InverseSystems - Macaulay2/Workshop-2015-Boise GitHub Wiki

Basic background on inverse systems:

• chapter 1 of the Iarrobino-Kanev book

• some lecture notes by Geramita here http://www3.nd.edu/~stolz/Math70330(F2008)/Geramita.pdf

• a little bit of information in some papers I have written or co-written,

  • http://arxiv.org/abs/1406.5145 (this is mostly expository)
  • http://arxiv.org/abs/1307.3314

  Those papers are mostly interested in using inverse systems (or equivalently, apolarity) in order to study Waring rank and stuff like that. That is not necessarily the goal of this team at the workshop. But anyway they have some basic facts about apolarity and inverse systems, and references to more. (Plus, I like Waring rank and I don't mind if people read about it :-) )

• http://www.math.illinois.edu/REGS/reports11/duarte.pdf

Noetherian operators and generalized inverse systems:

• http://www.uibk.ac.at/mathematik/personal/oberst/oberstnoether1999
• http://arxiv.org/pdf/math/0411574.pdf

Eigenvectors of tensors and algorithms for Waring decomposition:

• http://arxiv.org/abs/1103.0203

Singular vectors:

• http://arxiv.org/abs/1210.8316

To-do-list

• Write documentations.
• Create commands to make a generic symmetric tensor of variables and a generic skew-symmetric tensor of variables.
• Create a command to make Koszul flattenings.
• Create a command to perform group actions.