MaplePrimes - comments on Post, cube roots of negative numbers

MaplePrimes - comments on Post, cube roots of negative numbers http://www.mapleprimes.com/posts/38834-Cube-Roots-Of-Negative-Numbers en-us 2026 Maplesoft, A Division of Waterloo Maple Inc. Maplesoft Document System Tue, 09 Jun 2026 18:17:16 GMT Tue, 09 Jun 2026 18:17:16 GMT The latest comments added to the Post, cube roots of negative numbers http://www.mapleprimes.com/images/mapleprimeswhite.jpg MaplePrimes - comments on Post, cube roots of negative numbers http://www.mapleprimes.com/posts/38834-Cube-Roots-Of-Negative-Numbers x^3 = - 0.008 http://www.mapleprimes.com/posts/38834-Cube-Roots-Of-Negative-Numbers?ref=Feed:MaplePrimes:cube roots of negative numbers:Comments#comment70120 <pre> x^3 = - 0.008 has 3 solutions, 2 of them are imaginary, 1 is real and you want especially one of them</pre> <pre> see the 'surd' command (which is a bit difficult to follow in the help pages): "Note the differences among the outputs of the surd, ^, and root commands":</pre> <pre> (-8.0)^(1/3); root(-8.0, 3); surd(-8.0, 3);;                      1.000000000 + 1.732050807 I                      1.000000000 + 1.732050807 I                              -2.000000000</pre> <pre> For plotting: Maple does not plot imaginary number, if not been explicitely told<maple></maple><maple></maple> like </pre> <pre> plot( [Re(root(x,3)),Im(root(x,3))], x= -1 ..1, color=[red, blue]);  </pre> The latest comments added to the Post, cube roots of negative numbers 70120 Sat, 16 Aug 2008 18:33:38 Z Axel Vogt Axel Vogt principal value http://www.mapleprimes.com/posts/38834-Cube-Roots-Of-Negative-Numbers?ref=Feed:MaplePrimes:cube roots of negative numbers:Comments#comment70119 The reason is that Maple computes the principal value of the expression z^(1/3), which, for negative real z, lies in the upper right quadrant of the complex plane.  To see that, you may use conformalplot: plots[conformalplot](z^(1/3), z = -1..1) The latest comments added to the Post, cube roots of negative numbers 70119 Sat, 16 Aug 2008 19:04:59 Z Joe Riel Joe Riel conformal http://www.mapleprimes.com/posts/38834-Cube-Roots-Of-Negative-Numbers?ref=Feed:MaplePrimes:cube roots of negative numbers:Comments#comment82981 I guess that you mean <pre>plots[conformal](z^(1/3), z = -1..1); </pre> A nice plot of the cubic roots is got with 'DynamicSystems' (not obvious though): <pre>with( DynamicSystems ): NewSystem(1/s^3): RootLocusPlot(%); <img src="/view.aspx?sf=82981/plot1.gif" alt="" width="318" height="318"></pre> The latest comments added to the Post, cube roots of negative numbers 82981 Sun, 17 Aug 2008 04:44:19 Z jakubi jakubi To answer your plot question http://www.mapleprimes.com/posts/38834-Cube-Roots-Of-Negative-Numbers?ref=Feed:MaplePrimes:cube roots of negative numbers:Comments#comment70104 All of the aforementioned hopefully helped explained why Maple does what it does...although it does make sense, it's not the most intuitive operation. To get the plot that you asked for though, use the command plot(surd(x,3),x=-5..5). Hope that helps. The latest comments added to the Post, cube roots of negative numbers 70104 Mon, 18 Aug 2008 17:25:17 Z Tim Vrablik Tim Vrablik Successful plot http://www.mapleprimes.com/posts/38834-Cube-Roots-Of-Negative-Numbers?ref=Feed:MaplePrimes:cube roots of negative numbers:Comments#comment70099 My original question stemmed from the fact that Maple wouldn't give me any negative x-points in the graph of y= x^(1/3).  It was suggested that I use <o:p></o:p>  <o:p></o:p>           plot(Re(x^(1/3)) etc.<o:p></o:p>  <o:p></o:p> and this did give me points when x < 0.  But something was still not right since the graph didn't look as I expected.  It was only when I tried Tim's suggestion:  <o:p></o:p>          plot(surd(x,3) etc.<o:p></o:p>  <o:p></o:p> that the plot came out OK.<o:p></o:p>  <o:p></o:p> Alla<o:p></o:p>  <o:p></o:p>   The latest comments added to the Post, cube roots of negative numbers 70099 Tue, 19 Aug 2008 00:56:37 Z alla alla RealDomain http://www.mapleprimes.com/posts/38834-Cube-Roots-Of-Negative-Numbers?ref=Feed:MaplePrimes:cube roots of negative numbers:Comments#comment82973 Another possibility is <pre> with(RealDomain): plot(x^(1/3), x = -1..1);</pre> Note that Re(x^(1/3)) is incorrect, as you noticed.  It returns the real part of a complex root, which is different from the real root. The latest comments added to the Post, cube roots of negative numbers 82973 Tue, 19 Aug 2008 02:14:27 Z Joe Riel Joe Riel