Author: Harald Schilly
Views : 78
Compute Environment: Ubuntu 18.04 (Deprecated)
x = var('x')
f(x) = sqrt(x^2-1)/(x^2-2)^(1/3)
show(f)

$\displaystyle x \ {\mapsto}\ \frac{\sqrt{x^{2} - 1}}{{\left(x^{2} - 2\right)}^{\frac{1}{3}}}$
f.plot(-5, 5, ymin=0, ymax=5, plot_points=2000, detect_poles=True)

verbose 0 (2733: plot.py, generate_plot_points) WARNING: When plotting, failed to evaluate function at 566 points. verbose 0 (2733: plot.py, generate_plot_points) Last error message: 'negative number cannot be raised to a fractional power' ## Evaluation table shows, that it is complex

for i in srange(-5, 5, 0.2):
print 'f(%6.2f) → %s' % (i, f(x=i))

f( -5.00) → 1.72264719843614 f( -4.80) → 1.70055448044999 f( -4.60) → 1.67795417339814 f( -4.40) → 1.65482890505276 f( -4.20) → 1.63116443867153 f( -4.00) → 1.60695217198425 f( -3.80) → 1.58219317784044 f( -3.60) → 1.55690485085302 f( -3.40) → 1.53113210054574 f( -3.20) → 1.50496678499470 f( -3.00) → 1.47858278970966 f( -2.80) → 1.45230255639720 f( -2.60) → 1.42673152490289 f( -2.40) → 1.40305338123813 f( -2.20) → 1.38375594211395 f( -2.00) → 1.37472963699860 f( -1.80) → 1.39310370564784 f( -1.60) → 1.51530349007590 f( -1.40) → 1.43247029149361 - 2.48111132519994*I f( -1.20) → 0.402377480456089 - 0.696938239971499*I f( -1.00) → 5.77119491429242e-8 + 3.33200093731253e-8*I f( -0.80) → 0.468995755863732 + 0.270774825896718*I f( -0.60) → 0.587497472665636 + 0.339191823991730*I f( -0.40) → 0.647735451181058 + 0.373970237103048*I f( -0.20) → 0.678027888843566 + 0.391459584141907*I f( 0.00) → 0.687364818499301 + 0.396850262992050*I f( 0.20) → 0.678027888843566 + 0.391459584141907*I f( 0.40) → 0.647735451181057 + 0.373970237103047*I f( 0.60) → 0.587497472665635 + 0.339191823991729*I f( 0.80) → 0.468995755863728 + 0.270774825896716*I f( 1.00) → 3.33200093731253e-8 - 5.77119491429243e-8*I f( 1.20) → 0.402377480456097 - 0.696938239971512*I f( 1.40) → 1.43247029149377 - 2.48111132520021*I f( 1.60) → 1.51530349007589 f( 1.80) → 1.39310370564784 f( 2.00) → 1.37472963699860 f( 2.20) → 1.38375594211395 f( 2.40) → 1.40305338123813 f( 2.60) → 1.42673152490289 f( 2.80) → 1.45230255639720 f( 3.00) → 1.47858278970966 f( 3.20) → 1.50496678499470 f( 3.40) → 1.53113210054574 f( 3.60) → 1.55690485085302 f( 3.80) → 1.58219317784044 f( 4.00) → 1.60695217198425 f( 4.20) → 1.63116443867153 f( 4.40) → 1.65482890505276 f( 4.60) → 1.67795417339815 f( 4.80) → 1.70055448044999

## Complex

complex_plot(f, (-2, 2), (-2, 2)) 