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A method for finding roots of a polynomial equation f(x)=0. Now find an equation whose roots are the roots of this equation diminished by r, so (1) The expressions for f(r), ...

A digit sum s_b(n) is a sum of the base-b digits of n, which can be implemented in the Wolfram Language as DigitSum[n_, b_:10] := Total[IntegerDigits[n, b]]The following ...

cos(pi/(12)) = 1/4(sqrt(6)+sqrt(2)) (1) cos((5pi)/(12)) = 1/4(sqrt(6)-sqrt(2)) (2) cot(pi/(12)) = 2+sqrt(3) (3) cot((5pi)/(12)) = 2-sqrt(3) (4) csc(pi/(12)) = sqrt(6)+sqrt(2) ...

A square matrix that does not have a matrix inverse. A matrix is singular iff its determinant is 0. For example, there are 10 singular 2×2 (0,1)-matrices: [0 0; 0 0],[0 0; 0 ...

The study of number fields by embedding them in a local field is called local class field theory. Information about an equation in a local field may give information about ...

Parametric equations are a set of equations that express a set of quantities as explicit functions of a number of independent variables, known as "parameters." For example, ...

A plot of the map winding number W resulting from mode locking as a function of Omega for the circle map theta_(n+1)=theta_n+Omega-K/(2pi)sin(2pitheta_n) (1) with K=1. (Since ...

The number N_d^((b))(n) of digits d in the base-b representation of a number n is called the b-ary digit count for d. The digit count is implemented in the Wolfram Language ...

An idoneal number, also called a suitable number or convenient number, is a positive integer D for which the fact that a number is a monomorph (i.e., is expressible in only ...

A vertex coloring is an assignment of labels or colors to each vertex of a graph such that no edge connects two identically colored vertices. A vertex coloring that minimize ...