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. 

If you are interested in translating this Snapshot, please contact us at info@imaginary.org

Mathematical subjects

Algebra and Number Theory

Author(s)

Jean-Pierre Tignol
Senior Editor:
Carla Cederbaum
Junior Editor:
Sophia Jahns, Anja Randecker

License

DOI (Digital Object Identifier)

10.14760/SNAP-2017-012-EN

Download PDF

PDF

snapshots: overview

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

Connections to other fields

Chemistry and Earth Science
Computer Science
Engineering and Technology
Finance
Humanities and Social Sciences
Life Science
Physics
Reflections on Mathematics

These icons are available under the CC BY-SA 4.0 license. Please feel free to use them to classify your own content.
The vector icons can be downloaded here.