I would use V[2,1] instead of Column(V,1)[2], etc.

Alec

I would use V[2,1] instead of Column(V,1)[2], etc.

Alec

That also could be written as

[seq(a[[i,i+1]],i=1..nops(a)-1,2)];

which also fixes the case with odd number of elements (by ignoring the last element).

Alec

That also could be written as

[seq(a[[i,i+1]],i=1..nops(a)-1,2)];

which also fixes the case with odd number of elements (by ignoring the last element).

Alec

In LengthSplit, that can be fixed using pad - something like

[ListTools:-LengthSplit(a,2,pad=undefined)];

  [[1, 2], [3, 4], [5, 6], [7, 8], [9, 8], [7, 6], [5, 4], [3, 2],

        [17, undefined]]

Alec

In LengthSplit, that can be fixed using pad - something like

[ListTools:-LengthSplit(a,2,pad=undefined)];

  [[1, 2], [3, 4], [5, 6], [7, 8], [9, 8], [7, 6], [5, 4], [3, 2],

        [17, undefined]]

Alec

Also, that could be done as

P[..,[2,1]]

Alec

Also, that could be done as

P[..,[2,1]]

Alec

This picture looks definitely better, but still decreasing at the end of the interval looks suspicious. It is hard to tell without seeing the equations, but looking at the recent similar example in another thread, with the similarly decreasing partial sum at the end of the interval, and increasing solution gives an idea (which may be wrong, but also may be correct) that the actual solution in this example may be also increasing on the interval from 1 to 4.

Also, the choice of degree 15 looks rather arbitrary. If one stopped at degree 9, the picture would be different - it might be also different for, say, degree 24.

G:=(-1)-1+x+(1/2)*(-1+x)^2+(-1+x)^3+(2/3)*(-1+x)^4+
(37/60)*(-1+x)^5+(127/360)*(-1+x)^6+(31/140)*(-1+x)^7 +
(185/2016)*(-1+x)^8+(53/1620)*(-1+x)^9:

P54:= numapprox[pade](G,x=1,[5,4]):

plot({P54,P87}, x=0 .. 4);

Alec

This picture looks definitely better, but still decreasing at the end of the interval looks suspicious. It is hard to tell without seeing the equations, but looking at the recent similar example in another thread, with the similarly decreasing partial sum at the end of the interval, and increasing solution gives an idea (which may be wrong, but also may be correct) that the actual solution in this example may be also increasing on the interval from 1 to 4.

Also, the choice of degree 15 looks rather arbitrary. If one stopped at degree 9, the picture would be different - it might be also different for, say, degree 24.

G:=(-1)-1+x+(1/2)*(-1+x)^2+(-1+x)^3+(2/3)*(-1+x)^4+
(37/60)*(-1+x)^5+(127/360)*(-1+x)^6+(31/140)*(-1+x)^7 +
(185/2016)*(-1+x)^8+(53/1620)*(-1+x)^9:

P54:= numapprox[pade](G,x=1,[5,4]):

plot({P54,P87}, x=0 .. 4);

Alec

At some point, perhaps, in Maple 12, I don't remember exactly, many random tools were broken. You might choose a different way of generating a set of random 4-element lists or Vectors. It worked rather fast on my computer.

I didn't check the procedure that I posted though - Standard Maple produces a lot of garbage during copying and pasting, and I corrected it manually, so could accidentally make some mistake. I'll check that.

Alec

At some point, perhaps, in Maple 12, I don't remember exactly, many random tools were broken. You might choose a different way of generating a set of random 4-element lists or Vectors. It worked rather fast on my computer.

I didn't check the procedure that I posted though - Standard Maple produces a lot of garbage during copying and pasting, and I corrected it manually, so could accidentally make some mistake. I'll check that.

Alec

Well, I pasted the example from the original post in Maple and removed the order term without any problems just by deleting it. That doesnt solve the plotting problem though because the series seem to have the radius of convergence close to 1.5, and centered at x=1 - so the partial sum could be used reliably for plotting only on the beginning of the interval from x=1 to x=4 - say for x from 1 to 2, and has very little to do with the plot of the actual solution at the end of the interval - for x from 3 to 4.

Alec

Well, I pasted the example from the original post in Maple and removed the order term without any problems just by deleting it. That doesnt solve the plotting problem though because the series seem to have the radius of convergence close to 1.5, and centered at x=1 - so the partial sum could be used reliably for plotting only on the beginning of the interval from x=1 to x=4 - say for x from 1 to 2, and has very little to do with the plot of the actual solution at the end of the interval - for x from 3 to 4.

Alec

To get it working is not a big challenge. The challenge is to make it look nicely in Maple.

Alec