# [sage-devel] Re: Question about number_field_elements_from_algebraics (Ticket 20181)

```Haha! That could be a good Easter egg...

... and I would not mind if some algebraists had a look at the NumberField
elements that come out either from this adapted function either!```
```
Le mardi 10 avril 2018 11:02:38 UTC+2, Dima Pasechnik a écrit :
>
> I misread this as "getting_number_field_elements_from_algebraists"...
>
> On Monday, April 9, 2018 at 5:10:07 PM UTC+1, jplab wrote:
>>
>> Dear all,
>>
>> In order to get algebraic polyhedra using the normaliz backend [1], we
>> modify the function
>>
>> number_field_elements_from_algebraics of qqbar.py to give embedded number
>> fields and also accept a larger class of algebraic numbers, say coming from
>> cyclotomic fields [2].
>>
>> For example, this is now possible:
>>
>> sage: UCF = UniversalCyclotomicField()
>> sage: E = UCF.gen(5)
>> sage: L.<b> = NumberField(x^2-189*x+16, embedding=200)
>> sage: my_nums = [-52*E - 136*E^2 - 136*E^3 - 52*E^4,
>> L.gen()._algebraic_(AA),sqrt(2)]
>> sage: aa_my_nums = [AA(_) for _ in my_nums]
>> sage: res = number_field_elements_from_algebraics(aa_my_nums,embedded=True)
>> sage: res
>> (Number Field in a with defining polynomial y^8 - 35670*y^6 + 476899047*y^4
>> - 2832410271650*y^2 + 6305298701739921,
>>  [2310/26212773509*a^7 - 185432947/78638320527*a^5 +
>> 1652517502195/78638320527*a^3 - 4904676315215467/78638320527*a + 94,
>>   -1238/2803377488467023*a^7 + 185460719/11213509953868092*a^5 -
>> 2754936849443/11213509953868092*a^3 + 8180694680816975/3737836651289364*a +
>> 189/2,
>>   -1979/1887160880826*a^7 + 26472586/943580440413*a^5 -
>> 235822245043/943580440413*a^3 + 466325019915415/629053626942*a],
>>  Ring morphism:
>>    From: Number Field in a with defining polynomial y^8 - 35670*y^6 +
>> 476899047*y^4 - 2832410271650*y^2 + 6305298701739921
>>    To:   Algebraic Real Field
>>    Defn: a |--> 96.9475535136628?)
>> sage: res[0].gen_embedding()
>> 96.9475535136628?
>>
>>
>> The ticket 2018 needs review and it would be nice to have the opinion of
>> experts on number fields in Sage...
>>
>> For example, there is currently one failing doctest where it seems that
>> the newer version is smarter, so that the test is not necessary anymore.
>>
>> [1] https://trac.sagemath.org/ticket/25097
>> [2] https://trac.sagemath.org/ticket/20181
>>
>

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