Hallo,

Is there a fairly straightforward method for obtaining an array of coordinates from an implicit equation? I have an ellipse defined implicitly (by a horrendously involved expression) and can't figure out how to extract a set of coordinates from an implicitplot. I'm reluctant to use seq and fsolve with a fixed stepsize.

Would be grateful for some insight!

Thanks.

Weirp

I'm trying to create and populate the Array `A` with a sequence of lower triangular matrices based on the following relation:

A[k+1][i,j] = a (1+k) A[k][i,j] + b ((1+j) A[k][i-1,j] - j A[k][i-1,j-1])

The rows and columns of each matrix are given by i and j; a and b are scalars. The structure of A is not important provided a matrix can be accessed for a given k. The highest k value will not be more than about 100.

The starting matrix for k=1 is

[-1  0]
[ 1 -1]

Any guidance on where to start with setting up the appropriate procedure would be greatly appreciated.

Thanks.

I have defined the following procedure, S(x,a,b,s), in Maple with the goal of creating an exportable two column, multi-row array, containing the least positive real root of a high order polynomial f(x,y)=0 in the 2nd column, and a parameter y in the first column.

The procedure takes four numerical arguments (x,a,b,s) and varies parameter y from the initial non-negative value of a, by stepsize s, until the value min(b,1) is reached.

Unfortunately, the output 4x2 array only has the last calculated [y,solution] entries in the first row. Successive rows are filled with zeros.

Is there anyone kind enough to point out the error in the way I have defined this procedure? Many thanks in advance. Procedure is:

S := proc (x, a, b, s) 
   global R, y;
   for y from a by s to b while y < 1
     do R := Array(1 .. ceil((min(b, 1)-a)/s), 1 .. 2, [[y, FindMinimalElement(select(type, [fsolve(f(x) = 0)], positive))]])
     end do;
     end proc;

When attempting to use algsubs with a subscripted expression involving powers I am running into a problem.

I have assigned a numerical value to n, and I have a symbol subscripted with n+1 and raised to a power.

In the original expression I have a factor of the form: P^q + R_n^q which I should like to replace with the symbol B.

> n:= 2

> P^q + R_(n+1)^q

> algsubs(P^q + R_(n+1)^q = B, %)

This last input leads to the error message:

Error, (in algsubs) no variables appearing rationally in pattern.

If I attempt to use algsubs on a subscripted symbol which is not raised to a power, the result works. Is there a cure?

Thanks in advance.