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);
 

Dears, greeting for all

I have a problem, I try to explain it by a figure

This formula does not work.

I need to substitute n=0 to give G_n+1 as a function of the parameter s, then find the limit. 

.where G_n is a function in s.

this is the result

how to express eigenvector or eigenvalues in terms of fibonacci or lucas or golden ratio?

fibonacci ratio has many 

f(n)/f(n-1) , all eigenvector can not divided by any one of them

Hello!

I want to calculate Eigenvalues. Depending on values for digits and which datatype I choose Maple sometimes returns zero as Eigenvalues. Maybe there is a problem with the used routines: CLAPACK sw_dgeevx_, CLAPACK sw_zgeevx_.

Thank you for your suggestions!
 

Download Problems_LinearAlgebra_Eigenvalues.mw

How to get the functional form of interpolation in the given example below

GP.mw

Hi, 

The procedure Statistics:-ChiSquareSuitableModelTest returns wrong or stupid results in some situations.
The stupid answer can easily be avoided if the user is careful enough.
The wrong answer is more serious: the standard deviation (in the second case below) is not correctly estimated.

PS: the expression "CORRECT ANSWER" is a short for "POTENTIALLY CORRECT ANSWER" given that what ChiSquareSuitableModelTest really does is not documented
 

Download ChiSquareSuitableModelTest.mw

Dear Users!

I have made a code using loops. But when I exceute it I go unwanted expression please see the files and try to fix it. I shall be very thankful. 

Help.mw

Special request to:

@acer @Kitonum @Preben Alsholm @Carl Love

Hi,

I seeking for informations on the Statistics:-ChiSquareSuitableModelTest procedure:

1. Once you have choose the number of bins, what strategy does this procedure use to define the bins (equal width, equal probability, other one?).
    
2. It seems the procedure accepts any value for this number of bins and that its correct use then is under the sole responsability of the user. Am I right?

In the book below (but I'm sure this can also be found on the web) there is a detailed discussion concerning "good practices" in using the Chi-Square goodness of fit test: does anyone known is something comparable is used in ChiSquareSuitableModelTest ?

Statistical methods in experimental physics, W.T.Eadie, D. Drijard, F.F.James, M. Roos, B. Sadoulet
North-Holland 1971
Paragraph 11.2.3 "choosing optimal bin size"


Thanks in advance

I am writing a maths books using maple now. It is fantastic to use maple for writing books in maths.
 

Download cannotCopyWhy.mw

I enclose a part of my document where in I made a particular line with text and maths formats combined.Then I made changes in the line. Now copy paste does work only for the later half (both text and maths formats). The corrected first part is not being copied.

How do I do the corrections properly so that copy paste is not a problem at laer stages.

Thanks for the answer.

Ramakrishnan V

My problem is related to recovering orbits from invariant polynomials, and their ideal of relations.

The invariant polynomials I obtained are:

u = x² - x y + y²,
v = 2 x⁶ - 6 x⁵ y + 15 x⁴ y² - 20 x³ y³ + 15 x² y⁴ - 6 x y⁵ +  2 y⁶ ,
w = x⁶ - 4 x⁵ y + 10 x⁴ y² - 10 x³ y³ + 5 x² y⁴ - 2 x y⁵ + y⁶ .

Using the logic from the Cox et al. book I got that the algebraic relation (ideal of relations) between the invariants, which is:

11 u⁶ - 10 u³ v + 3 (v² - v w + w²) = 0

Then, using Reduce[] (exact symbolic solver which uses cylindrical algebraic decomposition) from Mathematica I solved for x and y under the assumption x > y > 0, u > 0, v > 0 and w > 0, but I got rather a complex solution.

My question is whether there is a way to try getting something more straightforward than the solution given by Mathematica.
 

I tried to use Maple's solve function, but it immediately stops without any result of an error message.

My input for Reduce is:

Reduce[{x² - x y + y² == u, 2 x⁶ - 6 x⁵ y + 15 x⁴ y² - 20 x³ y³ + 15 x² y⁴ - 6 x y⁵ + 2 y⁶ == v,  x⁶ - 4 x⁵ y + 10 x⁴ y² - 10 x³ y³ + 5 x² y⁴ - 2 x y⁵ + y⁶ == w, 11 u⁶ - 10 u³ v + 3 (v² - v w + w²) == 0, x > y > 0, u > 0, v > 0, w > 0}, {x, y}, Complexes]

and my input for solve:

solve({u = x^2 - x*y + y^2, v = 2*x^6 - 6*x^5*y + 15*x^4*y^2 - 20*x^3*y^3 + 15*x^2*y^4 - 6*x*y^5 + 2*y^6, w = x^6 - 4*x^5*y + 10*x^4*y^2 - 10*x^3*y^3 + 5*x^2*y^4 - 2*x*y^5 + y^6, 11*u^6 - 10*u^3*v + 3*v^2 - 3*v*w + 3*w^2 = 0, 0 < u, 0 < v, 0 < w, 0 < x, 0 < y, y < x}, {x, y})

Do you know what I am doing wrong, or what else could I try?

Hello Anybody can help me to write codes for PDE to solve by Galerkin finite element method or any other methods can be able to gain results? parameter omega is unknown and should be determined.

I attached a pdf file for more .

Thanks so much

fem2
 

Download fem2

buchanan2005.pdf