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In a local ring R, there is only one maximal ideal m. Hence, R has only one quotient ring R/m which is a field. This field is called the residue field.

For a given monic quartic equation f(x)=x^4+a_3x^3+a_2x^2+a_1x+a_0, (1) the resolvent cubic is the monic cubic polynomial g(x)=x^3+b_2x^2+b_1x+b_0, (2) where the coefficients ...

A method for predicting the onset of widespread chaos.

The sum of the aliquot divisors of n, given by s(n)=sigma(n)-n, where sigma(n) is the divisor function. The first few values are 0, 1, 1, 3, 1, 6, 1, 7, 4, 8, 1, 16, ... ...

A subspace A of X is called a retract of X if there is a continuous map f:X->X (called a retraction) such that for all x in X and all a in A, 1. f(x) in A, and 2. f(a)=a. ...

An algorithm for computing an Egyptian fraction.

For P and Q polynomials in n variables, |P·Q|_2^2=sum_(i_1,...,i_n>=0)(|P^((i_1,...,i_n))(D_1,...,D_n)Q(x_1,...,x_n)|_2^2)/(i_1!...i_n!), where D_i=partial/partialx_i, |X|_2 ...

A polyhedron with extra square faces, given by the Schläfli symbol r{p; q}.

A beautiful class of polyhedra composed of rhombic faces discovered accidentally by R. Towle while attempting to develop a function to create a rhombic hexahedron from a ...

The dual polyhedron of the rhombicosahedron U_(56) and Wenninger dual W_(96).