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- Deprecated function: TYPO3\PharStreamWrapper\Manager::initialize(): Implicitly marking parameter $resolver as nullable is deprecated, the explicit nullable type must be used instead in include_once() (line 19 of includes/file.phar.inc).
- Deprecated function: TYPO3\PharStreamWrapper\Manager::initialize(): Implicitly marking parameter $collection as nullable is deprecated, the explicit nullable type must be used instead in include_once() (line 19 of includes/file.phar.inc).
- Deprecated function: TYPO3\PharStreamWrapper\Manager::__construct(): Implicitly marking parameter $resolver as nullable is deprecated, the explicit nullable type must be used instead in include_once() (line 19 of includes/file.phar.inc).
- Deprecated function: TYPO3\PharStreamWrapper\Manager::__construct(): Implicitly marking parameter $collection as nullable is deprecated, the explicit nullable type must be used instead in include_once() (line 19 of includes/file.phar.inc).
- Deprecated function: UpdateQuery::expression(): Implicitly marking parameter $arguments as nullable is deprecated, the explicit nullable type must be used instead in require_once() (line 1884 of includes/database/database.inc).
- Deprecated function: MergeQuery::expression(): Implicitly marking parameter $arguments as nullable is deprecated, the explicit nullable type must be used instead in require_once() (line 1884 of includes/database/database.inc).
- Deprecated function: SelectQueryInterface::getArguments(): Implicitly marking parameter $queryPlaceholder as nullable is deprecated, the explicit nullable type must be used instead in require_once() (line 1884 of includes/database/database.inc).
- Deprecated function: SelectQueryInterface::preExecute(): Implicitly marking parameter $query as nullable is deprecated, the explicit nullable type must be used instead in require_once() (line 1884 of includes/database/database.inc).
- Deprecated function: SelectQueryExtender::getArguments(): Implicitly marking parameter $queryPlaceholder as nullable is deprecated, the explicit nullable type must be used instead in require_once() (line 1884 of includes/database/database.inc).
- Deprecated function: SelectQueryExtender::preExecute(): Implicitly marking parameter $query as nullable is deprecated, the explicit nullable type must be used instead in require_once() (line 1884 of includes/database/database.inc).
- Deprecated function: SelectQuery::getArguments(): Implicitly marking parameter $queryPlaceholder as nullable is deprecated, the explicit nullable type must be used instead in require_once() (line 1884 of includes/database/database.inc).
- Deprecated function: SelectQuery::preExecute(): Implicitly marking parameter $query as nullable is deprecated, the explicit nullable type must be used instead in require_once() (line 1884 of includes/database/database.inc).
==Hand Made Fiducials By Tensoring==
The file
Media:FiducialsByTensoring.pdf
consists of working notes for what will eventually be a published paper.
It is work in progress, and so will be updated regularly. I will also
attach a mathematica notebook giving the exact fiducial in dimension 6
in machine readable form, as soon as I can get the wiki to accept it (it
is being recalcitrant at the moment).
The pdf concerns methods for obtaining exact fiducials in composite
dimensions. It is based on David Gross's talk at the PI workshop in
October 2008 (so it is joint work of David and myself). So far I have
got as far as the exact solution in dimension 6. Of course Markus Grassl
did this some years ago. However, the solution given here was obtained
by purely pencil and paper methods (I used Mathematica to check
the result, but in the original calculation I didn't even use
Mathematica, let alone Magma).
I am currently working on dimension 12. I will then go on to
dimension 15. I happen to know the method works in these dimensions
because I had already obtained exact, pencil-and-paper solutions in
these dimensions before hearing David's talk using a different, but
related method (this different method also works in dimension 9, which
David's method in the present formulation of it, does not. Another aim
of this research is to clarify the exact relationship between David's
method and the less elegant method I was using before).
Of course the real aim of all this is not just to find exact
solutions, but to get enough algebraic insight into the problem to be
able to construct a proof. In that respect I am feeling just a little
bit hopeful. But it is very very slow (the algebra is really
complicated!).
Category:SICPOVM
Last modified:
Monday, October 26, 2015 - 17:56
