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:

Wolfram Research (1988), Quartics, Wolfram Language function, https://reference.wolfram.com/language/ref/Quartics.html.

Text

Wolfram Research (1988), Quartics, Wolfram Language function, https://reference.wolfram.com/language/ref/Quartics.html.

CMS

Wolfram Language. 1988. "Quartics." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/Quartics.html.

APA

Wolfram Language. (1988). Quartics. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/Quartics.html

BibTeX

@misc{reference.wolfram_2024_quartics, author="Wolfram Research", title="{Quartics}", year="1988", howpublished="\url{https://reference.wolfram.com/language/ref/Quartics.html}", note=[Accessed: 21-December-2024 ]}

BibLaTeX

@online{reference.wolfram_2024_quartics, organization={Wolfram Research}, title={Quartics}, year={1988}, url={https://reference.wolfram.com/language/ref/Quartics.html}, note=[Accessed: 21-December-2024 ]}