## Time data is not being updated. What does that mea...

In the right bottom corner of the Maple window, there is data on Time, Bytes, and Available. My task is supposed to perform computation, however the Time data reached the value of 33393.1 s (about 9 hours) and is not being updated (the value does not increase) anymore for at least half an hour. Is this normal or does it mean that something is wrong with my computation process? Windows Task Manager indicates that CPU Usage is 100% and mserver uses about 40-50%. The procedure I use (diffalg(04), Rosenfeld-Groebner) is such that I have no idea how much time the task will require.

Thank you

## Polynomial simplifications...

In the process of simplification I have the following multi-variable polynomial:

y:=-8*C*d1^2*(-2+d1)*(-1+d1)^3*r*L*R^3+(d1^4*(-2+d1)^2*L^2-4*C*(-2+d1)*(4*d1^3-13*d1^2+16*d1-8)*(-1+d1)^2*r^2*L+4*C^2*(-2+d1)^2*(-1+d1)^4*r^4)*R^2+(2*d1^4*(-2+d1)^2*r*L^2-2*C*(-2+d1)*(5*d1^3-24*d1^2+32*d1-16)*(-1+d1)^2*r^3*L+4*C^2*(-2+d1)^2*(-1+d1)^4*r^5)*R+d1^4*(-2+d1)^2*r^2*L^2-2*C*(-2+d1)*(d1^3-6*d1^2+8*d1-4)*(-1+d1)^2*r^4*L+C^2*(-2+d1)^2*(-1+d1)^4*r^6

This polynomial contains several (-2+d1), (-1+d1) terms with varying powers in each term. My question here is how to take out common terms and then form compact multi-variable polynomial (without having physical inspection).

MVC

## Roots dis-isolate the terms within roots...

I am solving "Fx=0" for geting "roots:x" using "solve(Fx,x)". Solution is in the form of "a+sqrt(b)", "a-sqrt(b)". One solution "f1" is given below.

f1:=1/2*(-8*R*d1^2*r^2*C+10*d1*r^2*C*R+5*d1*r^3*C+2*r*L*d1^2-2*C*r^3+2*R*L*d1^2-R*L*d1^3-r*L*d1^3-4*C*r^2*R+2*R*d1^3*r^2*C-4*r^3*d1^2*C+r^3*d1^3*C+sqrt(26*r^6*d1^4*C^2+41*r^6*d1^2*C^2-44*r^6*d1^3*C^2-20*C^2*r^6*d1+16*C^2*r^5*R-16*C*r^4*L-176*r^5*d1^3*C^2*R+164*r^5*d1^2*C^2*R-74*r^4*d1^4*C*L+136*r^4*d1^3*C*L-136*r^4*d1^2*C*L-80*C^2*r^5*d1*R+72*C*r^4*L*d1-64*C*r^3*R*L+104*R^2*d1^4*r^4*C^2-176*R^2*d1^3*r^4*C^2+164*R^2*d1^2*r^4*C^2-8*r^6*d1^5*C^2+r^2*L^2*d1^6-4*R^2*L^2*d1^5+104*r^5*d1^4*C^2*R+40*r*L*R^3*d1^5*C-72*r*L*R^3*d1^4*C+56*r*L*R^3*d1^3*C-16*r*L*R^3*d1^2*C+R^2*L^2*d1^6+20*r^4*L*C*d1^5-32*r^4*d1^5*C^2*R^2+2*R*L^2*d1^6*r-2*r^4*L*d1^6*C+4*R^2*d1^6*r^4*C^2+4*R*d1^6*r^5*C^2-306*r^3*d1^4*C*R*L+548*r^3*d1^3*C*L*R-544*r^3*d1^2*C*R*L+288*C*r^3*L*d1*R+16*C^2*r^4*R^2+4*R^2*L^2*d1^4-16*R^2*L*d1^6*r^2*C-10*R*L*d1^6*r^3*C+r^6*d1^6*C^2-32*r^5*d1^5*C^2*R-4*r^2*d1^5*L^2-352*R^2*d1^4*r^2*C*L+580*R^2*d1^3*r^2*C*L-552*R^2*d1^2*r^2*C*L-80*d1*r^4*C^2*R^2-8*R^3*d1^6*L*C*r+88*r^3*L*C*d1^5*R+116*r^2*L*R^2*d1^5*C+4*C^2*r^6-8*r*R*L^2*d1^5+288*d1*r^2*C*R^2*L-64*C*r^2*R^2*L+8*r*L^2*d1^4*R+4*r^2*L^2*d1^4)^(1/2))/(-3*r^2*d1*L*C-6*R*d1*L*C*r+2*L*C*r^2+r^2*d1^2*L*C+4*L*C*r*R+2*R*d1^2*L*C*r);

I used the following Maple syntax

patmatch(f1,XT::algebraic+sqrt(YT::algebraic),'q1');

Is there any modification in the syntax "patmatch" is required.

Here, my question is how to separate "a" and "b" in "a+sqrt(b)" (a, b are big expressions involving many variables).

## Polynomial roots simplifications...

I am solving "Fx=0" for geting "roots:x" using "solve(Fx,x)". Solution is in the form of

"a+sqrt(b)", "a-sqrt(b)"

Here my question is how to extract "a", "b" separately (a, b are complex and very big expressions).

## Polynomial simplification...

I am trying to simplify the following polynomial.

