When Solve cannot find solutions in terms of radicals to polynomial equations, it returns a symbolic form of the result in terms of Root objects. You can get numerical ...
Most mathematical functions in Mathematica are set up to apply themselves separately to each element in a list. This is true in particular of all functions that carry the ...
Functions to pick out pieces of polynomials. Here is an algebraic expression. This gives the coefficient of x in e.
Relational operators. This tests whether 10 is less than 7. The result is False. Not all of these numbers are unequal, so this gives False.
Simplifying expressions. Mathematica does not automatically simplify an algebraic expression like this. Simplify performs the simplification.
Evaluating sums. Mathematica recognizes this as the power series expansion of e^x. This sum comes out in terms of a Bessel function.
A symmetric polynomial in variables x_1,…,x_n is a polynomial that is invariant under arbitrary permutations of x_1,…,x_n. Polynomials are called elementary symmetric ...
Functions for manipulating trigonometric expressions. This expands out a trigonometric expression. This factors the expression.
Basic vector operations. This is a vector in three dimensions. This gives a vector u in the direction opposite to v with twice the magnitude.
Some common operations on special functions. Most special functions have simpler forms when given certain specific arguments. Mathematica will automatically simplify special ...