Unanswered Questions

This page lists MaplePrimes questions that have not yet received an answer

This is may be a philosophical question. But sometimes Maple suprises me when telling it to "simplify" expression. As in this example.

expr:=1/(y^3+1)^(2/3);

1/(y^3+1)^(2/3)

int(expr,y)

y*hypergeom([1/3, 2/3], [4/3], -y^3)

simplify(%)

(2/9)*y*Pi*3^(1/2)*LegendreP(-1/3, -1/3, (-y^3+1)/(y^3+1))/((-y^3)^(1/6)*(y^3+1)^(1/3)*GAMMA(2/3))

 


For me, the original result is "simpler". (Not only smaller leaf count, but it has one special function, vs. two: Legendre and Gamma). But may be Maple considers hypergeom always more "complex" than any other?

That is why I use simplify(expr,size) because I am scared of simplify without any option, as I have little idea how it decides which is simpler.

Any thoughts from the experts on how Maple decided to simplify something when no option is used? What kinds of rules it uses to decide how to transform the expression?

Maple 2019.1

 

Download simplify.mw

The video component is going to save me alot of hassle in that I was previously building external java applications for audio visual analysis purposes, with the downside of course being that I didnt have maple code at my disposal. 

I read in the manual for the video component that I can provide a HTTP address for which a video is located, which would mean i could probably stream an IP camera, but I can I use the localhost IP address with some sort of extension that directs to the I/O of a webcamera connected to my local machine?

Hi all, how to write description, suggestions for method (procedure) like image below. I tried searching for a solution but can't. Thank you very much

Is there extendable combinatorics experiment architect system design

such as new method can combine or use with old method and find relationship between them , these kind of big data system design in combinatorics experiment design?

How can I fix the error of ChangeOfVariables: Error, (in Student:-MultivariateCalculus:-ChangeOfVariables) unable to solve the change-of-variables equations for the original variables ?

Thanks!

Dear Maple users

 

I am just curious about how far Maplesoft is updating the Mac version of Maple to 64 bit (Catalina). This version of the Mac OS will hit the shelves in late September this year. As I have been told, no program built on 32 bit will be able to run on this new version of Mac OS. I am pretty sure there will be a lot of software troubles for students upgrading to this version. We can recommend the students not to upgrade immediately, but it would be interesting to hear how far Maplesoft is creating a 64 bit Maple-installer for Mac?

 

Regards,

Erik V.

Hi

I have trouble with solving this ODE system using dsolve command:

and 

 

This system have following solutions:

where

and

C's and A are constants of integration.

 

They're equations from this paper https://arxiv.org/abs/1710.01910 (45 and 47). 
               

However, my solution differs from correct one - in output there are hypergeometric functions everywhere.

Is there any way to fix/convert this solution? Or to get rid of these functions (my f1 solution looks very close to original one but with coupled hypergeometric function). 
 

`` ``

``

``

 

``

sysode := 2*q*(3*q-1)*f1(tau)/tau^2+2*q*(diff(f1(tau), tau))/tau+diff(f1(tau), tau, tau)+(kappa^2+f2(tau))*(1+omega)*(tau/t0)^(-(3*(3+omega))*q) = 0, (54*q^3-30*q^2+4*q)*f1(tau)/tau^3+(24*q^2-4*q)*(diff(f1(tau), tau))/tau^2+11*q*(diff(f1(tau), tau, tau))/tau+diff(f1(tau), tau, tau, tau)-3*omega*(1+omega)*(kappa^2+f2(tau))*q*(tau/t0)^(-(3*(1+omega))*q)/tau = 0;

2*q*(3*q-1)*f1(tau)/tau^2+2*q*(diff(f1(tau), tau))/tau+diff(diff(f1(tau), tau), tau)+(kappa^2+f2(tau))*(1+omega)*(tau/t0)^(-3*(3+omega)*q) = 0, (54*q^3-30*q^2+4*q)*f1(tau)/tau^3+(24*q^2-4*q)*(diff(f1(tau), tau))/tau^2+11*q*(diff(diff(f1(tau), tau), tau))/tau+diff(diff(diff(f1(tau), tau), tau), tau)-3*omega*(1+omega)*(kappa^2+f2(tau))*q*(tau/t0)^(-3*(1+omega)*q)/tau = 0

