Some things that a future software upgrade for the HP Prime should consider are the following. They are confusing, and more so from an educational point of view.
Logarithms behave differently in Home and CAS. CAS computes logarithms of negative numbers, while Home returns an error. Besides, the [LOG] key in CAS puts log10 on the input line, but typing LOG on the input line in CAS stays as LOG. In Home, LOG is LOG.
For negative numbers, nth root sign in CAS is different from 1/n power. In Home, the behavior is also different. The command HELP does not fully explain the different behavior, and the example provided in HELP seems wrong for the Help description.
Turn on the "allow complex results from real inputs" in home mode and you will see a difference in the home behavior.
I agree though that it would be nice to have consistency.
Try typing ln in wolfram alpha and see what it returns. This is one of those areas where "symbolic" packages behave totally different then the old established calcualtor behavior. Which should have priority? In short, it is not a simple question.
http://www.wolframalpha.com/input/?i=ln%28x%29
TW
Edited: 19 Nov 2013, 8:46 p.m.
Thanks, I did not know: "allow complex results from real inputs"
I am aware of the Mathematica treatment of logs, but it can be done better.
Indeed.
Its just one of those things that symbolic math packages seem to treat something totally different then what is the "traditional" behavior on a calculator is, or treatment in educational areas.
TW
Quote:
Indeed.
Its just one of those things that symbolic math packages seem to treat something totally different then what is the "traditional" behavior on a calculator is, or treatment in educational areas.
TW
No reflection upon those of you computer scientists out there, but many computer algebra software developers seem to do things in a way that computer scientists would do things and not always the way Physicists and Mathematicians would do things.
I used Maple for quite a while and never got used to it completely. I took one look at Mathematica and had our IT people here at school uninstall it.
The custom in Maths (take a look at any Real Analysis textbook) is to use log for the natural logarithm, and log_a for the logarithm base a.
There's nothing particularly exciting about the logarithm base 10 now that we have easy ways to calculate without logarithm tables (decibels, pH, etc are the very definition of conventional units). Calling the log_10: log, and the log_e: ln is just an old inconsistent notation.
Mathematica usually has mainstream notation... the problem is everybody believes that their discipline is the only one out there.