Which calculator purely for algebra solver (with quadratics, cubics)

[Calc Curious]

Hi and thanks for reading.

I am looking for a calculator to use purely in exam or tutorial situations where I don't have access to a computer and need to solve algebra problems (usually hydraulics (mannings, specific energy equations solving for flow depth) or geotech related) where the variable is repeated more than once in the equation, and would result in a quadratic or a cubic. All I want is to be able to enter the equation algebraically as its written and say solve for x, press enter, and all solutions are there in front of me.

I'm surprised as to why there isn't already a query like this out there as it seems to be the one thing those in my situation need in a 'higher level' calculator. I am in third year civil engineering and the only reason why anyone would need anything more than a simple $20 Casio scientific is the ability to solve the above mentioned problems. None of us civils, students or engineers, that I know of has any use for either graphing or programming on a calculator - we'd use excel or a design program. I don't understand the fascination with the programming of a calculator (I have no programming background and wouldn't have a clue where to begin - I own 3 old school HPs, but only for their RPN and build quality).

So I have come up with four calculators that would appear to be able to serve my purpose, with pros and cons for each:

1. TI 89 Titanium (Pros: low cost (2nd hand), build quality. Cons: trig functions are shifted keys)
2. TI Nspire CAS (Pros: low cost (2nd hand). Cons: Unusual keyboard layout)
3. HP 50G (Pros: RPN. Cons: high cost, not sure if this calculator can even handle the above problem, seems to have same limited solver functionality as the HP 48G I already own)
4. HP Prime (Pros: RPN. Cons: high cost, not a fan of touch screen, low battery life(?))

Just seems wrong to have a regularly worry about a calculator's batteries just to have a pretty screen to look at (but if someone says its really worth it then I'd consider it).

So if anyone can make a recommendation that would be great (even one I have not mentioned), given the use I have in mind for it.

 

[Greg Bernhardt]

I'm sorry you are not finding help at the moment. Is there any additional information you can share with us?

 

[Calc Curious]

Thanks for your concern, I will provide an update:

I am now heavily considering the HP 50G for my next purchase (based on very positive reviews and RPN), all I need to confirm is: can that machine solve the problem I described in my first post: can you solve an equation with the unknown repeated more than once, by typing it out as its written on paper, then pressing solve and it gives you all values for x (2 for a quadratic, 3 for a cubic, etc). As I mentioned before, my 48G will not solve these problems, the solver only finds one value for x, it can find roots of polynomials, but I would need to rearrange the equation and enter it in matrix form to do so - so I cannot use my 48G to check whether my algebra is correct, nor use it to solve algebra for me, for that matter. So if the 50G can indeed solve algebra and polynomials on the one 'transaction' (I suspect now that it can), I'd order it in an instant. Otherwise I'd get the TI 89.

 

[DuncanM]

I have the HP 48GX too; have had it for over twenty years and am very happy with it.

In fact, it is possible to compute all roots of a polynomial in a single transaction. You use the SOLVE application. The polynomial coefficients are entered as a vector. You then click "SOLVE", and all the roots of the equation are returned.

If an earlier generation (the 48GX) can do it, I am sure the HP 50G can do it.

 

[Calc Curious]

To DuncamM:

Ah yes, I am aware of that (I actually started a similar thread where I did happen to learn of that, in hindsight I probably should have kept on with the existing thread).

The issue lies in converting what is sometimes a complex algebraic equation into the vector format (especially where time is a factor on exams, and where numerous iterations of an equation may be required). I am aware of other students being able to solve from the equation as its written to all values of x in one go with their Ti Nspires. I'd much rather get an HP RPN calculator instead, but I'd just need to make sure it has this sort of algebra solving functionality first.

By the way, I saw an earlier version of your post where you mentioned that the solve equation function of the HP 48G (the non polynomial one), requires you to graph the function and enter guesses, for it to be able to find other solutions. I'm confused as to how one would enter guesses, there doesn't seem to be a place to enter anything once the solver has found one solution.

So, I'm still awaiting comment from an HP 50G user who is able to manipulate a complex algebraic equation and use it like a TI Nspire in that sense - the 50G would then really have the best of both worlds. I'd be looking to get one as soon as I can confirm this, so I can practice using it in advance of my exams in June.

 

[DuncanM]

To DuncanM:
. . .
The issue lies in converting what is sometimes a complex algebraic equation into the vector format . . .

I am curious to see the equations you are solving. Can you post them here?

. . .
By the way, I saw an earlier version of your post where you mentioned that the solve equation function of the HP 48G (the non polynomial one), requires you to graph the function and enter guesses, for it to be able to find other solutions. I'm confused as to how one would enter guesses, there doesn't seem to be a place to enter anything once the solver has found one solution.

On the 48GX, you can enter the value of x where you suspect a zero will be (see the attached image.) The arrows on the calculator can be used to move the cursor into this field, and then you can enter an initial guess value into this field before running the solver again.

Often, I start it at 1. If I want to look for other zeros, I might take a random guess.
Otherwise, I'd need a graph to better estimate what value to supply as a starting point for the solver; otherwise, it might converge to the wrong zero. The graph might be supplied ahead of time, or I might have drawn it with pencil and paper, or I could use the 48GX itself to draw a graph so I know approximately where the zeros will be.

