Z+80)/(_Z^2-16))+arctanh(1/3*(5*_Z^2+32*_Z+80)/(_Z^2-16)))+x^(16/5)*_Z^4*exp(_C11)^16-68*x^(16/5)*_Z^2*exp(_C11)^16+256*x^(16/5)*exp(_C11)^16)^2+16)/RootOf(-100*_Z^4*exp(arctanh(1/3*(5*_Z^2-32*_Z+80)/(_Z^2-16))+arctanh(1/3*(5*_Z^2+32*_Z+80)/(_Z^2-16)))+x^(16/5)*_Z^4*exp(_C11)^16-68*x^(16/5)*_Z^2*exp(_C11)^16+256*x^(16/5)*exp(_C11)^16)-1/2*(1/4*(RootOf(-100*_Z^4*exp(arctanh(1/3*(5*_Z^2-32*_Z+80)/(_Z^2-16))+arctanh(1/3*(5*_Z^2+32*_Z+80)/(_Z^2-16)))+x^(16/5)*_Z^4*exp(_C11)^16-68*x^(16/5)*_Z^2*exp(_C11)^16+256*x^(16/5)*exp(_C11)^16)^2+16)^2/RootOf(-100*_Z^4*exp(arctanh(1/3*(5*_Z^2-32*_Z+80)/(_Z^2-16))+arctanh(1/3*(5*_Z^2+32*_Z+80)/(_Z^2-16)))+x^(16/5)*_Z^4*exp(_C11)^16-68*x^(16/5)*_Z^2*exp(_C11)^16+256*x^(16/5)*exp(_C11)^16)^2-16)^(1/2))*x:

try
    timelimit(60,simplify(e));
catch:
    print("OK, cought error");
end try;

 

(1/4)*(RootOf(-100*_Z^4*exp(arctanh((1/3)*(5*_Z^2-32*_Z+80)/(_Z^2-16))+arctanh((1/3)*(5*_Z^2+32*_Z+80)/(_Z^2-16)))+x^(16/5)*_Z^4*exp(16*_C11)-68*x^(16/5)*_Z^2*exp(16*_C11)+256*x^(16/5)*exp(16*_C11))^2-((RootOf(-100*_Z^4*exp(arctanh((1/3)*(5*_Z^2-32*_Z+80)/(_Z^2-16))+arctanh((1/3)*(5*_Z^2+32*_Z+80)/(_Z^2-16)))+x^(16/5)*_Z^4*exp(16*_C11)-68*x^(16/5)*_Z^2*exp(16*_C11)+256*x^(16/5)*exp(16*_C11))^2-16)^2/RootOf(-100*_Z^4*exp(arctanh((1/3)*(5*_Z^2-32*_Z+80)/(_Z^2-16))+arctanh((1/3)*(5*_Z^2+32*_Z+80)/(_Z^2-16)))+x^(16/5)*_Z^4*exp(16*_C11)-68*x^(16/5)*_Z^2*exp(16*_C11)+256*x^(16/5)*exp(16*_C11))^2)^(1/2)*RootOf(-100*_Z^4*exp(arctanh((1/3)*(5*_Z^2-32*_Z+80)/(_Z^2-16))+arctanh((1/3)*(5*_Z^2+32*_Z+80)/(_Z^2-16)))+x^(16/5)*_Z^4*exp(16*_C11)-68*x^(16/5)*_Z^2*exp(16*_C11)+256*x^(16/5)*exp(16*_C11))+16)*x/RootOf(-100*_Z^4*exp(arctanh((1/3)*(5*_Z^2-32*_Z+80)/(_Z^2-16))+arctanh((1/3)*(5*_Z^2+32*_Z+80)/(_Z^2-16)))+x^(16/5)*_Z^4*exp(16*_C11)-68*x^(16/5)*_Z^2*exp(16*_C11)+256*x^(16/5)*exp(16*_C11))

restart;

#12178
ode:=diff(y(x),x) = lambda*arctan(x)^n*y(x)^2+beta*m*x^(m-1)-lambda*beta^2*x^(2*m)*arctan(x)^n:
try
    timelimit(60,DEtools:-symgen(ode));
catch:
    print("OK, cought error");
end try;

