Poly thinks sqrt(2) coefficient makes a polynomial multivariate

[oscarbenjamin]

I found this while looking at #15408.

The shorthand Poly(expr) for Poly(expr, x) should guess the polynomial variate from the expression expr. However it fails if the polynomial has a coefficient like sqrt(2):

In [6]: roots(sqrt(2)*x**3 + x, x)
Out[6]: 
⎧        3/4        4 ___        ⎫
⎪      -2   ⋅ⅈ      ╲╱ 2 ⋅√2⋅ⅈ   ⎪
⎨0: 1, ────────: 1, ──────────: 1⎬
⎪         2             2        ⎪
⎩                                ⎭

In [7]: roots(sqrt(2)*x**3 + x)
---------------------------------------------------------------------------
PolynomialError                           Traceback (most recent call last)
<ipython-input-7-df234384a5fa> in <module>()
----> 1 roots(sqrt(2)*x**3 + x)

/space/enojb/current/sympy/sympy/sympy/polys/polyroots.py in roots(f, *gens, **flags)
    906 
    907         if f.is_multivariate:
--> 908             raise PolynomialError('multivariate polynomials are not supported')
    909 
    910     def _update_dict(result, root, k):

PolynomialError: multivariate polynomials are not supported

In [9]: roots(Poly(sqrt(2)*x**3 + x, x))
Out[9]: 
⎧        3/4        4 ___        ⎫
⎪      -2   ⋅ⅈ      ╲╱ 2 ⋅√2⋅ⅈ   ⎪
⎨0: 1, ────────: 1, ──────────: 1⎬
⎪         2             2        ⎪
⎩                                ⎭

In [14]: roots(Poly(sqrt(2)*x**3 + x))
---------------------------------------------------------------------------
PolynomialError                           Traceback (most recent call last)
<ipython-input-14-8f8a5579b962> in <module>()
----> 1 roots(Poly(sqrt(2)*x**3 + x))

/space/enojb/current/sympy/sympy/sympy/polys/polyroots.py in roots(f, *gens, **flags)
    906 
    907         if f.is_multivariate:
--> 908             raise PolynomialError('multivariate polynomials are not supported')
    909 
    910     def _update_dict(result, root, k):

PolynomialError: multivariate polynomials are not supported

[asmeurer]

This is sort of expected behavior of Poly at the moment. The extension flag defaults to False. Maybe it would be better to use the EX domain instead of treating sqrt(2) as a generator, I don't know. For now, it's best practice to pass the variables as the second argument if you know what they are.

[oscarbenjamin]

Okay so shall I close this?