(1)

``

``

simplify(dsolve([sysode], build));

{f1(tau) = _C1*tau^(-q+1/2-(1/2)*(-20*q^2+4*q+1)^(1/2))+_C2*tau^(-q+1/2+(1/2)*(-20*q^2+4*q+1)^(1/2))+_C3*tau^(-9*q+2)*hypergeom([-(1/12)*(16*q+(-20*q^2+4*q+1)^(1/2)-3)/q, (1/12)*(-16*q+(-20*q^2+4*q+1)^(1/2)+3)/q], [-(1/12)*(4*q+(-20*q^2+4*q+1)^(1/2)-3)/q, (1/12)*(-4*q+(-20*q^2+4*q+1)^(1/2)+3)/q], -(1/2)*(tau/t0)^(6*q)*omega), f2(tau) = (-695520*(q^2+(11/21)*q+2/21)*(tau/t0)^(3*q*(omega+5))*_C3*(q-3/10)*omega*q*(q^2-(25/69)*q+2/69)*tau^(-9*q)*hypergeom([-(1/12)*(4*q+(-20*q^2+4*q+1)^(1/2)-3)/q, (1/12)*(-4*q+(-20*q^2+4*q+1)^(1/2)+3)/q], [-(1/12)*(-8*q+(-20*q^2+4*q+1)^(1/2)-3)/q, (1/12)*(8*q+(-20*q^2+4*q+1)^(1/2)+3)/q], -(1/2)*(tau/t0)^(6*q)*omega)-89424*(q^2*(tau/t0)^(3*q*(omega+7))*omega^2*tau^(-9*q)*_C3*(q^2-(25/69)*q+2/69)*hypergeom([-(1/12)*(-8*q+(-20*q^2+4*q+1)^(1/2)-3)/q, (1/12)*(8*q+(-20*q^2+4*q+1)^(1/2)+3)/q], [-(1/12)*(-20*q+(-20*q^2+4*q+1)^(1/2)-3)/q, (1/12)*(20*q+(-20*q^2+4*q+1)^(1/2)+3)/q], -(1/2)*(tau/t0)^(6*q)*omega)+(7/3)*(q^2+(11/21)*q+2/21)*(hypergeom([-(1/12)*(16*q+(-20*q^2+4*q+1)^(1/2)-3)/q, (1/12)*(-16*q+(-20*q^2+4*q+1)^(1/2)+3)/q], [-(1/12)*(4*q+(-20*q^2+4*q+1)^(1/2)-3)/q, (1/12)*(-4*q+(-20*q^2+4*q+1)^(1/2)+3)/q], -(1/2)*(tau/t0)^(6*q)*omega)*_C3*(tau/t0)^(3*(3+omega)*q)*(q^2-(25/69)*q+2/69)*tau^(-9*q)+(1/69)*kappa^2*(1+omega)))*(q^2-(7/9)*q+2/9))/((1+omega)*(4*q-(-20*q^2+4*q+1)^(1/2)-3)*(8*q-(-20*q^2+4*q+1)^(1/2)+3)*(8*q+(-20*q^2+4*q+1)^(1/2)+3)*(4*q+(-20*q^2+4*q+1)^(1/2)-3))}

(2)

NULL

NULL

``

NULLNULL

NULL

NULL

NULL

NULL

``


 

Download question.mw

I know you can call python from Maple, I am thinking if there is the other way around. That is use Maple (and its toolbox) as backend engine to do calculations (e.g. Global Optimization), and say manipulate the data in Python as the front-end.

Hello,

My question is mathematical in nature, so it might be a little out of place but I though I would give it a shot. 

