# Maple programs

Here are some Maple programs that I have made. They are mostly related to algebra and algebraic geometry. The programs are included here as HTML-files. To enter them into Maple, just cut and paste. Some of the programs include others before running. In the programs this is indicated by a read statement. This statement if run is not likely to work for you as it referes to my personal directory, but just change the directory reference and it will.

Below is a description of the programs. In order to use them, you may wish to read a bit about syntax and the Grobner package.

• pfaffer: Calculates the Pfaffer, sqrt(det M), of an antisymmetric matrix.
• pffunc(M,V): Calculates the Pfaffer of the submatrix of M given by indexes in V.
• pfaffer(M): Calculated the Pfaffer of M.
• cymatrix: (uses: linalg, pfaffer.txt) Calculates the Pfaffers from a particular matrix which gives a Calabi--Yau manifold.
• CYdim(dimen): Sets the number of variables - CYdimen - to be used. Calculates the matrices M and N from this. Outputs the list of variables x_0, ..., x_{CYdimen-1}. Is set to 7 at start.
• M: a square CYdimen x CYdimen matrix with elements [x_{i+j} y_{i-j}] where i and j are modulo CYdimen. Defined by CYdim.
• N: Parameters in M set to make the matrix antisymmetric: ie. y_i+y_{-i}=0. Defined by CYdim.
• CYpfaff(poly,matrix): Calculates the 7 Pfaffers of the matrix and puts them in poly_1-poly_{CYdimen}. Outputs a list containing all the polynomials.
• hilbert: (uses: grobner) Hilbert polynomial. Calculates on Grobner bases. In order to work, the basis used should be a Grobner basis. This may be obtained by running gbasis(basis,vars) from the grobner package.