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### Is there a way to compute the norm form of a number ring?

I have a cubic number field $M$, and I want to find the norm form of its integer ring (as a degree $3$ polynomial in $3$ variables). Does this functionality exist in SAGE?

For now, I found this solution:

O = M.maximal_order()
RRR.<a,b,c> = PolynomialRing(M)
lists = []
d = 1

for i in O.gens():
lists.append(i.galois_conjugates(M))

for i in range(3):
e = 0
e += a*lists[0][i]
e += b*lists[1][i]
e += c*lists[2][i]
d *= e

d

 2 retagged FrédéricC 4483 ●3 ●37 ●94

### Is there a way to compute the norm form of a number ring?

I have a cubic number field $M$, and I want to find the norm form of its integer ring (as a degree $3$ polynomial in $3$ variables). Does this functionality exist in SAGE?

For now, I found this solution:

O = M.maximal_order()
RRR.<a,b,c> = PolynomialRing(M)
lists = []
d = 1

for i in O.gens():
lists.append(i.galois_conjugates(M))

for i in range(3):
e = 0
e += a*lists[0][i]
e += b*lists[1][i]
e += c*lists[2][i]
d *= e

d