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# Def/Lax superbasis

Definition of Lax superbasis: Suppose that \$[a,b]\$, \$[c,d]\$, and \$[e,f]\$ are lax vectors. We say that the unordered triple \$S = \{ [a,b], [c,d], [e,f] \}\$ is a lax superbasis if the following condition is satisfied:

• Every subset of \$S\$ of cardinality two is a lax basis.

In other words, \$S\$ is a lax superbasis if the following three conditions are satisfied:

• The pair \$\{ [a,b], [c,d] \}\$ is a lax basis.
• The pair \$\{ [c,d], [e,f] \}\$ is a lax basis.
• The pair \$\{ [e,f], [a,b] \}\$ is a lax basis.

## Logical Connections

This definition logically relies on the following definitions and statements: Def/Lax vector, Def/Lax basis

The following statements and definitions logically rely on the material of this page: Def/Domain topograph, Def/Equivalence of binary quadratic forms, State/Binary quadratic forms are uniquely determined by their values at a superbasis, and State/Every lax basis is contained in exactly two lax superbases

To visualize the logical connections between this definition and other items of mathematical knowledge, you can visit any of the following clusters, and click the "Visualize" tab: Clust/Binary quadratic forms