Cubics

Cubics

is an option for functions that involve solving algebraic equations, that specifies whether explicit forms for solutions to cubic equations should be given.

Details

  • With Cubics->True, roots of cubics are given explicitly in terms of radicals. With Cubics->False, roots of cubics that do not have very simple forms are given implicitly in terms of Root objects.
  • Cubics->True may lead to fairly large outputs.

Examples

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Basic Examples  (1)

By default, Reduce does not use general formulas for solving cubics in radicals:

With Cubics->True, Reduce solves all cubics in terms of radicals:

Solving this simple cubic in radicals does not require the general formulas:

Scope  (2)

By default, Eigenvalues does not use general formulas for solving cubics in radicals:

With Cubics->True, all cubics are solved in terms of radicals:

By default, ToRadicals converts all cubic Root objects to radicals:

With Cubics->False, ToRadicals does not use the general formulas for solving cubics:

Introduced in 1988
 (1.0)