scholarly journals Witt equivalence classes of quartic number fields

1992 ◽  
Vol 58 (197) ◽  
pp. 355-355 ◽  
Author(s):  
Stanislav Jakubec ◽  
František Marko
Keyword(s):  
Number Fields ◽  
Equivalence Classes ◽  
Witt Equivalence

scholarly journals A construction of quintic rings

2004 ◽  
Vol 173 ◽  
pp. 163-203 ◽  
Author(s):  
Anthony C. Kable ◽  
Akihiko Yukie
Keyword(s):  
Number Field ◽  
Upper Bound ◽  
Number Fields ◽  
Equivalence Classes ◽  
Ring Of Integers ◽  
Isomorphism Classes ◽  
Cubic Forms

AbstractWe construct a discriminant-preserving map from the set of orbits in the space of quadruples of quinary alternating forms over the integers to the set of isomorphism classes of quintic rings. This map may be regarded as an analogue of the famous map from the set of equivalence classes of integral binary cubic forms to the set of isomorphism classes of cubic rings and may be expected to have similar applications. We show that the ring of integers of every quintic number field lies in the image of the map. These results have been used to establish an upper bound on the number of quintic number fields with bounded discriminant.

scholarly journals Quaternary quadratic lattices over number fields

2019 ◽  
Vol 15 (02) ◽  
pp. 309-325 ◽  
Author(s):  
Markus Kirschmer ◽  
Gabriele Nebe
Keyword(s):  
Quaternion Algebra ◽  
Number Fields ◽  
Equivalence Classes ◽  
Quadratic Space ◽  
Quadratic Lattices

We relate proper isometry classes of maximal lattices in a totally definite quaternary quadratic space [Formula: see text] with trivial discriminant to certain equivalence classes of ideals in the quaternion algebra representing the Clifford invariant of [Formula: see text]. This yields a good algorithm to enumerate a system of representatives of proper isometry classes of lattices in genera of maximal lattices in [Formula: see text].

Division probability for quaternion algebras over fields

2020 ◽  
pp. 2150098
Author(s):  
Leena Jindal ◽  
Anjana Khurana
Keyword(s):  
Rational Numbers ◽  
Equivalence Classes ◽  
Quaternion Algebras ◽  
Type Formula ◽  
Elementary Type ◽  
Witt Equivalence

Let [Formula: see text] be a field of [Formula: see text] with finitely many square classes. In this paper, we define a new rational valued invariant of [Formula: see text], and call it the division probability of [Formula: see text]. We compute it for all fields of elementary type. Further, we show that [Formula: see text], where [Formula: see text] is the number of Witt-equivalence classes of fields with [Formula: see text], and [Formula: see text] is the count of rational numbers that appear as division probabilities for fields [Formula: see text] of elementary type with [Formula: see text]. In the paper, we also determine [Formula: see text] for all [Formula: see text] and show that rational numbers of type [Formula: see text] always occur as division probability for a suitable field [Formula: see text].

scholarly journals MET: a Java package for fast molecule equivalence testing

2020 ◽  
Vol 12 (1) ◽  
Author(s):  
Jördis-Ann Schüler ◽  
Steffen Rechner ◽  
Matthias Müller-Hannemann
Keyword(s):  
Chemical Properties ◽  
Graph Isomorphism ◽  
Isomorphism Problem ◽  
Equivalence Classes ◽  
Equivalence Testing ◽  
Equivalence Test ◽  
Graph Isomorphism Problem ◽  
2D Structure ◽  
Node Labels ◽  
Labelled Graphs

AbstractAn important task in cheminformatics is to test whether two molecules are equivalent with respect to their 2D structure. Mathematically, this amounts to solving the graph isomorphism problem for labelled graphs. In this paper, we present an approach which exploits chemical properties and the local neighbourhood of atoms to define highly distinctive node labels. These characteristic labels are the key for clever partitioning molecules into molecule equivalence classes and an effective equivalence test. Based on extensive computational experiments, we show that our algorithm is significantly faster than existing implementations within , and . We provide our Java implementation as an easy-to-use, open-source package (via GitHub) which is compatible with . It fully supports the distinction of different isotopes and molecules with radicals.

scholarly journals Cutting towers of number fields

2021 ◽  
Author(s):  
Farshid Hajir ◽  
Christian Maire ◽  
Ravi Ramakrishna
Keyword(s):  
Number Fields

scholarly journals Theta series and number fields: theorems and experiments

2021 ◽  
Author(s):  
Adrian Barquero-Sanchez ◽  
Guillermo Mantilla-Soler ◽  
Nathan C. Ryan
Keyword(s):  
Theta Series ◽  
Number Fields

Kummer theory for number fields via entanglement groups

2021 ◽  
Author(s):  
Antonella Perucca ◽  
Pietro Sgobba ◽  
Sebastiano Tronto
Keyword(s):  
Number Fields ◽  
Kummer Theory

Parallel and Distributed Processability of Objects

1989 ◽  
Vol 12 (3) ◽  
pp. 317-356
Author(s):  
David C. Rine
Keyword(s):  
Software Engineering ◽  
Software Design ◽  
Equivalence Classes ◽  
Minimum Amount ◽  
Software Components ◽  
Limited Extent ◽  
Design Environment ◽  
Distributed Software

Partitioning and allocating of software components are two important parts of software design in distributed software engineering. This paper presents two general algorithms that can, to a limited extent, be used as tools to assist in partitioning software components represented as objects in a distributed software design environment. One algorithm produces a partition (equivalence classes) of the objects, and a second algorithm allows a minimum amount of redundancy. Only binary relationships of actions (use or non-use) are considered in this paper.

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