u:=[1,2,5]; op(u); max(op(u)); acer

Here's the default, usual situation in Maple,

> restart:

> about(x);
x:
  nothing known about this object

> is(sin(x),real);
                                     false

You can put assumptions on x, which is a sort of restriction of the domain when x is used as an argument of a function.

> assume(x::nonnegint);

> about(x);
Originally x, renamed x~:
  is assumed to be: AndProp(integer,RealRange(0,infinity))
 
> is(sin(x),real);
                                     true

acer

simplify( sqrt(4) ); assume(d>0); sqrt(d^2); acer

Have a look at ?LinearAlgebra,GenerateMatrix acer

To find the indeterminates, f := x^2*y + 10*z*w + 2*a*t; indets(f); nops(indets(f)); acer

This was in Maple 11.02, > e := (1+b)*x^2+a*(1+b)*x+b*(b-1)+2*b: > factor(expand(e)): > lprint(%); (1+b)*(b+x^2+a*x) Knowing the factor (b+1) in advance, this next was also possible for this example, > e := (1+b)*x^2+a*(1+b)*x+b*(b-1)+2*b: > (b+1)*simplify(e/(b+1)): > lprint(%); (1+b)*(b+x^2+a*x) acer

Plotting `xtba` vs `ytba` for a range of `T`, with fixed `press`.

ytba:=(press-exp(14.7569-2895.6078/(T+140.7459)))*exp(14.7569-2895.6078/(T+140.7459))/((exp(16.5270-3026.8900/(T+168.1400))-exp(14.7569-2895.6078/(T+140.7459)))*press);

xtba:=(press-exp(14.7569-2895.6078/(T+140.7459)))/(exp(16.5270-3026.8900/(T+168.1400))-exp(14.7569-2895.6078/(T+140.7459)));

plot(eval([xtba,ytba,T=30..50],press=100));

acer

Here's a couple of ideas. # replace with your procedure... `#mo("∇")`:=proc(V::Vector) map(sin,V); end proc: `#mo("∇")`:=`#mo("∇")`: Then after each time you grab the nabla from the Common Symbols palette (or cut and paste it) you would have to select the inserted symbol (only) with the mouse, and use the Context Menu action, 2D Math -> Convert To -> Atomic Identifer In this way, I was able to get it to look like a Del/nabla and act like a function on a Vector. I had to use round brackets though, like for any other procedure. Another way that worked for me was to issue, unprotect(VectorCalculus:-Nabla); After that, I could use the symbol from the palette without having to do Context Menu toggling each time. But even this way I couldn't get it to work without using brackets in order apply it, without receiving the error, Error, (in Typesetting:-delayGradient) unable to compute gradient until a co-ordinate system has been defined (see ?VectorCalculus:-SetCoordinates) I don't know if there's a clever workaround for that. acer

1) with(LinearAlgebra): A:=RandomMatrix(2): B:=RandomMatrix(2): X:=Vector(2,(i)->convert(cat("x",i),name)): Y:=LinearSolve(B,A.X); A.X-B.Y; 2) LinearAlgebra[GenerateMatrix]([x1-x3,x1+x2-x4, x1+x2, x3+x4],[x1,x2,x3,x4]); 3) evals:=Eigenvalues(evalf(A)); `+`( seq(`if`(Im(x)=0.0,signum(Re(x)),NULL),x in evals) ); acer

Here's my exam tip. When you do indefinite integrations, don't forget to add the constant (+ C). Those docked half-points add up. Do it like Maple does dsolve({diff(f(x),x)=x}) , not like it does f(x)=int(x,x) . acer

The colon at the end of a statement will instruct maple to suppress the printed or displayed output. A semicolon will not suppress the output. Your last three assignments ended with colons. acer

a:=n->1/((2*n-1)*(2*n+1)); # nth term in sum s:=(n)->n/(2*n+1); # proposed sum formula Is s(1) correct? Does s(N)+a(N+1) = s(N+1) ? acer

You are so close. Two things must match. The value the line attains at x=x1 must be equal to the value that f attaints at x=x1. That's because they touch. The value of the slope of the line must be equal to the value of the slope of f, at the point where they touch. (Not true of all functions, but true of "nice" or "smooth" functions. Not true if f has a "pointy" change of direction or cusp.) So, the first of those two matchings you can probably figure out. Evaluate both the equation of the line and of f, when x=x1. To get the second, you need formulas for the slope of f and for the slope of the line. You got the slope of f, as f'(x). Great. Now, what's the slope of the line? acer

If you issue ?Chebyshev in Maple then you should see suggestions from the help system. Those should include references to parts of the numapprox and orthopoly packages. Consider looking at ?numapprox,Chebyshev . I hope that I've understood what you're after. acer

There are lots of ways to program this. Some are easy to set up, but are probably not optimal for performance. Here are two easy ones. IR := n -> ArrayTools:-FlipDimension(LinearAlgebra:-MatrixScalarMultiply(LinearAlgebra:-IdentityMatrix(n,compact=false),-1,inplace=true),2); seq(IR(n), n=1..5); IR2:=n->Matrix(n,n,(i,j)->`if`(i=n-j+1,-1,0)); seq(IR2(n), n=1..5); acer