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A rational function P(x)/Q(x) can be rewritten using what is known as partial fraction decomposition. This procedure often allows integration to be performed on each term ...

A group that coincides with its commutator subgroup. If G is a non-Abelian group, its commutator subgroup is a normal subgroup other than the trivial group. It follows that ...

Let K be a number field and let O be an order in K. Then the set of equivalence classes of invertible fractional ideals of O forms a multiplicative Abelian group called the ...

A quartic algebraic curve also called the peg-top curve and given by the Cartesian equation a^4y^2=b^2x^3(2a-x) (1) and the parametric curves x = a(1+sint) (2) y = ...

A generalization to a quartic three-dimensional surface is the quartic surface of revolution (x^4-ax^3)+a^2(y^2+z^2)=0, (1) illustrated above. With a=1, this surface is ...

A group theoretic operation which is useful in the study of complex atomic spectra. A plethysm takes a set of functions of a given symmetry type {mu} and forms from them ...

Relationships between the number of singularities of plane algebraic curves. Given a plane curve, m = n(n-1)-2delta-3kappa (1) n = m(m-1)-2tau-3iota (2) iota = ...

A point group is a group of symmetry operations which all leave at least one point unmoved. Although an isolated object may have an arbitrary Schönflies symbol, the ...

Let u and v be any functions of a set of variables (q_1,...,q_n,p_1,...,p_n). Then the expression ...

For a polynomial P=sum_(k=0)^na_kz^k, (1) several classes of norms are commonly defined. The l_p-norm is defined as ||P||_p=(sum_(k=0)^n|a_k|^p)^(1/p) (2) for p>=1, giving ...