"OK, cought error"

restart;

#12181
ode:=diff(x(y),y) = x(y)/(x(y)^(2*m)*arctan(x(y))^m*a*y^2+x(y)^n*arctan(x(y))^m*b*y+arctan(x(y))^m*c-n*y):
try
    r:=timelimit(60,DEtools:-symgen(ode));
catch:
    print("OK, cought error");
end try;

restart;

#12187
ode:=diff(y(x),x)=lambda*arccot(x)^n*y(x)^2+beta*m*x^(m-1)-lambda*beta^2*x^(2*m)*arccot(x)^n:
try
    r:=timelimit(60,DEtools:-symgen(ode));
catch:
    print("OK, cought error");
end try;

"OK, cought error"

restart;

#12190
ode:=diff(x(y),y) = x(y)/(x(y)^(2*m)*arccot(x(y))^m*a*y^2+x(y)^n*arccot(x(y))^m*b*y+arccot(x(y))^m*c-n*y):
try
    r:=timelimit(60,DEtools:-symgen(ode));
catch:
    print("OK, cought error");
end try;

"OK, cought error"

restart;

#10708
e:=2/(ln(x)-exp(1/x))*x*diff(diff(u(x),x),x)-(-2/(ln(x)-exp(1/x))^2*x*(1/x+1/x^2*exp(1/x))+2/(ln(x)-exp(1/x))+8*x^3/(ln(x)-exp(1/x))^2)*diff(u(x),x)-4/(ln(x)-exp(1/x))^3*x^2*(-2*x^3+ln(x)-exp(1/x)-2*x)*u(x):
e:=evala(e):
try
    timelimit(60,int(e,x));
catch:
    print("OK, cought error");
end try;

"OK, cought error"

restart;

#6764
e:=1/2/x^(7/2)*2^(1/2)*Pi^(1/2)/(1/x)^(1/2)*cos(1/x)*(1+x):
try
    r:=timelimit(60,int(e,x));
catch:
    print("OK, cought error");
end try;

"OK, cought error"

restart;

#19337

sol:=-y+Intat((_a*((_a^2+1)/_a^2)^(1/2)+_a^2+1)*exp(-1/2*(arctanh(1/(_a^2+1)^(1/2))*((_a^2+1)/_a^2)^(1/2)*_a^3+2*_C3*(_a^2+1)^(1/2)*_a^2+(_a^2+1)^(1/2)*((_a^2+1)/_a^2)^(1/2)*_a+(_a^2+1)^(1/2))/(_a^2+1)^(1/2)/_a^2)/((_a^2+1)/_a^2)^(1/2)/_a^5,_a = RootOf(x(y)-exp(-1/2*(arctanh(1/(_Z^2+1)^(1/2))*((_Z^2+1)/_Z^2)^(1/2)*_Z^3+2*_C3*(_Z^2+1)^(1/2)*_Z^2+(_Z^2+1)^(1/2)*((_Z^2+1)/_Z^2)^(1/2)*_Z+(_Z^2+1)^(1/2))/(_Z^2+1)^(1/2)/_Z^2)))+_C4 = 0:
ode:=-1/2/(diff(x(y),y)^2+1)^(1/2)*(diff(x(y),y)*(arctanh(1/(diff(x(y),y)^2+1)^(1/2))*diff(x(y),y)^2+(diff(x(y),y)^2+1)^(1/2))*((diff(x(y),y)^2+1)/diff(x(y),y)^2)^(1/2)+(diff(x(y),y)^2+1)^(1/2))/diff(x(y),y)^2 = ln(x(y))+_C3:
try
    r:=timelimit(60,odetest(sol,ode));
catch:
    print("OK, cought error");
end try;
 

