Efficient Computation of Algebraic Local Cohomology Classes and Change of Ordering for Zero-Dimensional Standard Bases

2015 ◽  
pp. 334-348 ◽  
Author(s):  
Katsusuke Nabeshima ◽  
Shinichi Tajima
Keyword(s):  
Local Cohomology ◽  
Efficient Computation ◽  
Standard Bases

Alternative algorithms for computing generic μ∗-sequences and local Euler obstructions of isolated hypersurface singularities

2019 ◽  
Vol 18 (08) ◽  
pp. 1950156
Author(s):  
Katsusuke Nabeshima ◽  
Shinichi Tajima
Keyword(s):  
Local Ring ◽  
Local Cohomology ◽  
Rational Functions ◽  
Isolated Singularity ◽  
Euler Obstruction ◽  
Standard Bases ◽  
Hypersurface Singularities ◽  
Previous Algorithm ◽  
Computation Speed

A new algorithm is introduced for computing [Formula: see text]-sequences of isolated hypersurface singularities. It is shown that the new algorithm results in better performance, compared to our previous algorithm that utilizes parametric local cohomology systems, in computation speed. Furthermore, it can be used to compute local Euler obstruction of a hypersurface with an isolated singularity. The key idea of the new algorithm is computing standard bases in a local ring over a field of rational functions.

scholarly journals Standard bases and algebraic local cohomology for zero dimensional ideals

2019 ◽  
Author(s):  
Shinichi Tajima ◽  
Yayoi Nakamura ◽  
Katsusuke Nabeshima
Keyword(s):  
Local Cohomology ◽  
Standard Bases

No fear of George Kingsley Zipf

10.1558/37291 ◽  
2018 ◽  
Vol 2 (2) ◽  
pp. 242-263
Author(s):  
Stefano Rastelli ◽  
Kook-Hee Gil
Keyword(s):  
Minimalist Program ◽  
Classroom Research ◽  
Language Design ◽  
Efficient Computation ◽  
Generative Linguistics ◽  
The Third ◽  
Factor Effect ◽  
Language Classroom ◽  
Recent Developments ◽  
Insight Into

This paper offers a new insight into GenSLA classroom research in light of recent developments in the Minimalist Program (MP). Recent research in GenSLA has shown how generative linguistics and acquisition studies can inform the language classroom, mostly focusing on what linguistic aspects of target properties should be integrated as a part of the classroom input. Based on insights from Chomsky’s ‘three factors for language design’ – which bring together the Faculty of Language, input and general principles of economy and efficient computation (the third factor effect) for language development – we put forward a theoretical rationale for how classroom research can offer a unique environment to test the learnability in L2 through the statistical enhancement of the input to which learners are exposed.

Efficient Computation of Representative Families with Applications in Parameterized and Exact Algorithms

2016 ◽  
Vol 63 (4) ◽  
pp. 1-60 ◽  
Author(s):  
Fedor V. Fomin ◽  
Daniel Lokshtanov ◽  
Fahad Panolan ◽  
Saket Saurabh
Keyword(s):  
Exact Algorithms ◽  
Efficient Computation
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