You have a series of chebyshev coefficients in two connecting subdomains lets say S1 = [0,0.5] and S2=[0.5,1]. So far you are still in the spectral space. If you want to compute the solution in real space you can sum the coefficients with the Chebyshev polynomials. 

Now imagine you change the interval to S1 = [0,0.6] and S2 = [0.6,1]. Is there a way to manipulate the Chebyshev coefficients from both initial subdomains to create a new set of Chebyshev coefficients that fit the solution in the new subdomains. 

The brute force method would be to create the real solution of Chebyshev polynomials and then use that to form a new set of Chebyshev coefficients. Or you can use Clenshaw to compute the solution at several points, and then use the points to create new Chebyshev coefficients.

But what if we can stay in spectral space and create the new chebyshev coefficients. Is that possible? If so, how?

Hi, 

When creating a user random variable, I would like to instanciate some of its attributes, for instance ParentName.
But it seems that it's not always possible.

​​​​​​​Is it a Maple's limitation or am I not doing the things correctly ?
​​​​​​​
Example:
 

restart:

with(Statistics):

U := RandomVariable(Uniform(0, 1)):

interface(warnlevel=0):

A := attributes(U)[3]

_ProbabilityDistribution

(1)

AllAttributes := with(A);

[CDF, Conditions, HodgesLehmann, InverseSurvivalFunction, MGF, MaximumLikelihoodEstimate, Mean, Median, Mode, PDF, Parameters, ParentName, Quantile, RandomSample, RandomSampleSetup, RandomVariate, RousseeuwCrouxSn, Support, Variance]

(2)

A:-ParentName

UniformDistribution

(3)

# Define a user random variable

v := Distribution(PDF = (z -> piecewise(0 <= t and t < 1, 1, 0))):
V := RandomVariable(v):
A := attributes(V)[3];
AllAttributes := with(A);
A:-Conditions;

_ProbabilityDistribution0

 

[Conditions, PDF]

 

[]

(4)

# its definition can be augmented by adding some recognized attributes...
# even if the result returned by Mean is strange

v := Distribution(PDF = (z -> piecewise(0 <= t and t < 1, 1, 0)), 'Mean'=1/Pi, 'Median'=exp(-1)):
V := RandomVariable(v):
A := attributes(V)[3];
AllAttributes := with(A);
[Median, Mean](V)

_ProbabilityDistribution1

 

[Conditions, Mean, Median, PDF]

 

[exp(-1), 1/Pi(_R1)]

(5)

# but not all the recognized attributes seem to be able to be instanciated:

v := Distribution(PDF = (z -> piecewise(a <= t and t < b, 1/(b-a), 0)), 'Parameters'=[a, b]);
v := Distribution(PDF = (z -> piecewise(a <= t and t < b, 1/(b-a), 0)), 'ParentNames'=MyDistribution);

Error, (in Statistics:-Distribution) invalid input: too many and/or wrong type of arguments passed to NewDistribution; first unused argument is Parameters = [a, b]

 

Error, (in Statistics:-Distribution) invalid input: too many and/or wrong type of arguments passed to NewDistribution; first unused argument is ParentNames = MyDistribution

 

 

 


 

Download Attributes.mw

I'm new to Maple.

My problem is that if I input the command sqrt(3.0), for example, I get this strange result:

1.81847767202745*10^(-58) + (7.53238114626421*10^(-59))*I

The results is the same, no matter the argument of sqrt.

Also, when using ln, I get this:

-265.745524189222 + 0.785398163397448*I

Again, no matter the argument of ln, the result is the same.

What is happening?

Dear maple user  any one suggest me how to solve  second order coupled differential equation using galerkin finite element method for 8 elements and 10 elements using maple codes

 

Hi, Is there a way in which i can solve the following optimal control problem numerically with Maple ??

where P(t)=N(t)+S(t)+A(t) and N(0)=0.4897, S(0)=0.4018, A(0)=0.1085.

