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    Plotting a simply connected domain and multiple p...

    Asked by: Paras31 215
    convexhull domain plotting
    1 hour ago
    0  0

    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

    Integral exact value...

    Asked by: Zeineb 535
    integration
    4 hours ago
    0  1

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

    Thank you

    Simplification of (ln(x)^n)^(1/n)...

    Asked by: mmcdara 7601
    simplify simplification ln
    5 hours ago
    0  0

    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

    Discontinuities in branch cuts....

    Asked by: Christian Wolinski 1645
    discontinuity functionadvisor
    Yesterday at 6:33 PM
    0  1

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

    collection of problems in Maple 2025. Looking for ...

    Asked by: nm 11018
    simplify int odetest
    Yesterday at 5:42 PM
    3  0

    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

    why Maple 2025 hangs on this separable ode?...

    Asked by: nm 11018
    ode dsolve differential-equations
    April 20 2025
    2  0

    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

    Determine whether a vertex lies on a cycle of give...

    Asked by: lcz 1039
    graphtheory
    April 20 2025
    2  3

    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.

    Maple always automatically distribute coefficients...

    Asked by: bathudaide 25
    automatic-simplification inertform
    April 20 2025
    0  2

    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?

    unable to evaluate the function...

    Asked by: Mapleliquid 20
    syntax plotting
    April 20 2025
    1  3

    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

    The Old Simplification problem....

    Asked by: segfault 145
    radical simplification trig
    April 19 2025
    1  2

    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 find the parameter in PDE ?...

    Asked by: salim-barzani 950
    parameters substitution pde
    April 19 2025
    3  6

    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

    How to format this set of odes...

    Asked by: C_R 3212
    sort sorting sign
    April 19 2025
    1  5

    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

    Bug of "MatrixExponential" Function in t...

    Asked by: MathGuru 5
    linearalgebra matlab matrixexponential
    April 19 2025
    1  7

    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.

    Plot help requested...

    Asked by: Alfred_F 280
    rtfm plotting incomplete-question
    April 19 2025
    0  5

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

    chini dgl.mw

    How make number shorter in equation or finding poi...

    Asked by: salim-barzani 950
    decimal
    April 19 2025
    2  0

    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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