Even with "Newton methods" where the local model is based on the actual Hessian, unless you are close to a root or minimum, the model step may not bring you any closer to the ...

PolynomialLCM[poly_1, poly_2, ...] gives the least common multiple of the polynomials poly_i. PolynomialLCM[poly_1, poly_2, ..., Modulus -> p] evaluates the LCM modulo the ...

Factor[poly] factors a polynomial over the integers. Factor[poly, Modulus -> p] factors a polynomial modulo a prime p. Factor[poly, Extension -> {a_1, a_2, ...}] factors a ...

Mathematica symbolic expressions can represent an immense range of types of objects. Mathematica provides a rich collection of functions to test expressions. Functions that ...

Mathematica 6.0 fundamentally redefined Mathematica and introduced a major new paradigm for computation. Building on Mathematica's time-tested core symbolic architecture, ...

If you make a definition like f[x_]:=x Sin[x], Mathematica will store the expression x Sin[x] in a form that can be evaluated for any x. Then when you give a particular value ...

Do Basic Calculations Do Constrained Nonlinear Optimization Control the Precision and Accuracy of Numerical Results

Mathematica supports logical operators not only for programming, but for mathematical operations as well.

Newton's method for nonlinear equations is based on a linear approximation so the Newton step is found simply by setting M_k(p)=0, Near a root of the equations, Newton's ...

FactorSquareFree[poly] pulls out any multiple factors in a polynomial.