Invariants of Ternary Cubic Forms do not live in the base ring

[davidac897]

It seems that invariants of ternary cubic forms (and I assume other kinds of forms, but I didn't try) live in the polynomial ring, not in the base ring. Therefore, I get this, which shouldn't happen:

R.<a,b,c> = QQ[]
RR.<x,y,z> = QQ[]

f = 1994893*a^3 + 4498037*a^2*b + 3358044*a*b^2 + 830875*b^3 + 7859654*a^2*c + 11828845*a*b*c + 4420000*b^2*c + 10319781*a*c^2 + 7775375*b*c^2 + 4515625*c^3
ff = x^3 + 11*x^2*y - 14*x*y^2 + y^3 + 11*x^2*z + 135*x*y*z - 160*y^2*z - 14*x*z^2 + 3*y*z^2 + z^3


T = invariant_theory.ternary_cubic(f)
TT = invariant_theory.ternary_cubic(ff)

T.S_invariant(); TT.S_invariant(); T.S_invariant() == TT.S_invariant();  T.S_invariant() == QQ(TT.S_invariant())

produces outputs of -705911761/1296, -705911761/1296, False, True.

CC: @mstreng @sagetrac-kohel @sagetrac-florian @JRSijsling @jnoordsij

Component: algebra

Keywords: invariant theory

Author: Frédéric Chapoton

Branch/Commit: 7c7fc38

Reviewer: Sébastien Labbé

Issue created by migration from https://trac.sagemath.org/ticket/30035

[fchapoton]

comment:1

The problem comes from scaled_coeffs:

sage: [parent(u) for u in T.scaled_coeffs()]
[Multivariate Polynomial Ring in a, b, c over Rational Field,
 Multivariate Polynomial Ring in a, b, c over Rational Field,
 Multivariate Polynomial Ring in a, b, c over Rational Field,
 Multivariate Polynomial Ring in a, b, c over Rational Field,
 Multivariate Polynomial Ring in a, b, c over Rational Field,
 Multivariate Polynomial Ring in a, b, c over Rational Field,
 Multivariate Polynomial Ring in a, b, c over Rational Field,
 Multivariate Polynomial Ring in a, b, c over Rational Field,
 Multivariate Polynomial Ring in a, b, c over Rational Field,
 Multivariate Polynomial Ring in a, b, c over Rational Field]

and then from coeffs

sage: [parent(u) for u in T.coeffs()]
[Multivariate Polynomial Ring in a, b, c over Rational Field,
 Multivariate Polynomial Ring in a, b, c over Rational Field,
 Multivariate Polynomial Ring in a, b, c over Rational Field,
 Multivariate Polynomial Ring in a, b, c over Rational Field,
 Multivariate Polynomial Ring in a, b, c over Rational Field,
 Multivariate Polynomial Ring in a, b, c over Rational Field,
 Multivariate Polynomial Ring in a, b, c over Rational Field,
 Multivariate Polynomial Ring in a, b, c over Rational Field,
 Multivariate Polynomial Ring in a, b, c over Rational Field,
 Multivariate Polynomial Ring in a, b, c over Rational Field]

which calls
_extract_coefficients

[fchapoton]

comment:2

This seems from deep inside the invariant code. The choice not to separate true variables of the cubic forms and variables for the coefficients seems to be very wrong, and a serious flaw in the design.

[fchapoton]

New commits:

cfc52e9

fix base_ring for some invariants

[fchapoton]

Branch: u/chapoton/30035

[fchapoton]

Commit: cfc52e9

[fchapoton]

Changed author from jnoordsij to Frédéric Chapoton

[fchapoton]

comment:4

This still needs a doctest.

[sagetrac-git]

Changed commit from cfc52e9 to 7c7fc38

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. New commits:

7c7fc38

trac 30035 add indirect doctest

[fchapoton]

comment:6

now with doctest

[fchapoton]

comment:7

green bot, needs review

[fchapoton]

comment:8

GREEN BOT, please review !

[seblabbe]

Reviewer: Sébastien Labbé

[vbraun]

Changed branch from u/chapoton/30035 to 7c7fc38