## Eigenvalues and Characteristic Polynomial...

Hi!

I am comptuing the eigenvalues and the characteristic polynomial of a 8 by 8 symmetric matrix, say M. Thus, we define the matrix M, and compute its charast. plynm. by

and its eigenvalues with the command

Well, Maple returns the charast. polynm. an dthe eigenvalues. But, if we compute p(E[k]), for k=1,...,8, thats is, the values of the polynomial p(x) in the eingenvalues, Maple not turns cero!!! I'm really confused ... anyone know what could be happening?

Maple attached file with this example. Thank very much for your help!!

## Error when fsolving ...

Error, (in fsolve/polynom) Digits cannot exceed 38654705646

I am using fsolve to find numerical approximations to the roots of many fairly large polynomials (degrees up to ~80).  I often get this error message and I'm not sure why.  Is there any workaround?  Any help is much appreciated.

## Apollonius (geometry) problem...

Hello,

I am trying to use Apollonius procedure from geometry package. Here is an example:

restart;with(geometry): circle( c1, [ point( c1c, 0 , 0 ), 5 ] );circle( c2, [ point( c2c, 5 , 4 ), 2 ] );circle( c3, [ point( c3c, 13 , 0 ), 3 ] );A := Apollonius( c1, c2, c3 );

Unfortunatelly the Apollonius method does not give any result. The only message is:

intersection: there is no point of intersection

Anyone know what is wrong in my code?

Best regards

Rafał Nowak

## Surface/volume of revolution in polar coords...

Hi there,

How can we pl0t the volume or surface of revolution of cardioid r=1-cos(\theta) about  polar axis or the vertical axis in maple14.

Any help will be appreciated.

M.R.Yegan

## Error, (in soru) illegal use of a formal parameter...

Hello. I have a question. If you can help me, i am pleasure.

Have nice day. :)

restart;
soru := proc(n,x)
local top::0;
for x from 2 to n do
top =top+(((x^(2+i))*top)^(1/(n+2-i)));
print(top);
od;
end proc;

soru(5,1);

Error, (in soru) illegal use of a formal parameter

## Error, reserved word do unexpected...

Hello. I have a question. If you can help me, i am pleasure.

Have nice day. :)

Question: Enter a number after maple find(understand) to prime number or normal number.

restart;
> asal := proc(n)
> local m;
> if n<2 then
> m := s=n/2+1;
> print(m);
> else
> for i from 2 to n do
> if irem(n,i,0) then
> print("asal değil");
> if i = m then
> print("asaldir");
> end do;
> end if;
> end if;
> end proc;

Hi,

> whit*evalf; tx := evalf((t1+t2)*(1/2));
> t1 := 326*40; t2 := 327*40;
> y1, y2 := eval([y1, y2], Ns(t1), Ns(t2));
>while (t1 < tx) and (tx < t2) do:
yx := rhs(Ns(tx)[c2]):
if yx > 0 then
y2 := yx: t2 := tx:
else
y1 := yx: t1 := tx:
fi;
od;
>Tx = evalf(tx);
> Hx := floor((1/3600)*tx):
> Mx := floor((tx-3600*Hx)*(1/60)):
> Sx := tx-3600*Hx-60*Mx:
> Hx, Mx, Sx;
> XS := [seq(X[i], i = 0 .. 328)]: YS := [seq(Y[i], i = 0 .. 328)]:
> VxS := [seq(Vx[i], i = 0 .. 328)]: VyS := [seq(Vy[i], i = 0 .. 328)]:
> save(G,Mz,Xs,VxS,VyS, 'orbit.sav'):

can you help me?

hi friends

I encountered a problem and I can not draw the plot of this code

> sol := fsolve({diff(S, x) = 0, diff(S, y) = 0}, {x, y});

> with(VectorCalculus);
> with(linalg);
> s1 := evalf(subs(sol, linalg[grad](S, [x, y])));

