Add more latex names for number fields#6980
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…lti-quadratic fields
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For some families of number fields$K$ , we give a "pretty" latexed name for $K$ at the top of the field homepage, currently implemented for quadratic fields $\mathbb{Q}(\sqrt{D})$ , biquadratic fields $\mathbb{Q}(\sqrt{A}, \sqrt{B})$ , and cyclotomic fields $\mathbb{Q}(\zeta_n)$ . This PR extends the
field_prettyfunction to give latexed names for some additional families of number fields. :)The following three cases have been added:
General multi-quadratic fields$\mathbb{Q}(\sqrt{D_1}, \sqrt{D_2}, \dots, \sqrt{D_k})$ : For fields $K$ of degree $2^k$ with $2^k - 1$ quadratic subfields, this now selects the $k$ smallest quadratic subfields $Q(\sqrt{D_1}), \dots, Q(\sqrt{D_k})$ which generate $K$ .
http://localhost:37777/NumberField/8.0.12960000.1
http://localhost:37777/NumberField/16.0.63456228123711897600000000.10
http://localhost:37777/NumberField/32.0.4026692887688564776141139207792885760000000000000000.1
Imprimitive (non-biquadratic) quartic fields$\mathbb{Q}(√ (A + B \sqrt{D}))$ : This checks if a quartic field $K$ has exactly one quadratic subfield $\mathbb{Q}(\sqrt{D})$ , and then computes a generator for $K$ of the form $√(A + B \sqrt{D})$ by factoring the defining polynomial for $K$ over $\mathbb{Q}(\sqrt{D})$ . If $A = 0$ , then returns the latexed form as a pure quartic field $\mathbb{Q}(\sqrt[4]{n})$ .
http://localhost:37777/NumberField/4.0.512.1
http://localhost:37777/NumberField/4.2.2048.1
http://localhost:37777/NumberField/4.4.2048.1
Pure cubic fields:$\mathbb{Q}(\sqrt[3]{n})$ : Detects if a cubic field K is of the form $\mathbb{Q}(\sqrt[3]{n})$ , by computing a real root of the defining polynomial for $K$ .
http://localhost:37777/NumberField/3.1.108.1
http://localhost:37777/NumberField/3.1.243.1
http://localhost:37777/NumberField/3.1.300.1
As always, any comments/feedback very welcome! 🙂