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siognomi
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There are 8 letters in SIOGNOMI ( G2I1M3N1O1S1 )
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A signomial is an algebraic function of one or more independent variables. It is perhaps most easily thought of as an algebraic extension of multi-dimensional polynomials—an extension that permits exponents to be arbitrary real numbers (rather than just non-negative integers) while requiring the independent variables to be strictly positive (so that division by zero and other inappropriate algebraic operations are not encountered). * Formally, let * * * * X * * * {\displaystyle X} * be a vector of real, positive numbers.* * * * X * = * ( * * x * * 1 * * * , * * x * * 2 * * * , * * x * * 3 * * * , * … * , * * x * * n * * * * ) * * T * * * * * {\displaystyle X=(x_{1},x_{2},x_{3},\dots ,x_{n})^{T}} * Then a signomial function has the form * * * * * f * ( * * x * * 1 * * * , * * x * * 2 * * * , * … * , * * x * * n * * * ) * = * * ∑ * * i * = * 1 * * * M * * * * ( * * * c * * i * * * * ∏ * * j * = * 1 * * * n * * * * x * * j * * * * a * * i * j * * * * * * ) * * * * {\displaystyle f(x_{1},x_{2},\dots ,x_{n})=\sum _{i=1}^{M}\left(c_{i}\prod _{j=1}^{n}x_{j}^{a_{ij}}\right)} * where the coefficients * * * * * c * * k * * * * * {\displaystyle c_{k}} * and the exponents * * * * * a * * i * j * * * * * {\displaystyle a_{ij}} * are real numbers. Signomials are closed under addition, subtraction, multiplication, and scaling. * If we restrict all * * * * * c * * i * * * * * {\displaystyle c_{i}} * to be positive, then the function f is a posynomial. Consequently, each signomial is either a posynomial, the negative of a posynomial, or the difference of two posynomials. If, in addition, all exponents * * ... |