Adherence is Better than Adjacency: Computing the Riemann Index using CAD

J Beaumont; R Bradford; J H Davenport; N Phisanbut

doi:10.1145/1073884.1073892

Adherence is Better than Adjacency: Computing the Riemann Index using CAD

J Beaumont
, R Bradford
, J H Davenport
, N Phisanbut

Research output: Contribution to conference › Paper

5 Citations (SciVal)

Abstract

Given an elementary function with algebraic branch cuts, we show how to decide which sheet of the associated Riemann surface we are on at any given point. We do this by establishing a correspondence between the Cylindrical Algebraic Decomposition (CAD) of the complex plane defined by the branch cuts and a finite subset of sheets of the Riemann surface. The key advantage is that we no longer have to deal with the difficult 'constant problem'.

Original language	English
Pages	37--44
Number of pages	8
DOIs	https://doi.org/10.1145/1073884.1073892
Publication status	Published - Jul 2005
Event	Proceedings of the 2005 international symposium on Symbolic and algebraic computation - Duration: 1 Jul 2005 → …

Conference

Conference	Proceedings of the 2005 international symposium on Symbolic and algebraic computation
Period	1/07/05 → …

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10.1145/1073884.1073892

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title = "Adherence is Better than Adjacency: Computing the Riemann Index using CAD",

abstract = "Given an elementary function with algebraic branch cuts, we show how to decide which sheet of the associated Riemann surface we are on at any given point. We do this by establishing a correspondence between the Cylindrical Algebraic Decomposition (CAD) of the complex plane defined by the branch cuts and a finite subset of sheets of the Riemann surface. The key advantage is that we no longer have to deal with the difficult 'constant problem'. ",

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year = "2005",

month = jul,

doi = "10.1145/1073884.1073892",

language = "English",

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note = "Proceedings of the 2005 international symposium on Symbolic and algebraic computation ; Conference date: 01-07-2005",

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AU - Beaumont, J

AU - Bradford, R

AU - Davenport, J H

AU - Phisanbut, N

PY - 2005/7

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N2 - Given an elementary function with algebraic branch cuts, we show how to decide which sheet of the associated Riemann surface we are on at any given point. We do this by establishing a correspondence between the Cylindrical Algebraic Decomposition (CAD) of the complex plane defined by the branch cuts and a finite subset of sheets of the Riemann surface. The key advantage is that we no longer have to deal with the difficult 'constant problem'.

AB - Given an elementary function with algebraic branch cuts, we show how to decide which sheet of the associated Riemann surface we are on at any given point. We do this by establishing a correspondence between the Cylindrical Algebraic Decomposition (CAD) of the complex plane defined by the branch cuts and a finite subset of sheets of the Riemann surface. The key advantage is that we no longer have to deal with the difficult 'constant problem'.

U2 - 10.1145/1073884.1073892

DO - 10.1145/1073884.1073892

M3 - Paper

SP - 37

EP - 44

T2 - Proceedings of the 2005 international symposium on Symbolic and algebraic computation

Y2 - 1 July 2005

ER -

Adherence is Better than Adjacency: Computing the Riemann Index using CAD

Abstract

Conference

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