-(1/2)*RootOf(x(y)-exp(-(1/2)*(arctanh(1/(_Z^2+1)^(1/2))*((_Z^2+1)/_Z^2)^(1/2)*_Z^3+2*c__3*(_Z^2+1)^(1/2)*_Z^2+(_Z^2+1)^(1/2)*((_Z^2+1)/_Z^2)^(1/2)*_Z+(_Z^2+1)^(1/2))/((_Z^2+1)^(1/2)*_Z^2)))*arctanh(1/(RootOf(x(y)-exp(-(1/2)*(arctanh(1/(_Z^2+1)^(1/2))*((_Z^2+1)/_Z^2)^(1/2)*_Z^3+2*c__3*(_Z^2+1)^(1/2)*_Z^2+(_Z^2+1)^(1/2)*((_Z^2+1)/_Z^2)^(1/2)*_Z+(_Z^2+1)^(1/2))/((_Z^2+1)^(1/2)*_Z^2)))^2+1)^(1/2))*(1+1/RootOf(x(y)-exp(-(1/2)*(arctanh(1/(_Z^2+1)^(1/2))*((_Z^2+1)/_Z^2)^(1/2)*_Z^3+2*c__3*(_Z^2+1)^(1/2)*_Z^2+(_Z^2+1)^(1/2)*((_Z^2+1)/_Z^2)^(1/2)*_Z+(_Z^2+1)^(1/2))/((_Z^2+1)^(1/2)*_Z^2)))^2)^(1/2)/(RootOf(x(y)-exp(-(1/2)*(arctanh(1/(_Z^2+1)^(1/2))*((_Z^2+1)/_Z^2)^(1/2)*_Z^3+2*c__3*(_Z^2+1)^(1/2)*_Z^2+(_Z^2+1)^(1/2)*((_Z^2+1)/_Z^2)^(1/2)*_Z+(_Z^2+1)^(1/2))/((_Z^2+1)^(1/2)*_Z^2)))^2+1)^(1/2)-ln(x(y))-c__3-(1/2)*(1+1/RootOf(x(y)-exp(-(1/2)*(arctanh(1/(_Z^2+1)^(1/2))*((_Z^2+1)/_Z^2)^(1/2)*_Z^3+2*c__3*(_Z^2+1)^(1/2)*_Z^2+(_Z^2+1)^(1/2)*((_Z^2+1)/_Z^2)^(1/2)*_Z+(_Z^2+1)^(1/2))/((_Z^2+1)^(1/2)*_Z^2)))^2)^(1/2)/RootOf(x(y)-exp(-(1/2)*(arctanh(1/(_Z^2+1)^(1/2))*((_Z^2+1)/_Z^2)^(1/2)*_Z^3+2*c__3*(_Z^2+1)^(1/2)*_Z^2+(_Z^2+1)^(1/2)*((_Z^2+1)/_Z^2)^(1/2)*_Z+(_Z^2+1)^(1/2))/((_Z^2+1)^(1/2)*_Z^2)))-(1/2)/RootOf(x(y)-exp(-(1/2)*(arctanh(1/(_Z^2+1)^(1/2))*((_Z^2+1)/_Z^2)^(1/2)*_Z^3+2*c__3*(_Z^2+1)^(1/2)*_Z^2+(_Z^2+1)^(1/2)*((_Z^2+1)/_Z^2)^(1/2)*_Z+(_Z^2+1)^(1/2))/((_Z^2+1)^(1/2)*_Z^2)))^2

Download collection_of_problems_maple_2024_version.mw

This looks like regression in dsolve.

In Maple 2024.2, dsolve solves this with no problem and very quickly. 

In Maple 2025 it just hangs.

Any one could find why this is the case? infolevel does not show why. Below is Maple 2024.2 worksheet and Maple 2025 worksheet.  This is Maple 2024.2 NO HANG

interface(version);

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

ode:=diff(y(x),x)+((y(x)+1)*(y(x)-1)*(y(x)-2))/(x+1)=0;
IC:=y(1)=0;

diff(y(x), x)+(y(x)+1)*(y(x)-1)*(y(x)-2)/(x+1) = 0

y(1) = 0

DEtools:-odeadvisor(ode);

[_separable]

infolevel[dsolve]:=5;
dsolve([ode,IC])

5

 -> Computing symmetries using: way = 3

Methods for first order ODEs:

