Charles Greathouse on Mon, 22 Feb 2010 05:54:25 +0100

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Re: Getting the variable number of a lexical local variable

I still can't seem to make it work properly with multiple variables.
If I'm in a loop with formal variable y and I check polcoeff0(expr, 3,
-1) with expr = 3*y + 5*x, it gives me 5, not 3.  I would like a way
to get 3 when the formal variable is y and 5 when the formal variable
is x.  Can this be done?

I understand that there are no multivariable polynomials in Pari, so
that 3*y may simply be the constant term of a polynomial in x.  But at
the moment I can't even figure out whether my function was called with
sumformal(y=1, n, 3*y + 5*x)
sumformal(y=1, n, 3*y + 5*x)

I've attached my source, if this would help anyone understand what I'm
doing.  Faulhaber(n, a) returns the n-Faulhaber polynomial (in a).

sumformal(GEN start, GEN end, GEN expr)
	pari_sp ltop = avma;
	GEN c, F, res = gen_0, ret;
	GEN x = pol_x(-1);
	long t = typ(expr);
	if (t == t_INT || t == t_REAL || t == t_COMPLEX)
		ret = gmul(gaddgs(gsub(end, start), 1), expr);
		ret = gerepileupto(ltop, ret);
		return ret;
	if (t != t_POL)
		pari_err(notpoler, "sumformal; can only handle polynomials, not
arbitrary functions");

	pari_sp btop = avma, st_lim = stack_lim(btop, 1);
	long d = degree(expr) + 1;
	while (--d)
		c = truecoeff(expr, d);
		F = Faulhaber(d, x);
		res = gadd(res, gmul(c, gsub(gsubstpol(F, x, end), gsubstpol(F, x,
gsubgs(start, 1)))));
		if (low_stack(st_lim, stack_lim(btop, 1)))
			gerepileall(btop, 4, &d, &c, &res, &expr);
	ret = gadd(res, gmul(gaddgs(gsub(end, start), 1), truecoeff(expr, 0)));
	ret = gerepileupto(ltop, ret);
	return ret;

Charles Greathouse
Case Western Reserve University

On Wed, Feb 17, 2010 at 2:37 AM, Bill Allombert
<> wrote:
> On Tue, Feb 16, 2010 at 11:10:43PM -0500, Charles Greathouse wrote:
>> I'm trying to get the variable number of a lexical variable, but I
>> can't seem to figure out how to do that.
>> If I have a function with a V in the prototype, like a custom for
>> loop, how do I know which variable was used?
> This is always -1.
> See
> ??"Functions to deal with lexical local variables"@5
>> In my case, I would like to be able to distinguish between calls to
>> sumformal(x=1, N, x^2 * y)
>> and
>> sumformal(y=1, N, x^2 * y)
> What is the difference with sum() ?
> Cheers,
> Bill