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

open allclose all

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:

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

Text

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

CMS

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

APA

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

BibTeX

@misc{reference.wolfram_2024_cubics, author="Wolfram Research", title="{Cubics}", year="1988", howpublished="\url{https://reference.wolfram.com/language/ref/Cubics.html}", note=[Accessed: 22-November-2024 ]}

BibLaTeX

@online{reference.wolfram_2024_cubics, organization={Wolfram Research}, title={Cubics}, year={1988}, url={https://reference.wolfram.com/language/ref/Cubics.html}, note=[Accessed: 22-November-2024 ]}