Mathematica packages Fermat.m and psi.m: These packages implement the method for finding ”optimal” approximations to the Ricci-flat metric on an algebraic Calabi-Yau manifold, described in the paper ”Energy functionals for Calabi-Yau metrics” by myself and A. Nassar (arXiv: 0908.2635 [hep-th]). The use of these packages is illustrated in the notebook optimal.nb. If you want to look inside the packages (for example, to alter them for applications to a different set of Calabi-Yaus), you may find it useful to look at the set of notes strategy.pdf, which describes the calculations, and the notation used, in more detail.

References in zbMATH (referenced in 13 articles , 1 standard article )

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  1. Ashmore, Anthony; Deen, Rehan; He, Yang-Hui; Ovrut, Burt A.: Machine learning line bundle connections (2022)
  2. Anderson, Lara B.; Gerdes, Mathis; Gray, James; Krippendorf, Sven; Raghuram, Nikhil; Ruehle, Fabian: Moduli-dependent Calabi-Yau and SU(3)-structure metrics from machine learning (2021)
  3. Anderson, Lara B.; Gray, James; Larfors, Magdalena; Magill, Matthew; Schneider, Robin: Generalized vanishing theorems for Yukawa couplings in heterotic compactifications (2021)
  4. Anderson, Lara B.; Gray, James; Lukas, Andre; Wang, Juntao: Chern-Simons invariants and heterotic superpotentials (2020)
  5. Cui, Wei; Gray, James: Numerical metrics, curvature expansions and Calabi-Yau manifolds (2020)
  6. Blesneag, Ştefan; Buchbinder, Evgeny I.; Constantin, Andrei; Lukas, Andre; Palti, Eran: Matter field Kähler metric in heterotic string theory from localisation (2018)
  7. Hall, Stuart James; Murphy, Thomas: Numerical approximations to extremal toric Kähler metrics with arbitrary Kähler class (2017)
  8. Lin, Ying-Hsuan; Shao, Shu-Heng; Simmons-Duffin, David; Wang, Yifan; Yin, Xi: ( \mathcalN=4 ) superconformal bootstrap of the (K3) CFT (2017)
  9. Douglas, Michael R.: Calabi-Yau metrics and string compactification (2015)
  10. Kenton, Zachary; Thomas, Steven: D-brane potentials in the warped resolved conifold and natural inflation (2015)
  11. Headrick, Matthew; Nassar, Ali: Energy functionals for Calabi-Yau metrics (2013)
  12. Anderson, Lara B.; Braun, Volker; Ovrut, Burt A.: Numerical Hermitian Yang-Mills connections and Kähler cone substructure (2012)
  13. Anderson, Lara B.; Braun, Volker; Karp, Robert L.; Ovrut, Burt A.: Numerical Hermitian Yang-Mills connections and vector bundle stability in heterotic theories (2010)