## Start and end of a range...

Hello, perhaps my question is really stupid but I cannot find any hints on the help pages (Maple 10): How can I find the lower and upper bound of a range, i.e, "a" and "b" from "a..b"? The following does work lower:=proc(r::range) min(\$r) end proc ; but is, of course, very inefficient for large ranges and only works for integer bounds.

## Structured types...

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);
```

## Physics exercise...

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?

## Diagonalization Of Matrices...

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,

## logarithm rules...

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

## Is there a way to do this? [probably a bug]...

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

## CodeGeneration -- Some constants are not replaced ...

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...

## graphing a moving particle on two 3-D sphjeres...

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):

## Export data with a given display precision...

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

## Using the 'do' function...

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

## Load own library at start-up...

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 to solve the question...

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<><>

## Eigenvectors of 2x2 Matrix with trig functions...

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.