numerical_approx for polynomials

[Vincent Delecroix]

Dear devs,

Is it fine if I implement numerical_approx on polynomials by calling
it recursively on coefficients? For example, we would have

sage: x = polygen(QQ)
sage: p = 1343235439458/23 * x^2 - 234 / 143425*x + 1432/6512
sage: p.numerical_approx()
5.84015408460000e10*x^2 - 0.00163151472895241*x + 0.219901719901720

Right now, it does raise a TypeError (raised inside the generic
numerical_approx).

It would fit with what we have for matrices

sage: matrix(2, [11/23, -5/3, 132/7, 77/12]).n()
[0.478260869565217 -1.66666666666667]
[ 18.8571428571429 6.41666666666667]

Best
Vincent

[Thierry]

Hi,

i would prefer to raise an error promoting the use of change_ring (same
for matrices), which allows more tuning on the base ring.

By the way, note that the best approx with floating-point coefficients
(e.g. for the sup norm on [-1,1]), is not necessarilly obtained with the
best approx on each coefficients.

Ciao,
Thierry

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