random variables X q and X (Point q) for Oriented structure q.

Properties Let q be an instance of the class Oriented, then holds:

1. Let XStart xp xStart be in XOrtSite From q, then holds: For all p in Point q and x in the range of xStart p holds: start x == p.
2. Let XEnd xp xEnd be in XOrtSite To q, then holds: For all p in Point q and x in the range of xEnd p holds: end x == p.

Note The random variables xp should have a bias to non trivial random variables xp >>= xStart or xp >>= xEnd.

type for Oriented structures admitting XStandardOrtSiteTo and XStandardOrtSiteFrom.

Note The main point is that TransformableG Op OrtSiteX OrtSiteX holds!

standard random variable for XOrtSite.

standard random variable for XOrtSite To, helper class to avoid undecidable instances.

standard random variable for XOrtSite From, helper class to avoid undecidable instances.

to the dual of a XOrtSite s q, with inverse coXOrtSiteInv.

from the dual of a Dual (XOrtSite s q), with inverse coXOrtSite.

from the bidual.

the random variable of arrows in q having all as start the given point.

the random variable of arrows in q having all as end the given point.

tries to make a path at the given point with maximal length of the given length.

Properties Let xPath = xosPathMaxAt xos n x, then holds:

1. If xos matches XStart _ xq then for all p in the range of xPath holds:

   1. start p == x.
   2. If pthLength p < n then xq (end p) matches XEmpty.

2. If xos matches XEnd _ xq then for all p in the range of xPath holds:

   1. end p == x.
   2. If pthLength p < n then xq (start p) matches XEmpty.

random variable of paths with maximal length of the given length.

random variable of arrows given by an orientation.

Properties Let XOrtOrientation xo xArrow be in XOrtOrientation q for a Oriented structure q, then holds: For all o in Orientation q and x in the range of xArrow o holds: orientation x == o.

Note The random variable xo should have a bias to non trivial random variables xo >>= xArrow and as such the range of xo should be included in one connection component of q.

the underlying random variable of orientations.

the underlying random variable of arrow given by the orientation.

the underlying random variable of points, i.e. the union of the induced start and end random variable of xoOrientation.

to the dual.

the induced XOrtSite To

the induced XOrtSite From.

random variable of XOrtOrientation q for a total q.

the induced random variable of Orientation q.

standard random variable for XOrtOrientation.

the XOrtSite From for Orientation p of the given random variable.

the XOrtSite To of Orientation p of the given random variable.