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REAL PIECEWISE ALGEBRAIC VARIETY
Authors:Ren-hong Wang Yi-sheng Lai
Abstract:We give definitions of real piecewise algebraic variety and its dimension. By using the techniques of real radical ideal, P-radical ideal, affine Hilbert polynomial, Bernstein-net form of polynomials on simplex, and decomposition of semi-algebraic set, etc., we deal with the dimension of the real piecewise algebraic variety and real Nullstellensatz in $C^\mu$ spline ring.
Keywords:Dimension  Real piecewise algebraic variety  $C^\mu$ spline ring  
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