μ=0.000833, d=0.000666, ε1=0.0020, ε2=0.000634, β1=0.002453, β2=0.25*0.02, γ1=0.0048, γ2=0.25*0.02+0.00013, k1=1, k2=0.001, k3=0.99.

 where 

p1,p2,p3 are transversality conditions 

p1(60)=0 
p2(60)=0 
p3(60)=0

Answers and advice are very appreciated. 

Thank you all for reading.

Benz.

Hi

I have an optimization problem subjects with a system of ordinary differential equations with initial conditions.

I would like to obtain u^star, x^star and y^star solution of my problem 

I prefer if possible we implement hamilton jacobi bellman if possible

 

Optimal_control_problem.mw

 

thanks

 

whats wrong with the codes while running the codes in maple 13 it will take memory and time as 41.80M, 9.29s while the same code is running in maple 18 it will take 1492.38M , 911.79s

Why the same codes take different time and memory. The codes are here

 

 

restart:
Digits:=15:
d1:=0.2:d2:=0.6:L1:=0.2:L2:=0.2:F:=0.3:Br:=0.3:
Gr:=0.2: Nb:=0.1:Nt:=0.3:B:=1:B1:=0.7:m:=1:k:=0.1:
Ro:=1:R1:=1:q:=1:alpha:=Pi/4:
h:=z->piecewise( z<=d1,    1,
                 z<=d1+L1,   1-(gamma1/(2*Ro))*(1 + cos(2*(Pi/L1)*(z - d1 - L1/2))), 
                        z<=B1-L2/2,  1 ,          
                    z<=B1,  1-(gamma2/(2*Ro))*(1 + cos(2*(Pi/L2)*(z - B1))),
                 z<=B1+L2/2,  R1-(gamma2/(2*Ro))*(1 + cos(2*(Pi/L2)*(z - B1))),
                 z<=B,    R1):
A:=(-m^2/4)-(1/4*k):
S1:=(h(z)^2)/4*A-ln(A*h(z)^2+1)*(1+h(z)^2)/4*A:
a2:=Int((1/S1),z=0..1):
b2:=Int((sin(alpha)/F),z=0..1):
c2:=(1/S1)*(-h(z)^6/(6912*A)-h(z)^4/(9216*A)+h(z)^2/(4608*A^3)+ln(1+A*h(z)^2)*(h(z)^6/(576*A)+h(z)^4/(512*A^2)-1/(4608*A^4))):
c3:=Int(c2,z=0..1):
c4:=2*Gr*(Nb-Nt)*c3:
e2:=(1/S1)*(-7*h(z)^4/(256*A)-h(z)^2/(128*A^2)+ln(1+A*h(z)^2)*(3*h(z)^4/(128*A)+h(z)^2/(32*A^2)+1/(128*A^3))):
e3:=Int(e2,z=0..1):
e4:=2*(Nt/Nb)*Br*e3:
l1:=-a2:
l2:=-b2-c4+e4:
Dp:=q*l1+l2:

igRe:=subsindets(Dp,specfunc(anything,Int),
                         u->Int(Re(op(1,u)),op(2,u),
                                   method=_d01ajc,epsilon=1e-6)):

plot([seq(eval(igRe,gamma2=j),j=[0,0.02,0.06])],gamma1=0.02..0.1,
     adaptive=false,
     legend = [gamma2 = 0.0,gamma2 = 0.02,gamma2 = 0.04],
     linestyle = [solid,dash,dot],
     color = [black,black,black],
     labels=[gamma1,'Re(Dp)'],
     gridlines=false, axes=boxed);

igIm:=subsindets(Dp,specfunc(anything,Int),
                         u->Int(Im(op(1,u)),op(2,u),
                                   method=_d01ajc,epsilon=1e-6)):

plot([seq(eval(igIm,gamma2=j),j=[0,0.02,0.06])],gamma1=0.02..0.1,
     adaptive=false,
     legend = [gamma2 = 0.0,gamma2 = 0.02,gamma2 = 0.04],
     linestyle = [solid,dash,dot],
     color = [black,black,black],
     labels=[gamma1,'Im(Dp)'],
     gridlines=false, axes=boxed);
 

 

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