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Numerical Solution of Polynomial ...   (Mathematica Tutorial)
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 ...
Operations on Scalars, Vectors, and ...   (Mathematica Tutorial)
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 ...
Picking Out Pieces of Algebraic ...   (Mathematica Tutorial)
Functions to pick out pieces of polynomials. Here is an algebraic expression. This gives the coefficient of x in e.
Relational and Logical Operators   (Mathematica Tutorial)
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.
Simplification   (Mathematica Tutorial)
Simplifying expressions. Mathematica does not automatically simplify an algebraic expression like this. Simplify performs the simplification.
Summation of Series   (Mathematica Tutorial)
Evaluating sums. Mathematica recognizes this as the power series expansion of e^x. This sum comes out in terms of a Bessel function.
Symmetric Polynomials   (Mathematica Tutorial)
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 ...
Trigonometric Expressions   (Mathematica Tutorial)
Functions for manipulating trigonometric expressions. This expands out a trigonometric expression. This factors the expression.
Vector Operations   (Mathematica Tutorial)
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.
Working with Special Functions   (Mathematica Tutorial)
Some common operations on special functions. Most special functions have simpler forms when given certain specific arguments. Mathematica will automatically simplify special ...
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