Numerically Solving Polynomial Systems with Bertini

by Daniel J. Bates, Jonathan D. Hauenstein, Andrew J. Sommese, Charles W. Wampler

2013 · SIAM

This book is a guide to concepts and practice in numerical algebraic geometry ? the solution of systems of polynomial equations by numerical methods. Through numerous examples, the authors show how to apply the well-received and widely used open-source Bertini software package to compute solutions, including a detailed manual on syntax and usage options. The authors also maintain a complementary web page where readers can find supplementary materials and Bertini input files. Numerically Solving Polynomial Systems with Bertini approaches numerical algebraic geometry from a user's point of view with numerous examples of how Bertini is applicable to polynomial systems. It treats the fundamental task of solving a given polynomial system and describes the latest advances in the field, including algorithms for intersecting and projecting algebraic sets, methods for treating singular sets, the nascent field of real numerical algebraic geometry, and applications to large polynomial systems arising from differential equations. Those who wish to solve polynomial systems can start gently by finding isolated solutions to small systems, advance rapidly to using algorithms for finding positive-dimensional solution sets (curves, surfaces, etc.), and learn how to use parallel computers on large problems. These techniques are of interest to engineers and scientists in fields where polynomial equations arise, including robotics, control theory, economics, physics, numerical PDEs, and computational chemistry.

U.S. Politics and the Global Economy

by Ronald W. Cox, Daniel Skidmore-Hess

1999 · Lynne Rienner Publishers

This book investigates the influence of globalization on ideology and politics in the United States. Ronald Cox and Daniel Skidmore-Hess argue that U.S. policy has been motivated less by anxiety about the independence and stability of the domestic economy and more by worry about factors that might limit the participation of U.S. corporations in international markets. Connecting trends in domestic and foreign policy with the changing needs of industry, they associate increased globalization with the the breakup of the liberal, New Deal coalition; the collapse of the Bretton Woods Agreement in the 1970s; the neoconservative, antiregulatory movements of the 1980s; and the rightward drift of both the Republican and Democratic Parties.