Sole Cads or Not To CAS

[tim_crouse]

If I am working through algebra problems with 1 or 2 variables how am I to know when I should use the Solver in the CAS menu or the Solver in the Apps Menu ( the command line function not the actual app)?

I upgraded a Prime G2 to the latest firmware 2.1.14603 (2021.12.02)

When I try to enter the equation shown in the attachment into the CAS solver My calculator reboots every time. It will solve it using the App solver (non CAS I guess).

Thanks in Advance
-Tim C.

[rawi]

Hi,
this is a numeric problem, not a problem for CAS.
You have to go to the Solve App, than you press home to quit the app. This is necessary to be able to use the SOLVE function.
Then you type SOLVE(37/18+2X/3=-1+2/3*(-4X/3+9/4),X) and you get the solution -1.
If you are not in the SOLVE environment you can rewrite your equation so it equals zero and than you can can open the toolbox with CAS - solve - zeros to get CAS.zeros and then you get the same solution.
The use of CAS.solve delivers {X}, which is not a solution. I do not have a reason why CAS.zeros work and CAS.solve does not.

[jonmoore]

The CAS solve function solves your problem without error on my Prime G2 (also running the latest firmware). The correct answer is actually -11/3.

Sometimes it's worth bracketing your fractions just to make sure you're entering the equation accurately.

[tim_crouse]

Jonmore

I see you used CAS Solve. But why did you enter 2*x and not just 2x as it is in CAS mode?

Some of this seems a bit buggy to me:

I entered the same formula into a Casio FX50, TI-92 and both came back with -1.

Per the tutorial, I am following on Udemy the answer is shown to be -1.

Thank You for your replies.

Thanks Again
-Tim C.

[jonmoore]

(06-09-2022 10:47 AM)tim_crouse Wrote:  Jonmore

I see you used CAS Solve. But why did you enter 2*x and not just 2x as it is in CAS mode?

Some of this seems a bit buggy to me:

I entered the same formula into a Casio FX50, TI-92 and both came back with -1.

Per the tutorial, I am following on Udemy the answer is shown to be -1.

Thank You for your replies.

Thanks Again
-Tim C.

With HP calculators it's always best to include the implicit multiplication symbol.

I didn't attempt to solve the equation by hand so I can't comment any further ref the proper answer.

[Arno K]

and he forgot to enter an x in the equation.
Arno

[jonmoore]

(06-09-2022 12:36 PM)Arno K Wrote:  and he forgot to enter an x in the equation.
Arno

Good spot. The bracketed section on right-hand side of the equation should have begun -4*x/3. However, the important information for the OP to realise is that the CAS solve function calculates the correct value for this problem, but you must remember to include implicit multiplication symbols. There's no need to use the solve app or the zeros function to get the correct answer.

BTW, I just reentered the equation correctly and the answer is indeed -1.

[C.Ret]

(06-09-2022 10:47 AM)tim_crouse Wrote:  According to the tutorial, I'm on Udemy, the answer is -1.

This is the correct answer to the problem.
I get this solution in HOME as well as CAS mode.

In HOME mode, numerical solutions are preferred based on standard 12-digit machine arithmetic.

In CAS mode, by default, the HP Prime first tries to solve the equation symbolically.
In the simple examples, this approach leads to the same simple numerical solution(s). The only advantage of CAS in these cases is the ability to answer exact or exact long integers.
In CAS, the numerical answer can be forced, it is enough to indicate a guessed value for the variable to be solved.

But the real advantage of CAS mode is to used it for step by step symbolic resolutions (see capture).



In jonmoore's screenshot, we can see that he answers another problem where the unknown x is only present in the left side of the equation. That's why he gets a different solution.

Here are screenshots of the original tim_crouse problem in the SOLVE application, real resolution in CAS mode step by step or using the SOLVE command:    

P.S.: I type 2x and (-)4X directly without any implicit multiplication sign. But the Hp Prime feedback systematically add any multiplication to indicate, without any ambiguity, its interpretation of my inputs.

[jonmoore]

(06-09-2022 04:40 PM)C.Ret Wrote:  

(06-09-2022 10:47 AM)tim_crouse Wrote:  According to the tutorial, I'm on Udemy, the answer is -1.

This is the correct answer to the problem.
I get this solution in HOME as well as CAS mode.

In HOME mode, numerical solutions are preferred based on standard 12-digit machine arithmetic.

In CAS mode, by default, the HP Prime first tries to solve the equation symbolically.
In the simple examples, this approach leads to the same simple numerical solution(s). The only advantage of CAS in these cases is the ability to answer exact or exact long integers.
In CAS, the numerical answer can be forced, it is enough to indicate a guessed value for the variable to be solved.

But the real advantage of CAS mode is to used it for step by step symbolic resolutions (see capture).



In jonmoore's screenshot, we can see that he answers another problem where the unknown x is only present in the left side of the equation. That's why he gets a different solution.

Here are screenshots of the original tim_crouse problem in the SOLVE application, real resolution in CAS mode step by step or using the SOLVE command:

I think it's important with any advice we're providing that we go back to the OPs original post where he asks:

Quote:If I am working through algebra problems with 1 or 2 variables how am I to know when I should use the Solver in the CAS menu or the Solver in the Apps Menu ( the command line function not the actual app)?