> with(VectorCalculus);
> with(LinearAlgebra);
> s2 := evalf(subs(sol, linalg[hessian](S, [x, y]))); pmp0 := [x-subs(sol, x), y-subs(sol, y)]; sapprox := s0+evalm(&*(&*(transpose(pmp0), s2), pmp0));
> with(Statistics);
>
> with(stats); statevalf[icdf, chisquare[4]](.95);

> with(VectorCalculus);
> with(plottools);
> with(plots);
> with(linalg); ellips := {seq(stats*([statevalf[icdf, chisquare[4]]])(c) = sapprox, c = [.5, .95, .999])};
> plots(ellips(x, y), x = 950 .. 1000, y = 700 .. 750, grid = [50, 50], view = [950 .. 1000, 700 .. 750]);

can you helpe me?Thank you

## Error, invalid input: with expects...

hi friends

After this cods i see very error

> restart;

ax := -G*Mz*x/(x^2+y^2)^(3/2);
ay := -G*Mz*y/(x^2+y^2)^(3/2);
i := 'i'; j := i+1;
for k from 0 to 3 do
x := 7*10^6; Vx := 0;
y := 0; Vy := 9000;
dt := evalf(1/2^k);
for i from 0 to 328 do
X[i] := evalf(x); Y[i] := evalf(y);
for n to 40*2^k do
x := evalf((1/2)*ax*dt^2+Vx*dt+x); y := evalf((1/2)*ay*dt^2+Vy*dt+y);
Vx := evalf(ax*dt+Vx); Vy := evalf(ay*dt+Vy)
od;
if i mod 41= 0 then
dX[k, i] := X[i]-XS[j]; dY[k, i] := Y[i]-YS[j]
fi
od;
p[k] := plot([seq([(X[i]-XS[j])*(1/1000), (Y[i]-YS[j])*(1/1000)], i = 0 .. 328)], color = green) end do;
p1 := display({seq(p[k], k = 0 .. 3)}, thickness = 3)
SI := [seq(41*i, i = 0 .. 8)]
p2 := plot({seq([seq([(1/1000)*dX[k, i], (1/1000)*dY[k, i]], k = 0 .. 1), [0, 0]], i = SI)}, color = black)
display({p1, p2}, scaling = constrained, labels = ['dx', 'dy'])
display({p1, p2}, view = [-.1 .. .5, -.4 .. .2], scaling = constrained, labels = ['dx', 'dy'])

Thank you

## Error, invalid input:...

hi friends

i have a problem in maple with an error

dsnumsort:=proc(numpr::list,coor::list)
local i,j,n;
global C1,C2,C3,V1,V2,V3;
n:=nops(coor):
print("Order of the variables:");
for i from 2 to 2*n +1 do
for j from 1 to n do
if[numpr[i]]=
select(has,numpr,diff(coor[j](t),t)) then
C[j]:=i-1;V[j]:=i;
print(coor[j],C[j]," ",diff(coor[j](t),t),V[j]);
fi;
od;
od;
end :

Us:=subs(G=1,m=1,L=1,U):
D2r:=[diff(z(t),t,t),diff(x(t),t,t),diff(y(t),t,t)]:
IniC:=z(0)=0.75,D(z)(0)=0, x(0)=1,D(x)(0)=0,y(0)=0,D(y)(0)=1:

Ns:=dsolve({seq(D2r[i]=g[i],i=1..3),IniC},{z(t),x(t),y(t)},numeric);

dsnumsort(Ns(0),[z,x,y]):

for i from 0 to 1000 do ;
T:=i/25;
NsT:=Ns(T):

X[i]:=rhs(NsT[C1]); Vx[i]:=rhs(NsT[V1]);
Y[i]:=rhs(NsT[C2]); Vy[i]:=rhs(NsT[V2]);
Z[i]:=rhs(NsT[C3]); Vz[i]:=rhs(NsT[V3]);

KepVec[i]:=convert(crossprod([X[i],Y[i], Z[i]],[Vx[i],Vy[i], Vz[i]]),list);
KepAbs[i]:=norm(KepVec[i],2);
od:

but i see this error and I can't draw PLOT:

