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The idea of the Grobner basis first appeared in a 1927 paper by F. S. Macaulay, who succeeded in creating a combinatorial characterization of the Hilbert functions of homogeneous ideals of the polynomial ring. Later, the modern definition of the Grobner basis was independently introduced by Heisuke Hironaka in 1964 and Bruno Buchberger in 1965. However, after the discovery of the notion of the Grobner basis by Hironaka and Buchberger, it was not actively pursued for 20 years. A breakthrough was made in the mid-1980s by David Bayer and Michael Stillman, who created the Macaulay computer...

The idea of the Grobner basis first appeared in a 1927 paper by F. S. Macaulay, who succeeded in creating a combinatorial characterization of the Hilbert functions of homogeneous ideals of the polynomial ring. Later, the modern definition of the Grobner basis was independently introduced by Heisuke Hironaka in 1964 and Bruno Buchberger in 1965. However, after the discovery of the notion of the Grobner basis by Hironaka and Buchberger, it was not actively pursued for 20 years. A breakthrough was made in the mid-1980s by David Bayer and Michael Stillman, who created the Macaulay computer...

This book covers diverse environmental issues such as climate change; biodiversity preservation; prevention of air, water, and soil pollution; and resource recycling. Readers can acquire these four practical interdisciplinary abilities: 1. knowledge; 2. technology; 3. evaluation; and 4. strategy in the diverse issues related to the environment. These abilities are fundamental to identifying the core essence of economic and ecological interdependence, to look at and analyze problems from an overarching perspective, and to consider countermeasures to be taken. Each chapter of this book...

This book is the first systematic study of how the interdependence of fiscal and monetary policies and the interaction of party governments and central banks affect the fiscal-policy mix in eighteen industrial democracies in North America, Western Europe, Japan and Oceania. Sakamoto argues that central banks' influence on economic policy is far more extensive than has been conventionally believed. He demonstrates that central banks systematically affect fiscal policy that is conducted by party governments, and that independent central banks restrain the latter's fiscal policy.