In general, when it comes to basic algebra problems that would normally be solved symbolically by hand, I believe that first attempting to use the solve function in the CAS is the best approach because it only provides exact answers unless you force it for a numeric answer by including a decimal point in at least one of the numeric constants.

In this instance, the OP is going through a Udemy course, but he could just as easily have been a high school student checking his answers on the Prime and basic algebra problems like the example in this thread are the basis for teaching symbolic manipulation in high school. The last thing the student needs is to provide a floating-point answer when a rational answer would be the true result when the problem is solved symbolically.

[rawi]

Hi Jonmoore,

I think it is a little more complicated.

If I go to solve app, leave it and press CAS and type in SOLVE(37/18+2x/3=-1+2/3*(-4x/3+9/4),x) I get the right answer -1. If I leave CAS mode by pressing home and type in SOLVE(37/18+2X/3=-1+2/3*(-4X/3+9/4),X) (now X instead of x) I get the right answer as well.

If I go to another app (like function), activate CAS-mode and type in SOLVE(37/18+2x/3=-1+2/3*(-4x/3+9/4),x) the result is the duplication of the input, which is no solution.

If I stay in function, press home (i.e. leave CAS), press toolbox -> CAS -> Solve -> Solve the command CAS.solve is written in the display. If I apply it to the problem typing CAS.solve(37/18+2X/3=-1+2/3*(-4X/3+9/4),X) I get {X} which is not very helpful. If I replaxe the 'X' by 'x' in the command I get the message: Error: Syntax error.

If I stay in this environment, press the toolbox -> CAS -> Solve -> Zeros I get the command CAS.zeros. If I apply it to the problem by typing CAS.zeros(37/18+2X/3+1-2/3*(-4X/3+9/4),X) I get the right answer [-1].

Why is CAS.solve in the non-CAS mode not working? And why is CAS.zeros in the non-CAS mode working? In my opinion when I apply CAS to numerical problems the result is somewhat not predictable.

[jonmoore]

@rawi I agree things are more complicated than they need to be on the Prime - and this leads to a lot of confusion with users (both new and experienced).

It's bad enough that there are both CAS and non-CAS modes (although this can equally be viewed as a benefit once you know what you're doing - but the eulogizers will often attempt to convince you that there's only an upside!).

The link between apps and the Home and CAS modes deepens the possibility of confusion further still. I remember the first time I couldn't get the calculator to provide me with any more than 2 decimal places in Home. I hadn't realised that when you return to Home having used the Finance app, the Prime enforces 2 decimal places no matter the global preferences (and I forgot that the last time I used the Prime I'd used the Finance app). But you tend to only get caught out once. I now religiously always go back to the Function app when finishing a Prime session (before returning to Home or CAS), as this seems to have the least likelihood of changing settings in the background in an unpredictable manner.

The 28/48/49/50 generation of RPL calculators had symbolic capabilities and specialised apps, yet you didn't constantly need to enter different calculation modes for differing outcomes and those symbolic capabilities only improved with each new generation (the 50g has very few gaps in its XCAS features when compared to the Prime, which is remarkable really considering the intervening years).

I tend to only use the Prime for CAS functionality, as I prefer working with my 28/48/50 generation calculators. Added to that, is my SwissMicros DM41x which is my pocket calculator of choice. In fact, I carry my iPhone Pro Max, DM41x and pocket-sized cheat sheets for the 41x in this whenever I leave the house.



And if I need CAS features, I have a wealth of options on the phone inclusive of the Prime iOS app. However, I prefer to use PocketCAS on the iPhone as this is also based on XCAS, but the UX and interaction style are far better suited to the phone (plus it syncs via iCloud so you can pick up where you left off on the macOS version of XCAS at a later date).

As great as the Prime is, it has significant UX problems that were never resolved (and which now have next to no chance of being resolved).

[rprosperi]

The last thing on earth I need is another calculator case.

OK, now that I go that out of the way, can you please share where that case is available?

[jonmoore]

(06-10-2022 02:52 AM)rprosperi Wrote:  The last thing on earth I need is another calculator case.

OK, now that I go that out of the way, can you please share where that case is available?

I got it from Amazon (UK) but it should be available internationally.

https://www.amazon.co.uk/VIIGER-Leather-...08TMD8HK9/

The front pocket is perfect for DM42 form factor calculators and the back pocket has ample room for plus-sized phones (Android or iOS). The leather is decent quality too.

I tend to wear it on a belt loop but the cross-body strap is perfect for when you're travelling (under a jacket, lest you want to look like a metrosexual, manbag toting tool...). Plenty of space for your passport too.

Unfortunately, it's not quite tall enough for a 48GX/50g/Prime but I have a leather number by Samson Cables for that use case. As you say, who needs yet another calculator case!

BTW apologies for the super-massive image in my last post. I lazily linked to the Amazon hero image.

[tim_crouse]

I cannot believe you all comshawed my thread to discuss a merce

Thank you all for your replies
Best Regards
-Tim C.