--- Trying classification methods ---

trying a quadrature

trying 1st order linear

trying Bernoulli

trying separable

<- separable successful

y(x) = RootOf(-2048+(x^6+6*x^5+15*x^4+20*x^3+15*x^2+6*x+257)*_Z^18+(-6*x^6-36*x^5-90*x^4-120*x^3-90*x^2-36*x-1542)*_Z^12+(9*x^6+54*x^5+135*x^4+180*x^3+135*x^2+54*x+3081)*_Z^6)^6-1

 

 

Download dsolve_2024_no_hang_april_20_2025.mw

This is Maple 2025. HANGed. Had to terminate it after 15 minutes. It seems to hang on resolving initial conditions. 

interface(version);

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

ode:=diff(y(x),x)+((y(x)+1)*(y(x)-1)*(y(x)-2))/(x+1)=0;
IC:=y(1)=0;

diff(y(x), x)+(y(x)+1)*(y(x)-1)*(y(x)-2)/(x+1) = 0

y(1) = 0

DEtools:-odeadvisor(ode);

[_separable]

infolevel[dsolve]:=5;
dsolve([ode,IC])

5

 -> Computing symmetries using: way = 3

Methods for first order ODEs:

--- Trying classification methods ---

trying a quadrature

trying 1st order linear

trying Bernoulli

trying separable

<- separable successful

 

 

Download dsolve_2025_on_linux_hangs_april_20_2025.mw

Given a graph G and a vertex u of G, the problem of determining whether there exists a cycle of length k starting at u is a common one in graph theory.

Mathematica provides a function Findcycle for this task, though I am not sure which algorithm it employs—perhaps depth-first search (DFS)? Maple, on the other hand, does not appear to have a corresponding built-in function.

Hi, why does Maple always automatically distribute coefficients in expressions? For example, if I enter 2*(a + b + c), the result is always 2*a + 2*b + 2*c. Is there a way to keep it as 2*(a + b + c) instead?

Hello everyone,

How I get a plot for this function ? What means numeric values ? 

Thanks !

 

restart

T[S] := 290

eta := 17; lambda := 24

h := .2; `&ohm;` := 2*Pi*10; R := 2

T(x[2]) := eta*`&ohm;`^2*R^2*[x[2]/h-(1/2)*(x[2]/h)^2]/lambda+T[S]

eta*`&ohm;`^2*R^2*[x[2]/h-(1/2)*(x[2]/h)^2]/lambda+T[S]

(1)

plot(T(x[2]), x[2] = .1 .. .2)

Warning, unable to evaluate the function to numeric values in the region; see the plotting command's help page to ensure the calling sequence is correct

 

 


Download TSL_bung_9.mwTSL_bung_9.mw

I am just wondering why something that has been bothering me since Maple V up to including Maple 2024 has never been resolved properly.

Why is it so difficult for maple to solve a dead obvious and simple expression e.g.

sqrt(cos(gamma)^(5/3)/sin(2*gamma)^(5/3));

You can use algsubs to tell maple to use an elementary identity to substitute the double angle away, but even then it refuses to simplify the remaining fraction which is elementary at most.

So, when will e.g. this simple multiple generational issue be addressed  so maple can do the obvious simplifications.

There are much more severe examples concerning trigonometric functions under square roots, which was left out in this case to show just one issue.

How i can get this special parameter i try to do substitution in another mw file but stilli can't reach this parameter and without this parameter my PDE is not give me zero so i have to find this r[i] parameter, some letter of my mw file are not similar to paper but r[i]=l[i] as mention is paper al clear and i found all structure just this remain, i am looking for equation (14), thanks for any help 

restart

with(PDEtools)

with(LinearAlgebra)

NULL

with(SolveTools)

_local(gamma)

Warning, A new binding for the name `gamma` has been created. The global instance of this name is still accessible using the :- prefix, :-`gamma`.  See ?protect for details.

