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RootIntervals

RootIntervals
gives a list of isolating intervals for the real roots of any of the , together with a list of which polynomials actually have each successive root.
RootIntervals[poly]
gives isolating intervals for real roots of a single polynomial.
RootIntervals[polys, Complexes]
gives bounding rectangles for complex roots.
  • The coefficients of poly must be integers or rationals.
  • An isolating interval for a root of a polynomial poly is an interval where the only root of poly contained in the interval is .
  • If a root is real, the isolating interval is an open real interval, or a point. If a root is not real, the isolating interval is an open rectangle, disjoint from the real axis.
  • Multiple roots give multiple entries in the second list generated by RootIntervals.
Get isolating intervals, together with a list of which polynomial has which root:
The isolating intervals are always specified by exact rationals:
Get isolating intervals, together with a list of which polynomial has which root:
In[1]:=
Click for copyable input
Out[1]=
 
The isolating intervals are always specified by exact rationals:
In[1]:=
Click for copyable input
Out[1]=
Isolate the real roots of a polynomial:
Isolate the real roots of a list of polynomials:
Isolate the complex roots of a polynomial:
Isolate the complex roots of a list of polynomials:
Polynomials may have multiple roots; pairs of polynomials may have common roots:
Isolating intervals of rational roots may be single points:
Find numeric approximations of real roots of a polynomial:
Find isolating intervals:
Find root approximations:
Reduce uses a similar approach, but factoring the polynomial for Root objects takes time:
Compute approximations of the Root objects:
Find real and complex roots of polynomials:
Isolate the real roots; multiple roots are indicated in the second part of the output:
Use CountRoots to count the real roots; multiple roots are counted with multiplicities:
Use Reduce to find the real roots; multiple roots are given once:
Isolate the complex roots; multiple roots are indicated in the second part of the output:
Use Reduce to find the complex roots; multiple roots are given once:
Use Solve to find the complex roots with multiplicities:
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