Packed into functions like Solve and Reduce are a wealth of sophisticated algorithms, many created specifically for Mathematica. Routinely handling both dense and sparse ...

NumberFieldRootsOfUnity[a] gives the roots of unity for the field \[DoubleStruckCapitalQ][a] generated by the algebraic number a.

The main equations that Solve and related Mathematica functions deal with are polynomial equations. It is easy to solve a linear equation in  x. One can also solve quadratic ...

An expression like x^2+2x-7==0 represents an equation in Mathematica. You will often need to solve equations like this, to find out for what values of x they are true. This ...

Solve[expr, vars] attempts to solve the system expr of equations or inequalities for the variables vars. Solve[expr, vars, dom] solves over the domain dom. Common choices of ...

Mathematica automatically handles both numeric and symbolic matrices, seamlessly switching among large numbers of highly-optimized algorithms. Using many original methods, ...

NumberFieldFundamentalUnits[a] gives a list of fundamental units for the field \[DoubleStruckCapitalQ][a] generated by the algebraic number a.

The systems of equations that govern certain phenomena (in electrical circuits, chemical kinetics, etc.) contain a combination of differential equations and algebraic ...

Many large-scale applications of linear algebra involve matrices that have many elements, but comparatively few that are nonzero. You can represent such sparse matrices ...

In general, a system of ordinary differential equations (ODEs) can be expressed in the normal form, The derivatives of the dependent variables x are expressed explicitly in ...