 

NULL

declare(u(x, y, z, t))

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

(1)

declare(f(x, y, z, t))

f(x, y, z, t)*`will now be displayed as`*f

(2)

pde1 := a*(diff(u(x, y, z, t), x, t))-((a^4-6*a^2*b^2+b^4)*(1/16))*(diff(u(x, y, z, t), `$`(x, 4)))-(1/4)*(3*(-a^2+b^2))*(diff(u(x, y, z, t)^2, `$`(x, 2)))+alpha*(diff(u(x, y, z, t), `$`(x, 2)))+beta*(diff(u(x, y, z, t), x, y))+delta*(diff(u(x, y, z, t), x, z))+lambda*(diff(u(x, y, z, t), `$`(z, 2)))+mu*(diff(u(x, y, z, t), y, z))+mu^2*(diff(u(x, y, z, t), `$`(y, 2)))/(4*lambda)

a*(diff(diff(u(x, y, z, t), t), x))-(1/16)*(a^4-6*a^2*b^2+b^4)*(diff(diff(diff(diff(u(x, y, z, t), x), x), x), x))-(3/4)*(-a^2+b^2)*(2*(diff(u(x, y, z, t), x))^2+2*u(x, y, z, t)*(diff(diff(u(x, y, z, t), x), x)))+alpha*(diff(diff(u(x, y, z, t), x), x))+beta*(diff(diff(u(x, y, z, t), x), y))+delta*(diff(diff(u(x, y, z, t), x), z))+lambda*(diff(diff(u(x, y, z, t), z), z))+mu*(diff(diff(u(x, y, z, t), y), z))+(1/4)*mu^2*(diff(diff(u(x, y, z, t), y), y))/lambda

(3)

Tr := {beta = alpha, delta = alpha, mu = 2*lambda}

{beta = alpha, delta = alpha, mu = 2*lambda}

(4)

pde := subs(Tr, pde1)

a*(diff(diff(u(x, y, z, t), t), x))-(1/16)*(a^4-6*a^2*b^2+b^4)*(diff(diff(diff(diff(u(x, y, z, t), x), x), x), x))-(3/4)*(-a^2+b^2)*(2*(diff(u(x, y, z, t), x))^2+2*u(x, y, z, t)*(diff(diff(u(x, y, z, t), x), x)))+alpha*(diff(diff(u(x, y, z, t), x), x))+alpha*(diff(diff(u(x, y, z, t), x), y))+alpha*(diff(diff(u(x, y, z, t), x), z))+lambda*(diff(diff(u(x, y, z, t), z), z))+2*lambda*(diff(diff(u(x, y, z, t), y), z))+lambda*(diff(diff(u(x, y, z, t), y), y))

(5)

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

a*(diff(diff(u(x, y, z, t), t), x))-(1/16)*(diff(diff(diff(diff(u(x, y, z, t), x), x), x), x))*a^4+(3/8)*(diff(diff(diff(diff(u(x, y, z, t), x), x), x), x))*a^2*b^2-(1/16)*(diff(diff(diff(diff(u(x, y, z, t), x), x), x), x))*b^4+alpha*(diff(diff(u(x, y, z, t), x), x))+alpha*(diff(diff(u(x, y, z, t), x), y))+alpha*(diff(diff(u(x, y, z, t), x), z))+lambda*(diff(diff(u(x, y, z, t), z), z))+2*lambda*(diff(diff(u(x, y, z, t), y), z))+lambda*(diff(diff(u(x, y, z, t), y), y)), (3/2)*(diff(u(x, y, z, t), x))^2*a^2-(3/2)*(diff(u(x, y, z, t), x))^2*b^2+(3/2)*u(x, y, z, t)*(diff(diff(u(x, y, z, t), x), x))*a^2-(3/2)*u(x, y, z, t)*(diff(diff(u(x, y, z, t), x), x))*b^2

(6)

NULL

eq17 := u(x, y, z, t) = (-a^4+6*a^2*b^2-b^4)*((diff(diff(f(x, y, z, t), x), x))/f(x, y, z, t)-(diff(f(x, y, z, t), x))^2/f(x, y, z, t)^2)/(2*a^2-2*b^2)

``NULL

betai := k[i]*(t*w[i]+y*l[i]+z*r[i]+x)+eta[i]

k[i]*(t*w[i]+y*l[i]+z*r[i]+x)+eta[i]

(7)

W := w[i] = ((a^4-6*a^2*b^2+b^4)*k[i]^2-16*lambda*l[i]^2+(-32*lambda*r[i]-16*alpha)*l[i]-16*lambda*r[i]^2-16*alpha*r[i]-16*alpha)/(16*a)

