# Revision history [back]

You can turn v into a polynomial on the undeterminate j:

sage: v.parent()
Finite Field in j of size 10354717741769305252977768237866805321427389645549071170116189679054678940682478846502882896561066713624553211618840202385203911976522554393044160468771151816976706840078913334358399730952774926980235086850991501872665651576831^2

sage: P = v.polynomial()
sage: P


9207905618485976447392495823891126491742950552335608949038426615382964807887894797411491716107572732408369786142697750332311947639207321056540404444033540648125838904594907601875471637980859284582852367748448663333866077035709*j + 4651155546510811048846770550870646667630430517849502373785869664283801023087435645046977319664381880355511529496538038596466138807253669785341264293301567029718659171475744580349901553036469330686320047828171225710153655171014 sage: P.parent() Univariate Polynomial Ring in j over Finite Field of size 10354717741769305252977768237866805321427389645549071170116189679054678940682478846502882896561066713624553211618840202385203911976522554393044160468771151816976706840078913334358399730952774926980235086850991501872665651576831 (using NTL)

Then look at its coefficients:

sage: re, im = P.coefficients(sparse=False)
sage: re
4651155546510811048846770550870646667630430517849502373785869664283801023087435645046977319664381880355511529496538038596466138807253669785341264293301567029718659171475744580349901553036469330686320047828171225710153655171014
sage: im
9207905618485976447392495823891126491742950552335608949038426615382964807887894797411491716107572732408369786142697750332311947639207321056540404444033540648125838904594907601875471637980859284582852367748448663333866077035709


You The notion of real and imaginary part are very related to the particular polynomial x^2+1, so for me it makes sense that there is no suvh method for an arbitrary field extension.

Anuway, you can turn v into a polynomial on the undeterminate j:

sage: v.parent()
Finite Field in j of size 10354717741769305252977768237866805321427389645549071170116189679054678940682478846502882896561066713624553211618840202385203911976522554393044160468771151816976706840078913334358399730952774926980235086850991501872665651576831^2

sage: P = v.polynomial()
sage: P


9207905618485976447392495823891126491742950552335608949038426615382964807887894797411491716107572732408369786142697750332311947639207321056540404444033540648125838904594907601875471637980859284582852367748448663333866077035709*j + 4651155546510811048846770550870646667630430517849502373785869664283801023087435645046977319664381880355511529496538038596466138807253669785341264293301567029718659171475744580349901553036469330686320047828171225710153655171014 sage: P.parent() Univariate Polynomial Ring in j over Finite Field of size 10354717741769305252977768237866805321427389645549071170116189679054678940682478846502882896561066713624553211618840202385203911976522554393044160468771151816976706840078913334358399730952774926980235086850991501872665651576831 (using NTL)

NTL)

Then look at its coefficients:

sage: re, im = P.coefficients(sparse=False)
sage: re
4651155546510811048846770550870646667630430517849502373785869664283801023087435645046977319664381880355511529496538038596466138807253669785341264293301567029718659171475744580349901553036469330686320047828171225710153655171014
sage: im
9207905618485976447392495823891126491742950552335608949038426615382964807887894797411491716107572732408369786142697750332311947639207321056540404444033540648125838904594907601875471637980859284582852367748448663333866077035709