Dear Colleagues,

I am not sure if there exist a simple way to handle the issues I am facing. I am trying to obtain numeric roots for a polynomial f(x,a). I know for sure that there can be many roots depending on the value of parameter a. However, I cannot say for sure how many roots are possible for each value of parameter a. Some of these roots are complex numbers. Also, I need to choose only those roots that have following properties:

1. They are real.

2. f(x*,a) i.e., function value at a root is positive. 

How do I solve f(x,a)=0 to store all roots in a set? Furthermore, how do I select and print roots that have the properties mentioned above? Is there a way to do filtering of a set specifying properties of the members of the set? Please suggest. Your help is highly appreciated.

Regards,

Omkar

i want a scheme of fractional differential equation so that i solve my questions and make a code of it.

please provide me the scheme

i have an example, u[t] = u[xx]^2+u[yy]^2+u[zz]^2 with subject to b.c. u[0](x,y,z,t):=2*sin(x)*sin(y)*sin(z)
i used adomian method to solve this P.D.E, but i failed to construct a code of 2D P.D.E.
kindly help me in this regard

Typically sets are created like:

A:={a,b,c};

B:={c,q,w,e};

and then you can carryout A union B or B\A

what if  you wanted to create the set as

A:={values in some three dimensional space};

B:={volume, based on values taken from A};

Can these relationships be set up in Maple? If so, how? If there are commands that specifically handle these types of sets, what does maple call them?  I've seen the term 'set function' but what might Maple call them?

Note: I am not even sure i 'tagged' this correctly because it I am not sure the proper terms for these functions/sets.

Thanks in advance for any help.

Hi MaplePrimes,

I try again to ask about a procedure I wrote.  Maybee someone can spot my error.

collatz_conjecture_2.mw

Here is the broken procedure - 

cs := proc (n::integer)::integer;
local count;
description "Find the number of steps for a Collatz sequence to reach 1";
count := 1;
while 1 < n do
if `mod`(n, 2) = 0 then n := (1/2)*n else n := 3*n+1 end if;
count := count+1
end do;
return count
end proc

Regards,

Matt

Hi everyone!

I have a problem solving the nonlinear ode (as attached below). I got this error ---> Error, (in fproc) unable to store '-1.32352941215398+(-0.441176470717993e-1, -0.)' when datatype=float[8]

1) Could someone please explain to me what does the unable store .... error means? 

and i will be grateful if you could help me finding the solution out. Thanks in advance

How can I plot the complex function f(z)=1/(1-z) for |z|<1 into maple code? (z is a complex number)

Best regards,

Seda 

How can I modify the appearance of the arrowheads on the vectors displayed in phaseportrai? In particular, how can I "fill in" the arrowheads so that the arrowhead is not just an outline?

My code is:

phaseportrait([D(x)(t)=-0.4*x(t)+(0.5+4*x(t))*y(t),D(y)(t)=0.4*x(t)-(4.5+4*x(t))*y(t)],[x(t),y(t)],t=0..100,[[x(0)=1,y(0)=0.0]],x=0..1,y=0..0.1,stepsize=0.01,scaling=UNCONSTRAINED,linecolour=BLACK,dirgrid=[17,17],linestyle=1,arrows=SLIM,axes=BOXED);

Thank you

Hi everyone,

I'm kinda new here, and I really hope you guys can help me through this. In my new case study, after some revision, i thought i might be trying to implement a shooting method. I tried my best to make it work/understand but i couldn't get to any result.

So, as attached (i re-do PV Satya Naraya's paper first to be more understand but .....)

Here is my questions and the worksheet:

1) really stuck in mind - what is the purpose of shooting method for some related study?

2) what is the meaning of error .............'use midpoint method intead" 

3) Worksheet - 1MASS_JEFF_SATYA_on_Beta.mw

Thanks in advanced. Really hope that someone can help/teach me how to solve the boundary value problem by shooting method. 

Download 1MASS_JEFF_SATYA_on_Beta.mw

  Hi, there

How can I draw the excircles, incircles,circumcircle and their centers of a triangle simultaneously with maple13 in a geometric plot? please specify the commands.

many thanks for your help

M.R.Yegan

I am using maple 13 to found Eingenvalues of an hermitian matrix :

M1:=Matrix([
> [lambda3+lambda4,0,0,0,0,0,lambda4/sqrt(2),0,0,I*lambda4/sqrt(2)],
> [0,lambda3/4,0,0,0,0,0,0,0,0],
> [0,0,lambda3/4,0,0,0,0,0,0,0],
> [0,0,0,lambda3/4,0,0,0,0,0,0],
> [0,0,0,0,lambda3/4,0,0,0,0,0],
> [0,0,0,0,0,lambda3,0,0,0,0],
> [lambda4/sqrt(2),0,0,0,0,0,lambda3/2,0,0,0],
> [0,0,0,0,0,0,0,lambda2,0,0],
> [0,0,0,0,0,0,0,0,lambda2,0],
> [-I*lambda4/sqrt(2),0,0,0,0,0,0,0,0,lambda4/2]
> ]);

>Eigenvalues(M1);

my surprise is that maple gives me 8 correct solutions an 2 complex eigenvalues which are not acceptable (we now that the eigenvalues for an hermitian matrix are all real) .

