Quartics

Quartics

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

Details

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

Examples

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Basic Examples  (1)

By default Reduce does not use the general formulas for solving quartics in radicals:

With Quartics->True, Reduce solves all quartics in terms of radicals:

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

Scope  (2)

By default Eigenvalues does not use the general formulas for solving quartics in radicals:

With Quartics->True all quartics are solved in terms of radicals:

By default ToRadicals converts all quartic Root objects to radicals:

With Quartics->False, ToRadicals does not use the general formulas for solving quartics:

Introduced in 1988
 (1.0)