Magma V2.28-20 Patch Notes

Algebraic Function Fields¶

• A crash in WeilRestriction(F, n) for an algebraic function field $F$ and integer $n$ has been fixed. Reported (with supplied fix) by Yusuke Uesato.

Databases¶

• The Volume field of an item from the database of fundamental groups of 3-dimensional manifolds is now properly returned as a FldReElt instead of the obsolete FldPrElt.

Graphs¶

• OpenGraphFile now properly handles paths beginning with a tilde character. Reported by Primo\v{z} Poto\v{c}nik.

Groups¶

• A crash using Induction on a representation of a subgroup of a pc-group has been fixed. Reported by Eamonn O'Brien.

Lie Theory¶

• Arithmetic in groups of Lie type defined over rings is now possible provided all ring elements encountered during the conversion of the group elements to Bruhat normal form are invertible. Reported by Heiko Dietrich.
• For Coxeter groups defined by matrices $$A and $B$ of simple roots and simple coroots, the product A * Transpose(B) is now checked to ensure that it is a valid Cartan matrix.

Linear Algebra¶

• Checking v in V when v is already an element of the vector space V now succeeds even if there is no echelon algorithm over the base ring.

Modular Curves¶

• Fixed a bug in creating quotients of modular curves when the quotient is an elliptic curve. Reported by Sachi Hashimoto.

Power Series¶

• New function Coefficients(f, b, e, d) for power, Laurent or Puiseux series $f$, which is equivalent to [Coefficient(f, i / d): i in [b..e]] but faster.

Real and Complex Fields¶

• PowerRelation now allows the argument to have non-zero imaginary part when the maximum degree is 1. Note that this function is deprecated and it is recommended to use MinimalPolynomial instead, which already handled this case.
• Powering a negative real number by a small rational number with odd denominator now returns the appropriate value instead of @NaN@.
• Computing the n-th Root of a real number now raises an error if n is large, instead of (very slowly) computing a wrong result.

Representation Theory¶

• A bad slowdown in IsIsomorphism for G-modules defined over the rational field has been fixed. Reported by Eamonn O'Brien.

Schemes¶

• It is now ensured that a DivSchElt has a DivSch parent rather than possibly a DivCrv parent which has previously occured when the scheme was a curve. Reported by Eran Assaf.
• A crash in HasNonsingularPoint for a certain type of scheme defined over GF(2) has been fixed. Reported by David Zureick-Brown.

System¶

• User package files which were not explicitly "frozen" were accidentally frozen automatically (since V2.28-4). This has been fixed.