Abstract
We investigate the algebraic theory of quadratic forms from a constructive perspective.
To this aim, we examine several known existence statements from the theory of quadratic forms over fields.
For many such statements which assert the existence of a certain representation of a given object like a quadratic form or a central simple algebra, general principles from mathematical logic tell us that they should be accessible by a constructive proof, but the currently known proofs are not constructive and in particular do not give bounds on the parameters of the representation. This challenge is intriguing from the point of view of classical algebra as well as from that of constructive mathematics. The project will contribute to connect these two research areas, which promises a high potential for innovation.
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