HP Prime: Proper Use of Home View and CAS View

[James Williams]

Please help me understand when I should be in Home View and when in CAS View. As an illustration, when I type RANDOM(1,10) in CAS View, the (1,10) argument gets changed to the complex number 1+10*i (but does still seem to correctly return a random number between 1 and 10). In Home View, that does not happen. Does that mean I should not have used RANDOM() in CAS View?

My larger question is, should I use the functions on the Math tab of the Toolbox menus only in Home View, and the functions on the CAS tab only in CAS View? The Quick Start Guide seems to say something different, namely, "Use Home View when you want an approximate answer and CAS View when you want an exact (symbolic) answer."

What are the proper use cases here for the two views? Thanks. I love the Prime, by the way. Kudos to the engineers.

[Michael de Estrada]

That's weird. Anyway, you can use any operations in CAS view, but the way they operate depends on whether you check Exact: in the CAS settings. For example, using the square root symbol (Shift x^2) will yield a symbolic result in Exact mode and a numeric result in approximate mode, so if a=3, then Exact sqrt(a) = sqrt(a), but approximate sqrt(a) = 1.7321. As for using CAS operations in home view, this usually works provided it is a simple numeric operation. More complicated operations usually either require the use of a CAS. prefix or the form CAS(" <expression> ").

Edited: 4 Dec 2013, 10:41 a.m.

[James Williams]

Thanks, Michael, but that doesn't answer my question. I got all that. I was hoping for some members of the HP design team to weigh in here on what their use cases were for when to use Home View and when to use CAS View. Understanding that will help make me more proficient on this calculator.

[Joe Horn]

Quote:

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I was hoping for some members of the HP design team to weigh in here on what their use cases were for when to use Home View and when to use CAS View. Understanding that will help make me more proficient on this calculator.

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I'm not a design team member, or even an HP employee, but I think I understand the concept behind Home versus CAS.

HP Prime Home is like Approx mode on the HP 50g.

HP Prime CAS is like Exact mode on the HP 50g.

For those without 50g experience:

Home is primarily for approximate numeric calculations.

CAS is primarily for exact symbolic operations.

Simple example: A student is asked, "What is the square root of 12?" Should the student answer "Approximately 3.46410161514", or "Exactly 2 times the square root of 3"? Both answers are correct, and both are needed in different circumstances. That's why Prime offers both environments.

Another simple example: What is 2^1234? Home says it's approximately 2.958 times 10^371. That's plenty good enough for most real-world purposes. But if you ever need every digit of the exact answer (e.g. for Number Theory work), CAS returns all 372 digits of 2^1234. Whichever you need, Prime offers both.

I hope that this distinction clarifies why both modes exist, and why SIN(pi) (in radian mode) gets different results in Home and CAS.

Even 0.5-0.4-0.1 gets different results in Home and CAS. And it's not a bug. Nor is it a surprise to anyone who understands the difference in purpose and implementation of Home and CAS. It's only a surprise (and an annoyance) to those who expect Home and CAS to work the same. (If they worked the same, there would be no need for both to exist).

Hope that helped! Or at least I hope that it didn't make it worse.

-Joe-

"Everything above may be wrong." -- Richard Bach ("Illusions")

Edit: Oops, I even got that quote wrong. It's "Everything in this book may be wrong." *sigh*

Edited: 4 Dec 2013, 9:00 p.m.

[Michael de Estrada]

Excellent explanation. What I found confusing initially is that CAS behaves very differently, depending on its settings. If Exact: is checked, then it works very differently than Home, but if unchecked it often looks just the same. Then there's Simplify: which can be set to None, Minimum and maximum, yielding different results. If I have a symbolic matrix and pre-multiply it by it's inverse, I only get the the identity matrix as a result by using maximum simplification. I find CAS view most useful when I'm doing purely symbolic operations, such as expanding the determinant of a symbolic matrix for use with the numeric solver, which is a CAS function. The ultimate result is numeric, but the unknown is symbolic.

[Craig Thomas]

Great answer. Thanks.

[bluesun08]

Never fear: The concept of two views is user-friendly ... according to HP.

Edited: 4 Dec 2013, 2:30 p.m.

[Craig Thomas]

Great question...thanks for asking it.

[cyrille de Brébisson]

Hello,

Joe's answer is great for when to use CAS and when to use home.
A short summary would be:
- If you are expecting a NUMERICAL answer, go to home (1/3 -> 0.3333...)
- If you are Using the VALUES of variables, go to home
- If you are expecting a symbolic answer, go to CAS (sqrt(12) -> 2*sqrt(3)
- If you are using variables as variables, go to CAS

as for RANDOM, as it turns out, the CAS syntax for RANDOM is weired, it's RANDOM or RANDOM value; (with no ()!)
so, RANDOM (1,5); is RANDOM of a value. This value match the short syntax for complex numbers, hence the strange output!

Cyrille

[James Williams]

Joe and Cyrille, thanks much. That helps a lot.

Footnote on RANDOM to Cyrille:
You say the CAS RANDOM has the syntax

. RANDOM value (with no ()!)

Then why does the key sequence (in CAS view):

. Toolbox menus -> Math -> Probability -> Random -> Number -> Enter

automatically append ()? That's probably not what you intended, right?