Search results for "Universal geometric algebra"

showing 3 items of 3 documents

An Introduction to Geometric Algebra and Conics

2016

This chapter introduces the conics and characterizes them from an algebraic perspective. While in depth geometrical aspects of the conics lie outside the scopes of this chapter, this chapter is an opportunity to revisit concepts studied in other chapters such as matrix and determinant and assign a new geometric characterization to them.

Filtered algebraAlgebraMatrix (mathematics)Geometric algebraConic sectionUniversal geometric algebraFive points determine a conicConformal geometric algebraAlgebraic numberMathematics
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On the geometric structure of the class of planar quadratic differential systems

2002

In this work we are interested in the global theory of planar quadratic differential systems and more precisely in the geometry of this whole class. We want to clarify some results and methods such as the isocline method or the role of rotation parameters. To this end, we recall how to associate a pencil of isoclines to each quadratic differential equation. We discuss the parameterization of the space of regular pencils of isoclines by the space of its multiple base points and the equivariant action of the affine group on the fibration of the space of regular quadratic differential equations over the space of regular pencils of isoclines. This fibration is principal, with a projective group…

Nonlinear systemGeometric analysisApplied MathematicsAffine groupMathematical analysisUniversal geometric algebraFibrationDiscrete Mathematics and CombinatoricsEquivariant mapQuadratic differentialPencil (mathematics)MathematicsQualitative Theory of Dynamical Systems
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Fixed-size Quadruples for a New, Hardware-Oriented Representation of the 4D Clifford Algebra

2010

Clifford algebra (geometric algebra) offers a natural and intuitive way to model geometry in fields as robotics, machine vision and computer graphics. This paper proposes a new representation based on fixed-size elements (quadruples) of 4D Clifford algebra and demonstrates that this choice leads to an algorithmic simplification which in turn leads to a simpler and more compact hardware implementation of the algebraic operations. In order to prove the advantages of the new, quadruple-based representation over the classical representation based on homogeneous elements, a coprocessing core supporting the new fixed-size Clifford operands, namely Quad-CliffoSor (Quadruple-based Clifford coproces…

Settore ING-INF/05 - Sistemi Di Elaborazione Delle InformazioniSpeedupCoprocessorbusiness.industryApplied MathematicsClifford algebraUniversal geometric algebraOperandAlgebraGeometric algebraClifford algebra computational geometry embedded coprocessors application-specific processor FPGA-based prototypingAlgebraic operationComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATIONbusinessRepresentation (mathematics)Computer hardwareMathematics
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