The theory of linear representations of projective planes developed by Bruck and one of the authors (Bose) in two earlier papers [J. Algebra1 (1964), pp. 85–102 and4 (1966), pp. 117–172] can be further extende
If a line in 3D is parallel to two of the coordinate planes (that is, it is parallel to one of the coordinate axes), thenGetRepresentationreturns a sequence of two equations, like this:x=−1,z=2. – For a line in 2D, Maple typically returns an equation of the formx4−14=y5...
world in the way novices do not – expert readers see “run” as a word whereas novices see letters or just lines, experts in physics see force contact points whereas novices see blocks and inclined planes, chess experts see configurations of pieces like a knight fork whereas novices see ...
HomologicalAlgebra.2nded. Variables. 5 MAcLANE.CategoriesfortheWorking 39 ARVESON.AnInvitationtoc*-Algebras. Mathematician.2nded. 40 KEMENY/SNELLIKNAPP.Denumerable 6 HUGHES/PIPER.ProjectivePlanes. MarkovChains.2nded. 7 SERRE.ACourseinArithmetic. ...
where, andis a family of distinct binary vectors in. This formulation is implicit in the sense that it does not provide a description ofin terms of linear inequalities. Neverthless, Vielma determined the non-trivial facetsFootnote1of the convex hullfor the SOS2 constraints of [13], and also...
In the case N = 1, the Hochschild cohomology ring of the algebra Λ1 with m = 1 is discussed in [1], where q-analogues of Λ1 were used to answer negatively a question of Happel, in that they have fin...W. Chin and L. Krop, Representation theory of liftings of quantum planes,...
A technique is presented for representing linear features as probability density functions in two or three dimensions. Three chief advantages of this approach are (1) a unified representation and algebra for manipulating points, lines, and planes, (2) seamless incorporation of uncertainty information,...
The antisymmetric part of the geometric product produces a spanning operation that permits the construction of lines, planes, spheres and tangents from vectors. Since the sandwiching operation distributes over this construction, 'objects' are fully integrated with 'motions', in a structure preserving...