Conversion of rationals into the fraction field of integer polynomials

[sagetrac-spancratz]

sage: F = Frac(PolynomialRing(ZZ, 't'))
sage: F(1/2)
...
TypeError: no conversion of this rational to integer

Component: coercion

Author: Sebastian Pancratz, Mike Hansen

Reviewer: Mike Hansen, Sebastian Pancratz

Merged: sage-4.3.2.alpha0

Issue created by migration from https://trac.sagemath.org/ticket/7958

[sagetrac-spancratz]

Attachment: trac7958.patch.gz

[wjp]

comment:3

Your fix does work great for QQ, but this is actually a more general issue than just QQ:

sage: _.<x> = ZZ[]
sage: K.<a> = NumberField(x^2-2)
sage: R.<b> = K.ring_of_integers()
sage: S.<y> = R[]
sage: F = FractionField(S)
sage: F(1)/F(a)
1/a
sage: F(1/a)
*boom*

And a minor issue: I think the comment about QQ should be a code comment rather than in the doctest, since it might now confuse users (who might think they need to handle QQ specially themselves).

[sagetrac-spancratz]

Attachment: trac7958_b.patch.gz

Attachment: trac7958_c.patch.gz

[sagetrac-spancratz]

comment:4

To see that this issue is now resolved (for rationals and number fields), consider
{{{sage: _. = ZZ[]
sage: K. = NumberField(x^5-3x4+2424x^3+2x-232)
sage: R. = K.ring_of_integers()
sage: S. = R[]
sage: F = Frac(S)
sage: F(1/a)
a^4 - 3a^3 + 2424a^2 + 2/232
sage: F(1/a).numerator()
a^4 - 3a^3 + 2424*a^2 + 2
sage: F(1/a).denominator()
232
}}}

But the last three lines highlight a bug in the printing routines.

[mwhansen]

comment:5

Attachment: trac7958_d.patch.gz

sage: _.<x> = ZZ[]
sage: K.<a> = NumberField(x^5-3*x^4+2424*x^3+2*x-232)
sage: R.<b> = K.ring_of_integers()
sage: S.<y> = R[]
sage: F = Frac(S)
sage: F(1/a)
a^4 - 3*a^3 + 2424*a^2 + 2/232
sage: F(1/a).numerator()
a^4 - 3*a^3 + 2424*a^2 + 2
sage: F(1/a).denominator()
232

[mwhansen]

Combined version of the above patches.

[mwhansen]

Attachment: trac7958.2.patch.gz

Attachment: trac_7958-atomic.patch.gz

[sagetrac-spancratz]

comment:6

Applying the two patches

• trac7958.2.patch
• trac_7958-atomic.patch

this applies cleanly and passes all doctests.

[sagetrac-spancratz]

Changed author from spancratz to Sebastian Pancratz, Mike Hansen

[sagetrac-spancratz]

Reviewer: Mike Hansen, Sebastian Pancratz

[sagetrac-mvngu]

Merged: sage-4.3.2.alpha0

[sagetrac-mvngu]

comment:7

Merged patches in this order:

1. trac7958.2.patch
2. trac_7958-atomic.patch