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Add more nicknames for number fields #6966

@rvisser7

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@rvisser7

When searching for number fields in the search jump box, various short nicknames for certain fields are supported, e.g. Qsqrt5 for the quadratic field $\mathbb{Q}(\sqrt{5})$ and Qzeta11 for the cyclotomic field $\mathbb{Q}(\zeta_{11})$ (as described in the knowl nf.nickname).

I think it would be great to have more of these implemented! Here are some rough ideas:

  • QcbrtN for the pure cubic fields $\mathbb{Q}(\sqrt[3]{N})$.
  • Q(sqrtA, sqrtB) for the biquadratic field $\mathbb{Q}(\sqrt{A}, \sqrt{B})$ (or maybeQ(sqrtA + sqrtB) or Q(sqrtA_sqrtB), to avoid using commas if #6882 is implemented).
  • Q(sqrt(A + B*sqrt(D))) for other non-primitive quartic fields of the form $\mathbb{Q}(\sqrt{A + B\sqrt{D}})$.
  • More generally, maybe something like Q(sqrtA_sqrtB_..._sqrtZ) for larger multi-quadratic fields.
  • It would be nice to also have something for higher degree pure fields, (e.g. maybe Q4rootN for $\mathbb{Q}(\sqrt[4]{N})$ )?

(I'm sure others will have more/better ideas!)

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