Why won't the prime graph correctly?
05-23-2019, 03:42 PM
Post: #7
 Nigel (UK) Senior Member Posts: 344 Joined: Dec 2013
RE: Why won't the prime graph correctly?
(05-23-2019 09:14 AM)Aries Wrote:  Quite the contrary, teachers know very well what they are teaching, calculators are stupid and/or badly programmed
Best,

Aries
I suppose different people have different opinions. Here are what the four calculators with me at school (I teach Physics) today say:
• DM42: doing 1 +/- ENTER 3 1/x y^x gives the first complex cube root of -1, rather than -1.
• WP34S: doing 1 +/- ENTER 3 1/x y^x gives DOMAIN ERROR.
• Casio Classwiz fx-85GTX: doing (-1)^(1/3) gives -1.
• HP Prime: (-1)^(1/3) gives an error in Home mode (only integral powers of negative numbers allowed) and a complex result in CAS mode.
I like all of these calculators and I think they behave well.

On a calculator that can handle complex numbers, the complex result is what I would expect. If a calculator tells me that $$(-1)^{1/3}$$ is $$-1$$, I don't know what result it will give me for $$(-1\pm{\bf i}\epsilon)^{1/3}$$. The cut in the complex plane must be somewhere unusual.

On a calculator that handles only real numbers, I prefer an error. The problem is that when the power is a real number - for example, $$-0.4$$ - a calculator that tries to give a real answer must first turn the power into a rational number, express it in its lowest terms, and then throw an error only if the denominator is even. The Casio appears to do this - $$(-1)^{0.4}$$ gives 1, powers of 0.401 up to 0.407 give Math Error, and a power of 0.408 gives -1. It's logical, it's consistent, but is it sensible?

I think that to put the Prime's behaviour down to being "badly programmed" is to miss the point. There is a conceptual difference between a fractional power and an integral nth root: whether to ignore this difference, or if not, how to address it, aren't trivial questions. I think the Prime gets it right by having two separate functions, each behaving as I'd expect. If I were a maths teacher teaching fractional powers at a basic level, I might prefer the behaviour of the Casio. I'm surprised to hear that the TI NSpire appears to follow the Casio - is there a complex mode that needs to be turned on, and if so, does this change the behaviour?

Nigel (UK)
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 Messages In This Thread Why won't the prime graph correctly? - gba456 - 05-22-2019, 02:16 PM RE: Why won't the prime graph correctly? - Aries - 05-22-2019, 02:56 PM RE: Why won't the prime graph correctly? - ijabbott - 05-22-2019, 03:08 PM RE: Why won't the prime graph correctly? - DrD - 05-22-2019, 04:34 PM RE: Why won't the prime graph correctly? - cyrille de brĂ©bisson - 05-23-2019, 06:13 AM RE: Why won't the prime graph correctly? - Aries - 05-23-2019, 09:14 AM RE: Why won't the prime graph correctly? - Nigel (UK) - 05-23-2019 03:42 PM RE: Why won't the prime graph correctly? - Gilles - 05-23-2019, 06:21 PM RE: Why won't the prime graph correctly? - toml_12953 - 05-24-2019, 10:04 AM RE: Why won't the prime graph correctly? - roadrunner - 05-23-2019, 06:38 PM RE: Why won't the prime graph correctly? - toml_12953 - 05-23-2019, 06:59 PM RE: Why won't the prime graph correctly? - Gilles - 05-23-2019, 07:27 PM RE: Why won't the prime graph correctly? - Nigel (UK) - 05-24-2019, 09:16 AM RE: Why won't the prime graph correctly? - Tim Wessman - 05-24-2019, 10:43 AM RE: Why won't the prime graph correctly? - toml_12953 - 05-24-2019, 12:46 PM RE: Why won't the prime graph correctly? - ijabbott - 05-24-2019, 03:36 PM RE: Why won't the prime graph correctly? - toml_12953 - 05-24-2019, 04:06 PM RE: Why won't the prime graph correctly? - ijabbott - 05-24-2019, 04:44 PM

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