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keyword:small scale reflection keyword:mathematical components keyword:algebra keyword:algebraic structure hierarchies keyword:archimedean field keyword:floor keyword:ceil keyword:intervals keyword:matrices keyword:vectors keyword:block matrices keyword:determinant keyword:Cramer rule keyword:Vandermonde matrices keyword:LUP decomposition keyword:Gaussian elimination keyword:matrix rank keyword:eigen values keyword:single variable polynomials keyword:bivariate polynomials keyword:polynomial division keyword:integers keyword:rational numbers keyword:semirings keyword:rings keyword:left algebra keyword:left module keyword:unit rings keyword:field keyword:algebraically closed field keyword:additive morphisms keyword:ring morphisms keyword:finite dimensional vector spaces keyword:complex numbers keyword:square root logpath:mathcomp.algebra