The User Manuals for the 48GX and 50G are available online on the HP website. Perhaps browse through the 50G manual to see whether or not it has the functionality you want.

 

[MNI]

Surely not MS and ES series..

 

[Calc Curious]

Thanks for your response, I'll try to give some idea of the equations I'd be solving. However, keep in mind that even though these equations might seem fairly straightforward, under exam conditions I'd be looking to spend as little time on the algebra as I can. Here's a fairly simple one:

z1 + y1 + (q2 / 2gy1^2) = z2 + y2 + (q2 / 2gy2^2)

We're given everything except for y2 (depth after a hump in a water flume, y1 being the original depth). z is elevation, q is specific discharge, g gravity. It would be handy to be able to do superscripts and subscripts on here, so that's about as neat as I can write it. Now I know how to transform that one into a cubic polynomial, but only since practicing with that particular sort of problem. The above problem might not represent the extent of the difficulty we will be facing on the exam in terms of algebraic manipulation either.

Here's another example of something we had to deal with in an assignment (in such a situation I am aware that one would more likely use excel or Wolfram, but a condensed version might appear on our exam):

It involves Mannings equation, and solving again for depth of flow in an irregularly shaped open channel cross section that we drew from a contour map. We needed the height of the water in a Q100 flood to determine flood envelopes for a new development, level of culvert, that sort of thing.

Mannings equation is V (velocity) = 1/n R^2/3 S^1/2

n is a roughness coefficient, s is slope, the tricky one is R, hydraulic radius. It is the area divided by the wetted perimeter, or perimeter delineating the water's physical contact with the channel bed and sides. Its not easy to explain on here, but it essentially involved arranging the equation so only depth is unknown (solving for y, again), however this depth is necessary to work out both area and wetted perimeter. A summation of equations was used in order to work it out for 4 or 5 shapes that made up this channel cross section, mostly triangles. It was a pretty hideous thing actually, and we ended up using excel instead of my classmate's ti nspire, to come to an approximate solution. I shudder to think how engineers used to solve this stuff before the advent of computer programs. But then I suppose the way undergrad engineering instruction is, its often a game of 'finding the missing number', which involves a lot of algebra for the sake of it and seems a bit artificial, in real life, engineers don't sit around all day manipulating equations (perhaps they once did I don't know), but I digress.

I am having a look at the HP 50G manual online, and am encouraged by pages 6-3 to 6-5 of this document: http://h10032.www1.hp.com/ctg/Manual/c00748644.pdf

I also noticed pages 7-5 to 7-8 talk about Mannings equation, in regard to the 'multiple equation solver'.

Does it appear to have more solving functionality than the 48G/GX, from reading those pages? If not, it probably wouldn't be worth my while getting the 50G, and I'd most likely hang on to my 48G, as the prices they go for on ebay are shockingly low, its certainly worth a lot more to me than the $30-$40 I see them go for, even as a spare for the drawer (odd that the 11C goes for $100-$150 and the 48G with much more functionality doesn't keep its value).

I'll keep reading this online manual, it looks promising, but the learning curve looks quite steep. Would rather stick with HP than have to get a Ti...

 

[Calc Curious]

Here's an update to this thread that might be of interest to university students like myself who want to use RPN or RPL on an HP calculator, and be able to solve for an unknown variable with ease, like our Ti and Casio equipped peers.

I actually ordered an HP 50G, and it just arrived, so I was able to start putting it through its paces. Thankfully, this model DOES have the ability to solve the energy equations I described earlier for all values of x, using the SOLVEVX function. I only figured this out through trial and error, as neither the quick start guide nor the user's guide was able to explain very effectively which solve function to use in what scenario. Apparently there are several different 'solve' functions, but only one of them, seemingly, is the correct one for this application.

Here's how to do it:
To start writing your equation, use the equation writer by pressing the red shift key then the EQW key (this key is also the ', quotation mark). Once the equation is written, press enter - it will now appear on the first level of the stack. Now press the white shift key, and then S.SLV (this key is also the number 7). There will now appear a list of various solve functions. Scroll down to SOLVEVX, and select it. The (three, for the equation I used) solutions will now appear on the stack, they will be displayed with many decimal places showing, so you'll need to press 'View', or the F2 key, to view them in the equation writer environment (you may still need to use the scroll right key to see all the numbers).

So, to me, this makes the 50G a very worthy replacement to the 48G, its head and shoulders above it from a university student's perspective for that function alone. I'm sure I'll get accustomed to the different keyboard layout, and that 'Enter' key. I hope this is of assistance to someone out there.

 

[CalcNerd]

You might be best served by an Hp 35s. It has an equation solver and lots of RAM. AND its RPN by default (as you implied a liking for RPN). The Hp 50G is also a great way to go, but 2X the cost, big and bulky and not as elegant as the older Hp 48G for my tastes,... but it is fast.

You mentioned a concern about the Hp Prime. The Hp Prime is VERY well built. The battery is rechargeable and lasts for 2-3 weeks before needing a charge. It uses the same charger as a standard Cell phone (USB). It is not the same RPN calculator as your Hp 48G, more like an older Hp 28s when used in RPN mode. It is actually a better algebraic calculator and is configured to mimic the Ti line but with a selectable RPN calculation mode.