Roots of Functions: \( \quad F(z) = \displaystyle \sum_{j = 0}^n \alpha_j \; f_j(z) \)   where   \( \alpha_j \in \{ -1, +1 \} \)

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      \( f_j(z) \) = ,       n = ,     \( \alpha_i \)'s =

        Size =     x center =     y center =

      Renormalize intensity for real and complex roots together?

   


This app computes and plots all roots of functions of the form

\( F(z) = \displaystyle \sum_{j = 0}^n \alpha_j \; f_j(z) \)

for which all the coefficients \( \alpha_j \)'s are either \(+1\) or \(-1\) and the functions \( f_j(z) \) are arbitrary analytic functions on the complex plane. The functions \( f_j(z) \) can be selected using the pull-down menu above. The default choice of \( f_j(z) = z^j \) gives us \(n\)-th degree polynomials. The number of terms, \(n\), can also be changed.

Here's a related webpage by Dan Christensen:   http://jdc.math.uwo.ca/roots/
Here's a related webpage by John Baez:   http://math.ucr.edu/home/baez/roots/

Here's a screenshot for the \(18\)-degree polynomial case...

PlusMinusOne

Here's a screenshot for a closeup view of the \(18\)-degree polynomial case...

PlusMinusOne_18

Here's a screenshot for a closeup view of the \(16\)-degree polynomial case...

PlusMinusOne_16

Here's a screenshot for the \(12\)-degree polynomial case with +1,0,-1 coefficients...

PlusMinusOneZero_12

Here's a screenshot for a closeup view of the \(12\)-degree polynomial case with +1,0,-1 coefficients...

PlusMinusOneZero_12_closeup

Updated 2017 Oct 25