> with(Student[Calculus1]): > Roots( sin(x), 0..5*Pi ); [0, Pi, 2 Pi, 3 Pi, 4 Pi, 5 Pi] > nops(%); 6 Regards, Georgios

An example below of counting: > restart: > ans:=solve(x^6+1,x); > ans:=[ans]; > nops(ans); This returns "6", as it should. Regards, Georgios Kokovidis

Alec, when I copied the equations above, I did not have the colon operator for z1. The first thing I did was what you did with the sum, but I kept getting a strange answer with a z1 in it. It was a type on my side. Sorry for any confusion to the original poster of the question. //Georgios

> restart: with(linalg): > x1:=[1,2,3,4,5,6,7,8,9]; > y1:=[9,8,7,6,5,4,3,2,1]; > z1:=[4,5,6,3,2,1,9,8,7]; > a1:=matadd(x1,y1); > matadd(a1,z1); ([14, 15, 16, 13, 12, 11, 19, 18, 17]) Is this answer above what you are looking for? Regards, Georgios Kokovidis

From your original data above, the problem with the plot not working is that you did not put commas in between your array of variables. Try this below. If you remove the "axes=none" statement, you will see the x and y axis on your plot. Then you can right click in the plot and change the axes as you like. > restart: > plot([[0,1],[1,1],[1,0],[0,0],[0,1]],axes=none); Using plottools as Alec describes above is the preferred method, but the simple approach described here will work as well. Regards, Georgios Kokovidis

The following link(s) have examples that should work with version 9. The example specifically mentions the generalized nonlinear Schroedinger equation. http://www.geocities.com/optomaplev/programs/selff.html and the package of interest that is mentioned in the above worksheet can be found here: http://www.cs.uwaterloo.ca/~ecterrab/qft.html Regards, Georgios

I am using version 10.06 Classic Interface. I do not know if this is supported in version 9. Regards, Georgios

Start by looking at the Maple help pages. At the prompt type: > ?dsolve/numeric/DAE Scroll down, and take a look at the 1st example. The Lagrangian and modified Lagrangian are given. You can use this as a starting point. Hope this helps. Regards, Georgios Kokovidis

Your constraints are not visible, but you can fill them in later on when you implement this in Maple. > restart: > with(Optimization): > Maximize(3*x+2*y, {(3*x+2*y)<=100}); > Maximize(3*x+2*y, {x<=0,y<=20}); See the help page for the Optimization package for more details and examples: Type ?Optimization at the Maple prompt. Regards, Georgios Kokovidis

The Maple Applications Center has a listing for a package called: Ratappr: A package of function approximation http://www.maplesoft.com/applications/app_center_view.aspx?CID=5&SCID=18&AID=744 Regards, Georgios Kokovidis

The Maple minimax function is a front end to the remez algorithm, as implemented in Maple. Instead of using minimax, you can use remez directly, and see if that gets you there. ?numapprox[remez] for more details. Overall, this routine gives up rather quickly, with the reported error message about error curve fails to oscillate sufficiently. The remez alg. might give you more options to tweak to make the solution converge. The array of factors containing the initial estimate of the critical set will ultimately determine whether this will work or not, and if it does, the quality of the solution. Hope this helps. Regards, Georgios Kokovidis

The code above is fast and elegant. If you want something slower, with another twist, take a look at the code below. You can change the order of the function from a second order like I am using to anything you like, and superimpose the plots to see the effects of using higher order polynomials for approximation. Ultimately, it depends on the type of data you are fitting. > restart: > with(stats):with(statplots): with(plots): > Data:=[[75,7843],[80,11314],[90,17820],[95,21431]]; > X:=[seq(Data[i,1],i=1..nops(Data))]; > Y:=[seq(Data[i,2],i=1..nops(Data))]; > scatterplot(X,Y,color=blue,symbolsize=15);ptplt:=%: > fitfunc:=fit[leastsquare[[x,y],y=a*x^2+b*x+c]]([X,Y]); > plot(rhs(fitfunc),x=75..100); crvplt:=%: > display({crvplt,ptplt}); > ans:=unapply(fitfunc,x); > evalf(ans(85)); Regards, Georgios Kokovidis

Will the "alias" command do what you are looking for? Give it a try, and see what happens. > alias(theta=arctan(sin(theta)/cos(theta))); > x:=arctan(sin(theta)/cos(theta)); Regards, Georgios Kokovidis

Change your call from "solve" to "fsolve" and see if the result is what you are looking for: > ans := fsolve({-.373-.150*x+0.111e-1*x^2+0.20e-1*x^3-0.5e-4*x^4-0.6e-5*x^5+0.1e-2*(y-15) = 0, -5.35+.4*y-0.6e-2*(y-15)^2-0.4e-2*(y-15)^3+0.1e-2*x = 0}, {x, y}); Regards, Georgios Kokovidis

The code below will plot (various types) the output to the solution of your system: > restart: > with(plots): > odesys := diff(x(t), t) = 2*x(t)-y(t)-x(t)^3, diff(y(t), t) = x(t); > ics := x(0) = 4, y(0) = 3; > ans:=dsolve({odesys, ics}, type = numeric); > odeplot(ans,[[t,x(t)],[t,y(t)]],0..20,numpoints=200); > odeplot(ans,[t,x(t),y(t)],0..20,axes=boxed,numpoints=200); > odeplot(ans,[x(t),y(t)],0..20,axes=boxed,numpoints=200); Regards, Georgios Kokovidis