Changes between Initial Version and Version 57 of Ticket #16268
 Timestamp:
 07/03/18 08:12:40 (3 years ago)
Legend:
 Unmodified
 Added
 Removed
 Modified

Ticket #16268

Property
Status
changed from
new
toneeds_review

Property
Authors
changed from
to
Robert Bradshaw, Erik Massop, Marc Mezzarobba
 Property Cc tscrim cheuberg etn40ff jakobkroeker bhutz added

Property
Milestone
changed from
sage6.2
tosage8.3

Property
Summary
changed from
Better normalization for function field elements
toBetter normalization for fraction field elements

Property
Branch
changed from
to
u/mmezzarobba/16268normalize_fractions

Property
Commit
changed from
to
db762fc4082cf6af913a7637b895f970a7492a74

Property
Status
changed from

Ticket #16268 – Description
initial v57 1 Normalize the leading coefficient of the denominator to one when reducing elements of fraction fields of univariate polynomial rings over fields. Doing so 2  often leads to more readable results, 3  helps limiting coefficient blowup during computations with fractions over complicated base fields (e.g., elements of ℚ(x,y)(t)), typically leading to much better performance, 4  makes hashing more (though not 100%) reliable, see the original description and the comments below. 5 6 The following further improvements are IMO desirable but out of the scope of this ticket: 7  clearing denominators in the numerator and denominator instead of making the leading coefficient of the denominator monic when that makes sense (i.e., for printing, and perhaps for computations in nested rational function fields, but making it fast enough requires some work), 8  also normalizing the leading coefficients over nonfields where that makes sense. 9 10 Original description: 11 1 12 If K is a field then K(u), the function field, has a reduce() method which cancels the gcd but does not put into a canonical form by (for example) dividing through by the leading coefficient of the denominator to make the denominator monic. This means that equal elements may have different hashes, and hence that putting function field elements into a set does not work as a mathematician would expect. For example: 2 13 {{{