The "regulator" access routine should indeed at least allow to produce the
regulator with the precision that pari used.
If you look at the source of "regulator" you can see how to get the
regulator to better precision. If K is your number field, then:
K.pari_bnf().bnf_get_reg().sage()
gets you
See also
- Ask Sage question 60455: compute regulator with more precision
https://ask.sagemath.org/question/60455
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