Maple Routines for Mirror Symmetry

The file maple.ini gives various routines; only some of these are actually used here. The most important is fil which is used to load files from the directory given by the variable MyDirectory defined; the file should be edited so that MyDirectory gives the name of the directory where the files are placed.

Running HelpOn() will make some of the routines give some guidance. This may be turned of by HelpOff().


The file CYfamily (file-type is always txt unless otherwise specified) is a front for a series of other files and routines. Here is an overview of the purposes of each file:

This is the front, the file that you'd actually load from Maple: ie., run fil(CYfamily). This file defines a series of Calabi-Yau manifolds of interest with the aim of calculating the B-model Picard-Fuchs equation, the Yukawa coupling and the mirror map. Run HelpOn() first and you'll get help on which Calabi-Yaus are defined and what routines to run.
This gives the routines for defining the pfaffian Calabi-Yau.
pfaffer (used by cymatrix)
This gives routines for calculating pfaffians of matrixes.
This sets up the integral of the global section of the canonical form over the cycle gamma_0 as a power series, simplifies the series by including only the terms that contribute in the integral making it into a hypergeometric sum.
Simplify hypergeometric sum and make an evaluable expression.
Routines for actually evaluating these sums. However, to make routines efficient, they should be reprogrammed: not obtained using the MSUM or Msum routines.
From the above mentioned power series, find the Picard-Fuchs equations, etc. Assumes the power series to be given with Coef(i) as the i'th coefficient.

Please note that these routines may not be assumed to be bug free. Some problems may arise from the routines being written on an old Maple platform and some updating of the code may be needed. Also, once the routines have worked on my own examples, I have stopped looking for further errors.


The file QH is for doing quantum cohomology. It starts of by taking a matrix A such that V*p=V*A for V a basis: ie., if x=V*W is an element, W a vector representing the element in the V-basis, then multiplication by p amounts to W->A*W. From entering this matrix, the Picard-Fuchs differential operator may be found.

This package also contains routines for multiplying and dividing differential operators.

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Created 03 January 1999 by Einar Andreas Rødland.