@senthil36yours In your wprksheet you execute evalf@allvalues, to examine the results. Does this mean that floating-point approximations to the (real) roots is good enough?

Maybe some real root-finding technique like repeatedly calling fsolve with its `avoid` option, or RootFinding:-Isolate(..,numeric) would suffice?

You said this was an iterative process. Does that mean that each new EQ1,EQ2 is somehow built up from the preceding iteration's found roots? Where do those long integer coefficients come from?

Are the roots expected to be in the same general bounded area, at each iteration? (I ask because fsolve can be quite fast here, but may need to be passed suitable ranges in order to easily find all real roots, since the expressions become so steep.)

What you've described seems to be like the functionality of the DocumentTools[Retrieve] command.

But why not just savelib the data to an .mla Library archive file, when it first gets computed in the original worksheet? 

acer

What you've described seems to be like the functionality of the DocumentTools[Retrieve] command.

But why not just savelib the data to an .mla Library archive file, when it first gets computed in the original worksheet? 

acer

@Markiyan Hirnyk See here for the source.

@Markiyan Hirnyk See here for the source.

@serena88 The seq command takes an optional third argument, for the increment, which can be negative.

> j[[seq(i,i=13..4,-1)],1];

                    j[[13, 12, 11, 10, 9, 8, 7, 6, 5, 4], 1]

@serena88 The seq command takes an optional third argument, for the increment, which can be negative.

> j[[seq(i,i=13..4,-1)],1];

                    j[[13, 12, 11, 10, 9, 8, 7, 6, 5, 4], 1]

@Brettski If you lprint that  atomic-identifier name then you'll likely see something like `#msub(mi("P"),mn("0"))`.

And that is a name (because it is wrapped in single-left name quotes). But the Maple Standard GUI knows to display it as a subscripted name.

@Brettski If you lprint that  atomic-identifier name then you'll likely see something like `#msub(mi("P"),mn("0"))`.

And that is a name (because it is wrapped in single-left name quotes). But the Maple Standard GUI knows to display it as a subscripted name.

@Christopher2222 The eventual slowdown in the Standard GUI that you described when animating the globe also occurs in later Maple versions. I believe that it is due (effectively) to some kind of memory leak in the GUI that occurs when displaying many 3D plots/frames, which you might observe using the MS-Windows Task Manager or Unix/Linus `top` utility.

I encourage you (too) to submit an SCR on it. The more such problems are reported the better the chance it might get fixed.

Consider x^3-4*x+2=0 for which the solve command returns three explicit expressions containing I. Hence, some simplification may be necessary before testing for the presence of I.

restart:

p := x^3-4*x+2:
#plot(p, x=-3..3);

S := [solve( p=0, x )]:

remove( has, S, I );

                               []

remove(has, map(simplify,S,constant), I):
evalf(%);

           [1.675130870, -2.214319743, 0.5391888726]

And simplify(...,constant) may not suffice, in general. And `is` will depend upon Digits (akin to fnormal after evalf), so can also be caught out. Applying evalc@Im can turn this into zero-testing.

acer

Consider x^3-4*x+2=0 for which the solve command returns three explicit expressions containing I. Hence, some simplification may be necessary before testing for the presence of I.

restart:

p := x^3-4*x+2:
#plot(p, x=-3..3);

S := [solve( p=0, x )]:

remove( has, S, I );

                               []

remove(has, map(simplify,S,constant), I):
evalf(%);

           [1.675130870, -2.214319743, 0.5391888726]

And simplify(...,constant) may not suffice, in general. And `is` will depend upon Digits (akin to fnormal after evalf), so can also be caught out. Applying evalc@Im can turn this into zero-testing.

acer

@Markiyan Hirnyk I was just querying what you wanted. It's not hard to get it as a sum (of a product of two numbers of combinations, ie. combinat[numbcomb] calls).

N:=(s,k)->add(combinat[numbcomb](s, i)*combinat[numbcomb](i, k-i),i=0..s);

But you want a closed form for that as a symbolic sum? Can it be in terms of calls to GAMMA and hypergeom (...I'm guessing not)?

Is it just this, for n=0,1,2,3,4,...?

 PolynomialTools:-CoefficientList(expand( (1+x+x^2)^n ),x)

So, do you want something in terms of factorials?

acer

@J4James Since eq2 and bc are both sets, pass the DE system to the dsolve command as the argument,

eq2 union bc

rather than as,

{eq2 union bc}