This has been brought up many times before, but I'd like to bring up
the possibility of adding two commands to Sage: cuberoot(x) and
nthroot(x, n)
The reason is that currently plot( x^(1/3), -5, 5) only shows values for
x>0,
and not for x<0. The current work-around recommended is
plot(sign(x)*abs(x)^(1/3), -5, 5)
(Track ticket #11458)
which replaced the hideous
plot(lambda x: RR(x).nth_root(3), -5, 5, plot_points=20)
This is true in classes like Precalculus and Calculus 1, where trying to
explain
workarounds like these would just really a headache for the instructor and
extremely fragile students.
Also the cube root can occur in many other situations and applications.
This is urgent, because my textbook "Sage for Undergraduates" is due
at the American Mathematical Society on June 30th.
The namespace is so huge, can't we just add two more commands?
I suggest:
def cuberoot(x):
return sign(x)*((x*sign(x))^(1/3))
Last but not least, links to previous demands for exactly this problem:
https://www.mail-archive.com/sage-support@googlegroups.com/msg11563.html
https://groups.google.com/forum/#!msg/sage-devel/_JeSMD-Kvfk/xeNstGrcvXQJ
https://groups.google.com/forum/#!topic/sage-support/icZ8ekC_P4Y
https://groups.google.com/forum/#!topic/sage-devel/_JeSMD-Kvfk
http://trac.sagemath.org/ticket/11458
https://sage.uwstout.edu/home/pub/32/
https://groups.google.com/forum/#!topic/sage-support/ZtRWScqMHMM
https://groups.google.com/forum/#!topic/sage-devel/_JeSMD-Kvfk
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