AA := A[12] = (16*(l[1]-l[2]+r[1]-r[2])^2*lambda+3*(k[1]-k[2])^2*(a^2+2*a*b-b^2)*(a^2-2*a*b-b^2))/(16*(l[1]-l[2]+r[1]-r[2])^2*lambda+3*(k[1]+k[2])^2*(a^2+2*a*b-b^2)*(a^2-2*a*b-b^2))

F2 := 1+exp(beta[1])+A[1, 2]*exp(beta[1]+beta[2])+exp(beta[2])

1+exp(beta[1])+A[1, 2]*exp(beta[1]+beta[2])+exp(beta[2])

(8)

NULL

F22 := f(x, y, z, t) = 1+exp((a^4*t*k[1]^3-6*a^2*b^2*t*k[1]^3+b^4*t*k[1]^3-16*lambda*t*k[1]*l[1]^2-32*lambda*t*k[1]*l[1]*r[1]-16*lambda*t*k[1]*r[1]^2+16*a*y*k[1]*l[1]+16*a*z*k[1]*r[1]-16*alpha*t*k[1]*l[1]-16*alpha*t*k[1]*r[1]+16*a*x*k[1]-16*alpha*t*k[1]+16*a*eta[1])/(16*a))+exp((a^4*t*k[2]^3-6*a^2*b^2*t*k[2]^3+b^4*t*k[2]^3-16*lambda*t*k[2]*l[2]^2-32*lambda*t*k[2]*l[2]*r[2]-16*lambda*t*k[2]*r[2]^2+16*a*y*k[2]*l[2]+16*a*z*k[2]*r[2]-16*alpha*t*k[2]*l[2]-16*alpha*t*k[2]*r[2]+16*a*x*k[2]-16*alpha*t*k[2]+16*a*eta[2])/(16*a))

eq := eval(eq17, F22)

