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
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
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
Mathematica notebooks for the paper Non-decomposable quadratic forms over totally real number fields (with P. Yatsyna)
Program for the determination of all non-decomposable binary quadratic forms (up to equivalence) in real quadratic fields Q(sqrt D)
classical forms
D = 2, 3 (mod 4): indeformy_repr23.nb, indeformy_repr23.pdf
D = 1 (mod 4): indeformy_repr1.nb, indeformy_repr1.pdf
non-classical forms
D = 2, 3 (mod 4): indeformy_repr23_nonclass.nb, indeformy_repr23_nonclass.pdf
D = 1 (mod 4): indeformy_repr1_nonclass.nb, indeformy_repr1_nonclass.pdf
Program for the determination of all binary quadratic forms Q (up to equivalence) with det(Q) <= some bound and such that Q cannot be written as Q = Q1 + Q2 where det(Q1)=0
classical forms
D = 2, 3 (mod 4): indeformy_repr23_count.nb, indeformy_repr23_count.pdf
D = 1 (mod 4): indeformy_repr1_count.nb, indeformy_repr1_count.pdf
non-classical forms
D = 2, 3 (mod 4): indeformy_repr23_nonclass_count.nb, indeformy_repr23_nonclass_count.pdf
D = 1 (mod 4): indeformy_repr1_nonclass_count.nb, indeformy_repr1_nonclass_count.pdf