Codes
On the Pythagoras number of the simplest cubic fields
Mathematica notebooks for the paper On the Pythagoras number of the simplest cubic fields
Program for the determination of squares totally smaller than some given element: pythagoras_simplest_undersquares.nb, pythagoras_simplest_undersquares.txt
Program for finding all elements (up to given trace), which can be written as a sum of n squares but not as a sum of n-1 squares where 1 <= n <= 6: pythagoras_simplest_sumsofsquares.nb, pythagoras_simplest_sumsofsquares.txt
Check for a = 0: check_a0.nb
Additive structure of non-monogenic simplest cubic fields
Mathematica notebook for the paper Additive structure of non-monogenic simplest cubic fields (with D. Gil Muñoz)
Program for the determination of squares totally smaller than some given element (for non-monogenic simplest cubic fields with p = 3 and (k, l) = (1, 1)): pythagoras_simplest_undersquares_p3.nb, pythagoras_simplest_undersquares_p3.txt
Arithmetic of cubic number fields: Jacobi-Perron, Pythagoras, and indecomposables
Mathematica notebooks for the paper Arithmetic of cubic number fields: Jacobi-Perron, Pythagoras, and indecomposables (with V. Kala and E. Sgallová)
Program for the determination of squares totally smaller than some given element in Ennola's cubic fields: pythagoras_ennola_undersquares.nb, pythagoras_ennola_undersquares.txt
Program for the determination of totally positive indecomposables (up to some trace) in real cubic number fields; then it checks if (semi)convergents of a given periodic JPA expansion are associated with these elements: inde_jacper.nb, inde_jacper.txt
The same program modified for Thomas' family (together with the determination of indecomposables not associated with totally positive elements): inde_jacper_thomas.nb, inde_jacper_thomas.txt
Programs for Jacobi-Perron expansions in Ennola's cubic fields created by E. Sgallová: Find_hJPA.nb, Find_hJPA.txt, Find_iJPA.nb, Find_iJPA.txt, UnitGenerator.nb, UnitGenerator.txt, FindingIndecomElementInExpansion.nb, FindingIndecomElementInExpansion.txt