> R1 := collect(((3*d1^2-2*d1-d1^3)*r-3*d1^2+d1^3+2*d1)*R^3+((-6*d1+7*d1^2-d1^3)*r^2+(d1-d1^3-3*d1^2+2)*r)*R^2+((-6*d1+6*d1^2)*r^3+(-4*d1^3+6-7*d1+2*d1^2)*r^2)*R+(2*d1^2-2*d1)*r^4+(-2*d1^2-4*d1+4)*r^3,[R,r,d],recursive);

With the "collect along with rucursive" unable to give compact version. In the above polynomial most of the bracket terms will have factors([3*d1^2-2*d1-d1^3]=-d1*(d1-1)*(d1-2)), but the collect command unable give these factors, doing such manual simplification in bigger polynomial case is complex. Is there any way to represent above polynomial in compact form.

MVC

## Animating combined 3d plots...

Hi everyone,

I am using the following code (by dr. Corless) to animate a Riemann surface:

restart;
with(plots);
B := 1.5;
u2 := r*cos(th); v2 := r*sin(th);
w1 := u1+I*v1; w2 := u2+I*v2;
z1 := evalc(w1^2); z2 := evalc(w2^2);
x1 := evalc(Re(z1)); x2 := evalc(Re(z2));
y1 := evalc(Im(z1)); y2 := evalc(Im(z2));
f1 := proc (theta) options operator, arrow; plot3d([-x1, -y1, v1], u1 = -6 .. 1, v1 = -B .. B, grid = [50, 50], orientation = [theta, 80], color = u1) end proc;
f2 := proc (theta) options operator, arrow; plot3d([-x2, -y2, v2], r = 1 .. 1, th = -Pi .. Pi, grid = [50, 50], orientation = [theta, 80], color = black) end proc;
display(seq([f1(10*k), f2(10*k)], k = -17 .. 18), insequence = true, axes = box, view = [-1 .. 1, -1 .. 1, -B .. B]);

f1 is the Riemann surface and f2 is the winding curve.

The animation works fine on the individual plots, i.e. when I do:

display(seq(f1(10*k), k = -17 .. 18), insequence = true, axes = box, view = [-1 .. 1, -1 .. 1, -B .. B]);

or

display(seq(f2(10*k), k = -17 .. 18), insequence = true, axes = box, view = [-1 .. 1, -1 .. 1, -B .. B]);

but with both f's (as in my modification)  the animation does not combine correctly the two plots and shows them separately. Is there any way I can combine the plots so that display produces a smooth animation with each rotated frame containing its winding curve?

Many thanks,

Yiannis

## Truncated floating point (bug?)...

I have run into some queer behaviour of my Maple 9 software. I gave the following commands:

##############################################################
with(numtheory):
xx := invcfrac([[0],[5,1,5,1,4,1]]);
...

## a integral embedded in Diff eq........

i am solving for a system of df eq's, but the eq's have these little tricky integrals inside them.....so it either retards operation or no solutoin can be found...They look like...

```B_12:=(10*a_2*a_3)*(u/( ((10^2+u)^(3/2)) * ((a_2^2+u)^(3/2)) * ((a_3^2+u)) )):
B_122:=(10*a_2*a_3)*(u/( ((10^2+u)^(3/2)) * ((a_2^2+u)^(5/2)) * ((a_3^2+u)) )):
B_123:=(10*a_2*a_3)*(u/( ((10^2+u)^(3/2)) * ((a_2^2+u)^(3/2)) * ((a_3^2+u)^(3/2)) )):
B_23:=(10*a_2*a_3...```

## Plotting a point plot..........

`My problem looks as follows................pts1FIXED comes from dsolved solution......it plots a empty figure...and i checked that l(the data pairs looks fine)..`
`--------------------------------------`
```Energy:=array(1..450);
Time:=array(1..450);
for i from 1 to 450 do

Energy[i]:=-1*((32*G*Inertia^2*e^2)/(5*c^2))*pts1FIXED(i);
end do:
l := [[t,Energy[t]] \$t=1..450]:
plot(l,style=point,symbol=circle,color=blue);
```

## Very Urgent...Please....Runge-Kutta method for sys...

I need some help...i need a solver using the Runge-Kutta method adaptive size control, to solve a sytem of 5 diff eq's, all of them are interlinked...

And

Say that dsolve numeric produces a results, called Solution, Now ex  solution(0)=1, and in general solution(t) can be evaluated, now, i want to use this, in E(t)=2*solution(t), in a plot, thus...

plot(E(t),t=0..100,....), but returns the error....

## Solving a system of 5 non-linear diff eq's...

I am trying to solve a tricky system of diff eq....can somebody point me in the right direction, the error message is involved with the initial conditions..

## Plotting options...

A very useful feature of the plotting program gnuplot is that you can generate an output which is a file instead of a graph. For instance the following short script

################
f(x)=sin(x)+cos(pi*x)
set samples 5000
set table "outfile.dat"
plot [0:10][] f(x)
################

produces a  file containing a sampling of the function f(x) on the interval [0,10] based on a grid...

## writefile syntax...

I have some numerical data, which are very accurate (500 digits) and want to copy them on a text file.

For pratical reason I would like the procedure writefile to write just 20 digits figures: which is the right syntax to use?

## Concatenating strings and floats...

Here is a simple example from the Maple Help (nersion 9.03):
###
i := 5; cat( "The value of i is ", i, "." );
###
which yields
"The value of i is 5."

I would like to use the same syntax to generate a string to be printed at the beginning of a data file (so that I can remember what are the figures in the files); for instance I want to specify that this set has been generated choosing the value of a parameter alpha to be 0.618. So I write

## Bug in procedure writefile of Maple9...

I think I have found a subtle bug in my Maple 9.

If I execute the following code:

###
B:=[ 3.5, 0.0001, 73.45]; A:=[[seq(1/op(j,B), j=1..3)]];
writedata("a.txt",A);
###

the output file a.txt contains the line
0.2857142857    1       0.01361470388
(beware: maple has written "1" instead than "10000"!)

Questions:
1) is this bug already known? Is there a patch?
2) does it affect newer versions of Maple?

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