Graphing the complex plane

18082016, 05:10 AM
Post: #1




Graphing the complex plane
I have noticed a curious feature in the HP Prime that seems to be a holdover from early development days  it refuses to graph any expression that contains 'i', or (0, 1), the positive square root of negative one, in any form.
I am very interested in graphs of the complex plane, but every attempt results in an error message "Error: Invalid object". And this happens ANY TIME A COMPLEX NUMBER IS PART OF THE EXPRESSION. This is no problem, by the way, plotting the ABS or ARG of a complex expression for the hp48, 49 or 50. You just have a bit of a waiting period while the calculator works. I see no reason to prevent expressions involving complex polynomials or ratios thereof, except perhaps to simplify the code excessively. Plots of the complex plane are a staple of stability theory, for example, in the study of numerical differential equations. At the very least, I note the error message is inappropriately vague and unhelpful. I therefore suggest that the HP Prime ONLY give an error message if a graphing expression RESULTS IN A COMPLEX VALUE (which has no universally accepted means of plotting), and the error message should be something more descriptive, such as: "Error: only real values can be directly graphed. Please take the ABS or ARG of complex expressions to convert these to real values." I believe it makes sense that taking the ARG or ABS of such an expression should be completely allowed, in particular because it specializes in graphing. Disallowing these possibilities needlessly limits its capabilities and makes the calculator less valuable to those who study the complex plane. I have long loved the fact that upscale HP calculators handle complex numbers in very flexible ways  arrays, lists, polynomials can all be complex and work just the same way. Given this fine tradition, is it excessive to suggest the addition of an actual mechanism to plot either the argument or absolute value of expressly complex expressions as a routine matter? To me, such capability seems appropriate for a calculator of this rank. Thoughts, anyone? 

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