On Tuesday, June 25, 2019 at 3:10:29 AM UTC-7, Peter Luschny wrote:
>
> Am Di., 25. Juni 2019 um 10:49 Uhr 'luisfe' :
>
> | When n =0, k ranges from 0 to -1 so there is no k and the list
> constructed in ib(n,m)
> | is just the empty list. Not an empty list of polynomials, just an empty
> list.
>
> Well, then the way 'sum' is implemented is possibly improvable?
>
> The type information for "binomial(m*n-1, m*k)*polynomial(m,k)"
> is there, regardless of what the value of the integers m, n, and k is.
>
No, it's not there, that's the problem. Do this:
sage: def list_polys(m, n): return [binomial(m*n-1,
m*k)*cyclotomic_polynomial(m*(k+1)) for k in (0..n-1)]
sage: list_polys(2,0)
[]
Python evaluates the argument inside sum(...) before applying the sum
function to it. In this case, it gets an empty list, and so has no way of
knowing whether it came from a polynomial or anything else. I'm not sure
what behavior would improve this. If you wanted to try to parse the
arguments and determine that the expression binomial(m*n-1,
m*k)*cyclotomic_polynomial(m*(k+1)) was supposed to be a polynomial, you
need to plug in actual numbers for m, n, and k: Python functions don't have
defined output types, so you can't tell what "cyclomic_polynomial(m*(k+1))"
will be until you plug in numbers. In this case, m=2 and n=0, but what
value should you plug in for k? I can imagine situations where plugging in
k=0 is right but k=-1 is wrong, and vice versa, so what would a good
default be?
Sage's solution, as pointed out by slelievre, seems like the right choice.
> (The definition of 'polynomial' here does not matter as long as it is a
> polynomial.)
>
> To see this try this:
>
> def ib(m, n):
> R = ZZ['x']
> p = lambda m,n,k: binomial(m*n-1, m*k)*cyclotomic_polynomial(m*(k+1))
> print type(R(p(2,n,0)))
> return [p(m,n,k) for k in (0..n-1)]
>
> for n in (0..3):
> r = ib(2,n)
> print(type(r), r)
>
> The output includes in *all* cases
> <type
> 'sage.rings.polynomial.polynomial_integer_dense_flint.Polynomial_integer_dense_flint'>
>
> So why not use this information to return the zero of this ring if the sum
> range (a..b) has not a <= b?
>
>
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