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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.
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  • 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.
EXAMPLESCLOSE 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:
By default, Reduce does not use general formulas for solving cubics in radicals:
In[1]:=
Click for copyable input
Out[1]=
With Cubics->True, Reduce solves all cubics in terms of radicals:
In[2]:=
Click for copyable input
Out[2]=
Solving this simple cubic in radicals does not require the general formulas:
In[3]:=
Click for copyable input
Out[3]=
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:
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