All the files in this folder contain a brief explanation and some codes working on the software Mathematica. The lines starting with "//" are comments and must not be included in the code.

The files named "p=a mod 12, n odd.txt", with a=1,5,7,11, contain the check that the particular solution written in the paper "Intersection matrices for the minimal regular model of X_0(N) and applications to the Arakelov canonical sheaf" in Proposition 4.5 defining the divisors V_0 and V_\infty makes true each row of the corresponding linear system when the level is N=Mp^n for every M>0 coprime with 6, n odd and p a prime such that p=a modulo 12.

The files named "p=a mod 12, n even, M not 1.txt", with a=1,5,7,11, contain the check that the particular solution written in the paper "Intersection matrices for the minimal regular model of X_0(N) and applications to the Arakelov canonical sheaf" in Proposition 4.5 defining the divisors V_0 and V_\infty makes true each row of the corresponding linear system when the level is N=Mp^n for every M>1 coprime with 6, n even and p a prime such that p=a modulo 12.

The files named "p=a mod 12, n even, M=1.txt", with a=1,5,7,11, contain the check that the particular solution written in the paper "Intersection matrices for the minimal regular model of X_0(N) and applications to the Arakelov canonical sheaf" in Proposition 4.5 defining the divisors V_0 and V_\infty makes true each row of the corresponding linear system when the level is N=Mp^n for every M=1, n even and p a prime such that p=a modulo 12.

The file named "small o, n even and M=1.txt" contain the check that the summand (b) written in the paper "Intersection matrices for the minimal regular model of X_0(N) and applications to the Arakelov canonical sheaf" in first equation of Section 4.4 can be written as the expression showed in Equation (19) of the same section when n is even and M=1.

The file named "small o, n odd or M not 1.txt" contain the check that the summand (b) written in the paper "Intersection matrices for the minimal regular model of X_0(N) and applications to the Arakelov canonical sheaf" in first equation of Section 4.4 can be written as the expression showed in Equation (19) of the same section when either n is odd or M>1.