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Solving quadratic equations in many variables

Snapshots of modern mathematics from Oberwolfach

Solving quadratic equations in many variables

Fields are number systems in which every linear equation has a solution, such as the set of all rational numbers Q or the set of all real numbers R. All fields have the same properties in relation with systems of linear equations, but quadratic equations behave differently from field to field. Is there a field in which every quadratic equation in five variables has a solution, but some quadratic equation in four variables has no solution? The answer is in this snapshot. 

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Mathematical subjects

Algebra and Number Theory

Author(s)

Jean-Pierre Tignol

License

DOI (Digital Object Identifier)

10.14760/SNAP-2017-012-EN

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snapshots-2017-012.pdf

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snapshots: overview

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      Mathematical subjects

      Algebra and Number Theory
      Analysis
      Didactics and Education
      Discrete Mathematics and Foundations
      Geometry and Topology
      Numerics and Scientific Computing
      Probability Theory and Statistics

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      Chemistry and Earth Science
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      Finance
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      Life Science
      Physics
      Reflections on Mathematics

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