Gottfried Helms on Fri, 18 Nov 2022 00:18:49 +0100

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 Re: Conversion of a function/closure with rational coefficients into one with real coefficients

```Am 17.11.2022 um 20:02 schrieb Bill Allombert:
> Well, if you define
> p[4] =  1/4*x^2-2/3*x+1/6
> then you can define
> my(f=p[4]);(pp[4]=x->eval(f));
> my(f=p[4]*1.);(pr[4]=x->eval(f));
>
> or
> if you really want to use pp[4](x) =  1/4*x^2-2/3*x+1/6,
> then you can do
>
> my(f=pp[4](x)*1.);ppr[4]=x->eval(f);
>
Bill -

many thanks for your help. Unfortunately I couldn't
get your ideas working as I have it intended.
After rethinking (and consultation of the user.pdf)
I understand now, that my intention would best be
described by the (impossible) construction

{for(k=1,4,
component(ppr[4](x))[k] = 1.0*component(pp[4](x)[k];
);}

this means, the creation or alteration of the components
of the closure programmatically. But this idea belongs
to the old 70'ies programming in PL/I where you have
pointers and I would have found how to access the internal
constants of a function/closure...
But this is impossible (and likely not wanted: protected
memory and so on) here in Pari/GP.

What I do at the moment is to use the 'eval(Str("..."))'-
construct to define the function-array, where I already
have the polynomials with rational coefficients in
array of closures 'pp[1..128]'
so

{default(realprecision,60);
default(format,"g0.60");\\ or something I want
ppr=vectorv(128);
for(r=1,128,
st=Str("ppr[",r,"]=x->",1.0*pp[r](x));
eval(st);
);
default(format,"g0.12");
default(realprecision,200); \\ resetting to my standard
}

With this I can give it another try; my implementation
with the rational 'pp[r](x)' polynomials needed in a
certain loop with call on various 'x' 20 sec, while a
concurring implementation from someone else using
real valued (50 dec digits) coefficients/polynomials
ran with 0.2 secs... or so...
I think this shows also the way to implement it as
program-initialization; the strings 'st' in the 'for'-
loop shall be stored as strings in a file which should

Thanks for help and making me rethink the problem!

Kind regards-

Gottried

```