Magma V2.20-10 Patch Notes

Algebraic Function Fields¶

• Using the Al := "Round2" parameter to MaximalOrderFinite and MaximalOrderInfinite applied to abelian extensions to use to Round 2 algorithm has been fixed when the input is an abelian extension of an algebraic function field which has an equation order which is not maximal.
• The computation of MaximalOrderFinite and MaximalOrderInfinite of an abelian extension which is actually cyclic has been made more efficient by avoiding an unnecessary discriminant computation. The discriminant check at the end of these computations for abelian extensions whose components have maximal orders with coprime discriminants has been fixed.
• CoveringStructure of some algebraic function fields has been fixed.
• The Check parameter is no longer ignored when set to false when constructing a function field defined by more than one polynomial.

Algebraic Number Fields¶

• Some problems with precision in internal computations have been resolved. Reported by M. Stoll.
• When constructing a number field $K$ from a non-monic or non-integral defining polynomial, the generator K.1 was not set correctly.

Elliptic Curves¶

• EllipticCurveSearch now works for $\mathbb{Q}(i)$ and $\mathbb{Q}(\zeta_3)$. Reported by John Cremona.
• A bug (runtime error) in FourDescent has been fixed. The bug occurred in rare cases when the option RemoveTorsion was used.
• A problem with odd symmetric powers of L-functions of elliptic curves with complex multiplication was fixed (the product did not contain the L-function of the elliptic curve itself).

Finitely-Presented Algebras¶

• A crash in ChangeRing for finitely-presented algebras has been fixed. Reported by F. Lunnon.

Groups¶

• A crash in LowIndexSubgroups has been fixed. This was related to giving a maximum subgroup index of zero. Crash found by unknown calculator user.
• A crash when computing a centralizer of an element in a matrix group over an inexact field (the real numbers) has been fixed. This now causes a runtime error. Generally only element operations are allowed in such a matrix group.

Isotropic Subspaces¶

• The changes (efficiency improvements) in the ordering of reduction and minimisation steps in the previous patch release failed to properly account for the unimodular case (there are thus no primes to minimise, and hence reduction is not done). Reported by T. A. Fisher.

Lattices¶

• A memory leak with the Coordinates function has been fixed.

Newton Polygons¶

• A fix has been made to Newton Polygons constructed from a polynomial over a local ring with zero coefficients. Such zero coefficients no longer correspond to a finite point on the polygon.

Schemes¶

• In the routine LiftPoint (for Hensel lifting a local point), the Random option has been fixed. Previously, randomness failed due to one variable being overlooked.
• Errors have been corrected in the function HeightOnAmbient.

Transcendental Functions¶

• A crash with Psi (equivalently LogGamma) at arguments with negative real part has been fixed. Reported by E. Crane.