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

Additively indecomposable quadratic forms over number fields

Mathematica notebooks for the paper Additively indecomposable 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

Additively indecomposable quadratic forms over biquadratic and simplest cubic fields

Mathematica notebooks for the paper Additively indecomposable quadratic forms over biquadratic and simplest cubic fields (with S. Fryšová)

• Program for the determination of all totally positive algebraic integers totally smaller than 3 in the simplest cubic fields: simplest_dec_of_3.nb, simplest_dec_of_3.pdf