Here is a technique which I need to do over and over and over in Maple. I am currently writing a research paper for the International Journal of Mathematics and Mathematical Sciences. I need to get this example out as soon as possible. Suppose I want to create a matrix where the (i,j) entry is the polynomial x^i + (x+1)^j whatever the entry is.. it doesn't matter. Point is that the entry depends upon the row i and column j How can I create and fill such a matrix? My matrices a slightly more complicated, involving entries such as diff(x^i + (x+1)^j,x) where it is actually easier

I can't believe that the examples for do loops provided by the Maple tutorial does not show how to put more than one state in a do loop. Maple refers to this as a "statement sequence". Yet, an internal search of keyword "statement sequence" in Maple Help yields No Matches. Example: how can I do this simple example: for n from 1 to 10 do x:=2*n y:=3*n end do; ?

None of the built-in features of Maple will help me numerically solve the kinds of complicated differential equations I want. I was hoping that Maple's option in dsolve of solving by Taylor series would at least grind out the first nine terms of the Taylor series expansion of the solution y(x) of e.g. x^3 + (y'(x) - 9*x)^(5/(y(x)+2)) + 4*(x-y(x))^(y'(6*x+4)) = 0 subject to y(1)=0. I dumped in functional equations, too, to see if Maple could handle it. Ok. So, for something like this, R(x,y(x),y'(x),y'(6x+4))=0 Maple should be at least able to do the first 9 differentiations to express

The command root(f(x),x, K) to compute roots of a univariate polynomial f(x), (let f(x) have integer coefficients), will not return an answer unless *I* do the WORK FIRST of FINDING THE ROOT to determine over WHICH FIELD (algebraic field, if it's algebraic) some of the roots of f(x) lie. The help manual demonstrates this with simple quadratics only. One writes the radical part of the quadratic solution for K, i.e. root(x^2-3,x,3^(1/2)) Mathematica had the complete Cardano formulae programmed in for both the cubic and the quartic polynomials with completely indeterminate coefficients.