To understand the output of maple, first,  I suspect that the complex part of the roots was null but without success I haven't found how to do it zero...

is it a bug? Thanks a lot to cooperation

Dear Maple researchers

I have a problem in solving a system of odes that resulted from discretizing, in space variable, method of lines (MOL).

The basic idea of this code is constructed from the following paper:

http://www.sciencedirect.com/science/article/pii/S0096300313008060

If kindly is possible, please tell me whas the solution of this problem.

With kin dregards,

Emran Tohidi.

My codes is here:

> restart;
> with(orthopoly);
print(`output redirected...`); # input placeholder
> N := 4; Digits := 20;
print(`output redirected...`); # input placeholder

> A := -1; B := 1; rho := 3/4;
> g1 := proc (t) options operator, arrow; 1/2+(1/2)*tanh((1/2)*(A-(2*rho-1)*t/sqrt(2))/sqrt(2)) end proc; g2 := proc (t) options operator, arrow; 1/2+(1/2)*tanh((1/2)*(B-(2*rho-1)*t/sqrt(2))/sqrt(2)) end proc;
print(`output redirected...`); # input placeholder
> f := proc (x) options operator, arrow; 1/2+(1/2)*tanh((1/2)*x/sqrt(2)) end proc;
print(`output redirected...`); # input placeholder
> uexact := proc (x, t) options operator, arrow; 1/2+(1/2)*tanh((1/2)*(x-(2*rho-1)*t/sqrt(2))/sqrt(2)) end proc;
print(`output redirected...`); # input placeholder
> basiceq := simplify(diff(uexact(x, t), `$`(t, 1))-(diff(uexact(x, t), `$`(x, 2)))+uexact(x, t)*(1-uexact(x, t))*(rho-uexact(x, t)));
print(`output redirected...`); # input placeholder
                                      0
> alpha := 0; beta := 0; pol := P(N-1, alpha+1, beta+1, x); pol := unapply(pol, x); dpol := simplify(diff(pol(x), x)); dpol := unapply(dpol, x);
print(`output redirected...`); # input placeholder
> nodes := fsolve(P(N-1, alpha+1, beta+1, x));
%;
> xx[0] := -1;
> for i to N-1 do xx[i] := nodes[i] end do;
print(`output redirected...`); # input placeholder
> xx[N] := 1;
> for k from 0 to N do h[k] := 2^(alpha+beta+1)*GAMMA(k+alpha+1)*GAMMA(k+beta+1)/((2*k+alpha+beta+1)*GAMMA(k+1)*GAMMA(k+alpha+beta+1)) end do;
print(`output redirected...`); # input placeholder
> w[0] := 2^(alpha+beta+1)*(beta+1)*GAMMA(beta+1)^2*GAMMA(N)*GAMMA(N+alpha+1)/(GAMMA(N+beta+1)*GAMMA(N+alpha+beta+2));
print(`output redirected...`); # input placeholder
> for jj to N-1 do w[jj] := 2^(alpha+beta+3)*GAMMA(N+alpha+1)*GAMMA(N+beta+1)/((1-xx[jj]^2)^2*dpol(xx[jj])^2*factorial(N-1)*GAMMA(N+alpha+beta+2)) end do;
print(`output redirected...`); # input placeholder
> w[N] := 2^(alpha+beta+1)*(alpha+1)*GAMMA(alpha+1)^2*GAMMA(N)*GAMMA(N+beta+1)/(GAMMA(N+alpha+1)*GAMMA(N+alpha+beta+2));
print(`output redirected...`); # input placeholder
> for j from 0 to N do dpoly1[j] := simplify(diff(P(j, alpha, beta, x), `$`(x, 1))); dpoly1[j] := unapply(dpoly1[j], x); dpoly2[j] := simplify(diff(P(j, alpha, beta, x), `$`(x, 2))); dpoly2[j] := unapply(dpoly2[j], x) end do;
print(`output redirected...`); # input placeholder
print(??); # input placeholder
> for n to N-1 do for i from 0 to N do BB[n, i] := sum(P(jjj, alpha, beta, xx[jjj])*dpoly2[jjj](xx[n])*w[i]/h[jjj], jjj = 0 .. N) end do end do;
> for n to N-1 do d[n] := BB[n, 0]*g1(t)+BB[n, N]*g2(t); d[n] := unapply(d[n], t) end do;
print(`output redirected...`); # input placeholder
> for nn to N-1 do F[nn] := simplify(sum(BB[nn, ii]*u[ii](t), ii = 1 .. N-1)+u[nn](t)*(1-u[nn](t))*(rho-u[nn](t))+d[nn](t)); F[nn] := unapply(F[nn], t) end do;
print(`output redirected...`); # input placeholder
> sys1 := [seq(d*u[q](t)/dt = F[q](t), q = 1 .. N-1)];
print(`output redirected...`); # input placeholder
[d u[1](t)                                                                
[--------- = 40.708333333333333334 u[1](t) + 52.190476190476190476 u[2](t)
[   dt                                                                    

