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Fix local_height_arch weighting real places as complex at prec=53 - #42678

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Fix local_height_arch weighting real places as complex at prec=53#42678
breatn wants to merge 1 commit into
sagemath:developfrom
breatn:breatn-patch-4

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@breatn

@breatn breatn commented Aug 16, 2026

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Summary

  • local_height_arch tested for a real place with isinstance(Kv, sage.rings.abc.RealField), but places(prec=53) maps into RDF/CDF, and RDF is not a sage.rings.abc.RealField; real places were therefore given the complex local
    degree 2
  • this made global_height_arch and global_height wrong at prec=53: QuadraticField(2).gen().global_height(prec=53) returned 0.693147180559945 instead of 0.346573590279973
  • add sage.rings.abc.RealDoubleField to the check, matching the idiom already used in NumberField_generic.hilbert_symbol

Fixes #31185.

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NumberField element method local_height_arch returns wrong values on prec=53

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