Considering updating my old package

COSVAM, which treats complex-octonionic-valued scalars, vectors, and matrices, first of all I want a much better type check of whether an expression is indeed a complex-octonionic scalar.
A complex-octonionic-valued scalar is a linear combination over the complex numbers of the eight units of the octonions 1,e1,...,e7, say. So all the following expressions are valid examples of complex-octonionic-valued scalars

expr1 := 10;
expr2 := e1;
expr3 := e1*I;
expr4 := e1*cos(t)+e2*sin(t);

I have one awful, long way to solve the problem below, but I am sure there is also an elegant solution; unfortunately, it currently escapes me.
Consider a rigid sphere of radisu 1 and center at 0 that rotates about its center. The angular velocity is omega(t) = Vector([ cos(t), sin(t), sqrt(3) ]). Does the path of the point starting at (0,0,1) ever reach the same point at a later time?

A quick question to help with some Classical Mechanics homework.
If the determinant of a matrix is zero does that mean that it cannot be diagonalized ?
Please feel free to elaborate. I truly appreciate everyone's help on this site.
In case your interested the text is "Classical Mechanics" 3rd ed. by Goldstein, Poole, and Safko.
Chapter 4, specifically problem 4.8.
Thanks,
v/r,

is there a way to get maple to perform simple logarithm manipulations i.e.
ln(a*b^c)=ln(a)+c*ln(b) ? I've noodled around with the convert utility with no luck.
I am trying to do a power law regression via the normal equation "showing my work". I have the answer using CurveFitting so I'm just trying to fill in the steps thanks

From an exercise in "Game Physics", we have the following piecewise position vector r. We wish to show that it is well-defined (as well as twice differentiable) at 0. The goal of the exercise is then to show that the Normal vector is not even continuous. So we try:
```
p1,p2 := <t,t^3,0>, <t,0,t^3>;
r := piecewise( t<0, p1, p2);
limit(r,t=0,left);
```

and unfortunately that limit gives
RTABLE(149559852,MATRIX([[t], [t^3], [0]]),Vector[column])
as a result!
The obvious thing to try next is to "push in" the piecewise into the components. But the

Hi,
I have a small problem. I want to export code to Matlab. The code is mostly a long expression with some named constants. The constants are set to some values in Maple and in Maple only the x-variables are therefore unknown in the expression. However, in the exported code, some of the constants are not replaced by their values. Does someone have a clue what this depends on?
Best regards
Johan

can I change the behavior of maple to not represent 1/sqrt(2) as sqrt(2)/2? I guess in a mathmatician's view this is a simplification, but not from an engineering standpoint.
also, if I perform combine(sqrt(2)/(sqrt(m)*sqrt(k)),radical,symbolic) I get sqrt(2)*sqrt(1/m k) instead of the desired sqrt(2/(k*m))..is this related?
I'm sure there is a nuance that I am not getting...

i am trying to plot a moving particle on two separate sphers of different radii. i have the code:
restart:
> with(plots):
> with(plottools):
> p1:=plot3d([3*sin(u)*cos(v),3*sin(u)*sin(v),3*cos(u)], u=0..Pi, v=0..2*Pi,color=red,
> style=wireframe,axes=normal,scaling=constrained):
> p2:=plot3d ([2.9*sin(u)*cos(v),2.9*sin(u)*sin(v),2.9*cos(u)], u=0..Pi, v=0..2*Pi,color=blue,axes=normal,scaling=constrained):
> p3:=display(p1,[seq( pointplot( { [3*sin(u)*cos(v)(k/50)(n/50),3*sin(u)*sin(v)(k/50)(n/50),3*cos(u)(k/50)(n/50)],[2.9*sin(u)*cos(v)(k/50)(n/50), 2.9*sin(u)*sin(v)(k/50)(n/50),2.9*cos(u)(k/50)(n/50) ] } ) , (k,n)=(0..314,0..314) ) ],insequence=true):

Hello,
I learned in this forum that if one wants to display the elements of a matrix up to 6 decimal figures one uses
interface(displayprecision=6);
But then I tried to export a matrix with ctrl+c / ctrl+v to another application and when I pasted it the matrix appeared with a different number of decimal figures. My question is: how do I export a matrix with a given number of decimal figures?
Thanks,
Bernardo

If i have a sequence of r[i+1] = 2r[i-1] + 3r[i] (where [i] represents subscript i) how do I use the 'do' function to go from the point where initially r[i-1] is, for example, 3 and r[i] is 4 to the point at which r[i-1] is first greater than 300 and find r[i+1] at this point.
I hope this question makes sense!
Thankyou

Have spent much of the weekend reading the maple help files and googling but still haven't found a current way to do this on XP with v9.5. Tried editing the maple9.5.ini file to point to the folder, but it doesn't work and seems to behave more like a log file. I can use libname as a line in the worksheet but would prefer to do without as I use the modules a lot.
Any suggestions would be welcome.
Neil

How do I plot f(x) in the following question?
f:=x->sum(h(2^n*x)/(2^n),n = 0 .. 20)
h(x)={ 2x , 0<><>

How can I evaluate the eigenvectors of a 2x2 Matrix with trig functions as entries? This is what I did:
```
with(LinearAlgebra):
K:=<<cos(theta)|sin(theta)>,<sin(theta)|-cos(theta)>>;
Eigenvectors(K);
Error, (in LinearAlgebra:-LA_Main:-Eigenvectors) expecting either Matrices of rationals, rational functions, radical functions, algebraic numbers, or algebraic functions, or Matrices of complex(numeric) values
```

I'm wondering why cos(theta) shouldn't be an algebraic function ??
Assuming theta to be real I get the same.

How can I plot some velocity vectors on a circle. the function of velocity vectors is
(1+cos(t))i+(sin(t))j
thank you very much

So, why are we given two ways of defining a function, one using " := " and the other using " -> "? The latter seems pretty clunky. What use is it?