                                                                  2          3
   + 39.958333333333333334 u[3](t) - 1.7500000000000000000 u[1](t)  + u[1](t)

   + 7.3392857142857142858

   - 3.6696428571428571429 tanh(0.35355339059327376220

   + 0.12500000000000000000 t) - 3.6696428571428571429 tanh(
                                                     d u[2](t)   
-0.35355339059327376220 + 0.12500000000000000000 t), --------- =
                                                        dt       
-20.416666666666666667 u[1](t) - 25.916666666666666667 u[2](t)

                                                                  2          3
   - 20.416666666666666667 u[3](t) - 1.7500000000000000000 u[2](t)  + u[2](t)

   - 3.7500000000000000000

   + 1.8750000000000000000 tanh(0.35355339059327376220

   + 0.12500000000000000000 t) + 1.8750000000000000000 tanh(
                                                     d u[3](t)                
-0.35355339059327376220 + 0.12500000000000000000 t), --------- = 29.458333333\
                                                        dt                    

  333333333 u[1](t) + 38.476190476190476190 u[2](t)

                                                                  2          3
   + 30.208333333333333333 u[3](t) - 1.7500000000000000000 u[3](t)  + u[3](t)

   + 5.4107142857142857144

   - 2.7053571428571428572 tanh(0.35355339059327376220

   + 0.12500000000000000000 t) - 2.7053571428571428572 tanh(
                                                   ]
-0.35355339059327376220 + 0.12500000000000000000 t)]
                                                   ]
> ics := seq(u[qq](0) = evalf(f(xx[qq])), qq = 1 .. N-1);
print(`output redirected...`); # input placeholder
    u[1](0) = 0.38629570659055483825, u[2](0) = 0.50000000000000000000,

      u[3](0) = 0.61370429340944516175
> dsolve([sys1, ics], numeic);
%;
Error, (in dsolve) invalid input: `PDEtools/sdsolve` expects its 1st argument, SYS, to be of type {set({`<>`, `=`, algebraic}), list({`<>`, `=`, algebraic})}, but received [[d*u[1](t)/dt = (20354166666666666667/500000000000000000)*u[1](t)+(13047619047619047619/250000000000000000)*u[2](t)+(19979166666666666667/500000000000000000)*u[3](t)-(7/4)*u[1](t)^2+u[1](t)^3+36696428571428571429/5000000000000000000-(36696428571428571429/10000000000000000000)*tanh(1767766952966368811/5000000000000000000+(1/8)*t)-(36696428571428571429/10000000000000000000)*tanh(-1767766952966368811/5000000000000000000+(1/8)*t), d*u[2](t)/dt = -(20416666666666666667/1000000...

How difficult is it to simulate gravitational influences and perturbing effects on celestial orbits with Maple? Could this syntax http://www.maplesoft.com/applications/view.aspx?SID=4484&view=html be altered without excessive changes to consider these aspects?

Are there somewhere worksheets to take a look at as an introduction and to see how such goals would be approached and implemented?

Some time ago, I have used the Virtual 3D Solar System code to plot a few interesting figures with asteroids. It can be found here: http://www.maplesoft.com/applications/view.aspx?SID=4484&view=html . I plotted the asteroid belt as a closed, warped surface according to how the asteroids are inclined, with the arguments of perihelion and longitude of ascending node where they cross the equatorial plane to the other celestial hemisphere. The plot was only done with axes in units of distances, for convenience's sake in astronomical units of 1 AU = 150 million km.

But I am strongly wondering if it were somehow possible to alter or adjust the code such that there is a zylinder placed around such plot where one can see celestial coordinates (Rectascension, Declination) on the inside, so that if one wants to know what coordinates an orbit of a specific asteroid has that one can look in the chart and go out on the balcony and set the telescope to these coordinates. Of course the asteroid most likely is not there on his entire orbital path, but you have at least the location where the asteroid CAN be. Would this be possible to plot?

This probably doesn't work if a closed cylinder is placed around the Virtual Solar System. But how about scrolling the cylinder and the orbits flat on a 2D plot?

I need to calculate Weyl scalar for a metric using null tetrad using debever package in maple 13. However, I am stuck at the defination of h (representing the covariant complex null tetrad). Is it the product of covariant null tetrad? I have worked it out by using covariant, contravariant and both covariant and contravariant null tetrad (like l_a*l_a, l^a*l^a, l_a*l^a), however, i am not getting the right result not even for the example given in the maple help for plane wave. please help me out that how should i define this h.

thanks,
suresh