u(x, y, z, t) = (-a^4+6*a^2*b^2-b^4)*((k[1]^2*exp((1/16)*(a^4*t*k[1]^3-6*a^2*b^2*t*k[1]^3+b^4*t*k[1]^3-16*lambda*t*k[1]*l[1]^2-32*lambda*t*k[1]*l[1]*r[1]-16*lambda*t*k[1]*r[1]^2+16*a*y*k[1]*l[1]+16*a*z*k[1]*r[1]-16*alpha*t*k[1]*l[1]-16*alpha*t*k[1]*r[1]+16*a*x*k[1]-16*alpha*t*k[1]+16*a*eta[1])/a)+k[2]^2*exp((1/16)*(a^4*t*k[2]^3-6*a^2*b^2*t*k[2]^3+b^4*t*k[2]^3-16*lambda*t*k[2]*l[2]^2-32*lambda*t*k[2]*l[2]*r[2]-16*lambda*t*k[2]*r[2]^2+16*a*y*k[2]*l[2]+16*a*z*k[2]*r[2]-16*alpha*t*k[2]*l[2]-16*alpha*t*k[2]*r[2]+16*a*x*k[2]-16*alpha*t*k[2]+16*a*eta[2])/a))/(1+exp((1/16)*(a^4*t*k[1]^3-6*a^2*b^2*t*k[1]^3+b^4*t*k[1]^3-16*lambda*t*k[1]*l[1]^2-32*lambda*t*k[1]*l[1]*r[1]-16*lambda*t*k[1]*r[1]^2+16*a*y*k[1]*l[1]+16*a*z*k[1]*r[1]-16*alpha*t*k[1]*l[1]-16*alpha*t*k[1]*r[1]+16*a*x*k[1]-16*alpha*t*k[1]+16*a*eta[1])/a)+exp((1/16)*(a^4*t*k[2]^3-6*a^2*b^2*t*k[2]^3+b^4*t*k[2]^3-16*lambda*t*k[2]*l[2]^2-32*lambda*t*k[2]*l[2]*r[2]-16*lambda*t*k[2]*r[2]^2+16*a*y*k[2]*l[2]+16*a*z*k[2]*r[2]-16*alpha*t*k[2]*l[2]-16*alpha*t*k[2]*r[2]+16*a*x*k[2]-16*alpha*t*k[2]+16*a*eta[2])/a))-(k[1]*exp((1/16)*(a^4*t*k[1]^3-6*a^2*b^2*t*k[1]^3+b^4*t*k[1]^3-16*lambda*t*k[1]*l[1]^2-32*lambda*t*k[1]*l[1]*r[1]-16*lambda*t*k[1]*r[1]^2+16*a*y*k[1]*l[1]+16*a*z*k[1]*r[1]-16*alpha*t*k[1]*l[1]-16*alpha*t*k[1]*r[1]+16*a*x*k[1]-16*alpha*t*k[1]+16*a*eta[1])/a)+k[2]*exp((1/16)*(a^4*t*k[2]^3-6*a^2*b^2*t*k[2]^3+b^4*t*k[2]^3-16*lambda*t*k[2]*l[2]^2-32*lambda*t*k[2]*l[2]*r[2]-16*lambda*t*k[2]*r[2]^2+16*a*y*k[2]*l[2]+16*a*z*k[2]*r[2]-16*alpha*t*k[2]*l[2]-16*alpha*t*k[2]*r[2]+16*a*x*k[2]-16*alpha*t*k[2]+16*a*eta[2])/a))^2/(1+exp((1/16)*(a^4*t*k[1]^3-6*a^2*b^2*t*k[1]^3+b^4*t*k[1]^3-16*lambda*t*k[1]*l[1]^2-32*lambda*t*k[1]*l[1]*r[1]-16*lambda*t*k[1]*r[1]^2+16*a*y*k[1]*l[1]+16*a*z*k[1]*r[1]-16*alpha*t*k[1]*l[1]-16*alpha*t*k[1]*r[1]+16*a*x*k[1]-16*alpha*t*k[1]+16*a*eta[1])/a)+exp((1/16)*(a^4*t*k[2]^3-6*a^2*b^2*t*k[2]^3+b^4*t*k[2]^3-16*lambda*t*k[2]*l[2]^2-32*lambda*t*k[2]*l[2]*r[2]-16*lambda*t*k[2]*r[2]^2+16*a*y*k[2]*l[2]+16*a*z*k[2]*r[2]-16*alpha*t*k[2]*l[2]-16*alpha*t*k[2]*r[2]+16*a*x*k[2]-16*alpha*t*k[2]+16*a*eta[2])/a))^2)/(2*a^2-2*b^2)

(9)

pdetest(eq, pde)

Download fusion-undon.mw

In the below I would like to format the odes as they appear in the second and third ode (in green brackets).

I.e. making the first operand with the minus sign inside the parentheses the second one. I was hoping for simplify,size but that does not do the trick.

How to do this?

Format_odes.mw

Dear Maple Support Team and Community,

    I would like to report what seems to be a bug in Maple's MatrixExponential function in the LinearAlgebra package.

    Consider the following 8×8 skew-Hermitian matrix B:
 

B := Matrix(8, 8, [[0, I, 0, -I, 0, I, 0, -I], 
                   [-I, 0, I, 0, -I, 0, I, 0], 
                   [0, -I, 0, I, 0, -I, 0, I], 
                   [I, 0, -I, 0, I, 0, -I, 0], 
                   [0, I, 0, -I, 0, I, 0, -I], 
                   [-I, 0, I, 0, -I, 0, I, 0], 
                   [0, -I, 0, I, 0, -I, 0, I], 
                   [I, 0, -I, 0, I, 0, -I, 0]]);

    Now compute the matrix exponential exp(I*t*B) using MatrixExponential

H := LinearAlgebra:-MatrixExponential(I * t * B);

However, this result is inconsistent with the matrix exponential computed using MATLAB and SageMath, both of which give the same result, different from Maple's.

I would appreciate it if someone from the development team could look into this.

For the attached file I ask for help with the plot of sol_1 for x>0.1 .

chini dgl.mw

i want to find critical point but becuase the equation is ong the result not shown up i try to put variable and then result show up but the number are to ugly and so long i want make them be 1 number without any decimal can we do that?

short-Dc.mw

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