Error, invalid input: rhs received Ns(0)[C1], which is not valid for its 1st argument, expr

this cods is for draw plot:

spacecurve({[seq([X[i], Y[i], Z[i]], i = 0 .. 1000)], [[-1/2, 0, 0], [1/2, 0, 0]]}, labels = ['x', 'y', 'z']);

spacecurve([seq(KepVec[i], i = 0 .. 1000)], orientation = [0, 90], labels = ['x', 'y', 'z'])

plot([seq([(1/25)*i, KepAbs[i]], i = 0 .. 1000)], labels = ['t', 'MofI'])

can you helpe me?Thank you

## How do I solve this problem?...

hi friends

i have a problem in maple with an error

dx := diff(x(t), t, t) = -G*Mz*x(t)/(x(t)^2+y(t)^2)^(3/2):

dy := diff(y(t), t, t) = -G*Mz*y(t)/(x(t)^2+y(t)^2)^(3/2):

G := 6.67*10^(-11); Mz := 6*10^24:
IniC := x(0) = 7*10^6, (D(x))(0) = 0, y(0) = 0, (D(y))(0) = 9*10^3:
Digits := 15:
Ns := dsolve({dx, dy, IniC}, {x(t), y(t)}, numeric):
dsnumsort(Ns(0), [x, y]);

>for i from 0 to 400 do T := 40*i; NsT := Ns(T); X[i] := rhs(NsT[C1]); Vx[i] := rhs(NsT[V1]); Y[i] := rhs(NsT[C2]); Vy[i] := rhs(NsT[V2]); MofI[i] := X[i]*Vy[i]-Y[i]*Vx[i] end do:

> with(plots);
> p1 := polarplot(6378*10^3, phi = 0 .. 2*Pi);
> p2 := plot([seq([X[i], Y[i]], i = 0 .. 327)], thickness = 2);

display({p1, p2}, labels = ['x', 'y'], scaling = constrained);

but i see and I I can't draw PLOT:

Error, invalid input: rhs received [t = HFloat(0.0), x(t) = HFloat(1.0), diff(x(t), t) = HFloat(0.0), y(t) = HFloat(0.0), diff(y(t), t) = HFloat(1.0), z(t) = HFloat(0.75), diff(z(t), t) = HFloat(0.0)][C1], which is not valid for its 1st argument, expr

can you helpe me?

## Solving non-linear ODE...

Hi,

I'm trying to solve the following non-linear ODE numerically:

by ececuting

but maple gives me this error-message:

"Error, (in dsolve/numeric/make_proc) Could not convert to an explicit first order system due to 'RootOf'"

I couldnt find any useful information in the manual. What does this error mean? Is there something wrong with my maple code or is there just no solution for this particulare differential equation?

## ODE: Fit parameters to multiple experiments...

Hi,

I'm trying to fit some parameters to the data of multiple slightly different experiments.

I've written a function which returns the sums of the error for all experiments.

The function which has to be minimized does the following:

1) Set parameters for the model ODE based on the input parameters

2) calculate the difference (numeric solution of ODE <-> experimentel data)

3) repeat step 1+2 for all experiments

4) return the sum of all differences

The function works as aspected. But when I try to minimize it by calling:

I got an error:

"Error, (in dsolve/numeric/process_parameters) parameter values must evaluate to numeric, got A = A"

For some reason Maple isnt able to set the new parameters of the ODE.

Anyone got an idea how to fix this?

## How we use Gamma function...

Hi!

Please find my Maple-worksheet attached below.

How do I solve this problem? I can not drawn it.

I would really appriciate if somebody could help me.

## Isolating Expressions...

Hi there,

I'm doing my first steps with Maple and am a little confused with a problem:
I want to solve something like

and expect the result to be z=-m*a. However I get empty brackets as result.
I tried to dig a little and I find that maple has problems isolating x1+x2+x3+x4

Error, (in isolate) x1*a+x2*a+x3*a+x4*a does not contain x1+x2+x3+x4

When I isolate it myself Maple even tells me they wouldn't be the same

false

I even reduced the problem to x1*a+x2*a and Maple still has problems with that. As this is a really simple problem I strongly assume the issue lies with the user. Can anyone help me there?

Thanks

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