CAS Simplify: HP Prime vs. TI Nspire

[JDW]

I was reading the following comparative review of the two calculators when I found something interesting:

https://mathclasscalculator.com/index.ph...-prime-v2/

The article gives 2 examples where the Nspire simplifies properly but the Prime does not. Does anyone know why CAS on the Prime has not been improved?

[roadrunner]

They turned the simplification flag off on the prime then claimed the inspire is better because the prime doesn't simplify:

   

That article is biased and insincere. It ignores the multitude of examples where the prime is superior to the in-spire.

-road

[StarTrekken]

(08-13-2018 03:00 PM)roadrunner Wrote:  They turned the simplification flag off on the prime then claimed the inspire is better because the prime doesn't simplify:



That article is biased and insincere. It ignores the multitude of examples where the prime is superior to the in-spire.

-road

Can I ask where the simplification flag is?
Thanks

[roadrunner]

   

[JDW]

That "Simplify" setting changes nothing that I can see. Here is one of the simplification examples put forth in that article:



As you can clearly see, the Nspire simplifies it down to (sin(x))^2 but the Prime "simplifies" to -(1/2)*COS(2*x)+(1/2).

This is true with the CAS Setting "Simplify" set to None or Minimum or Maximum.

If you can get your Prime to simplify the said expression down to (sin(x))^2 in a single step, please provide the procedure.

[Joe Horn]

(08-13-2018 08:24 PM)JDW Wrote:  If you can get your Prime to simplify the said expression down to (sin(x))^2 in a single step, please provide the procedure.

Prime, and the 50g before it, offer many specialized flavors of simplification. The most appropriate Prime function for your purposes is probably the trigsin() function:

trigsin(sin(x)*cos(x)*tan(x)) --> sin(x)^2

Many math expressions do NOT have a single correct "fully simplified" form, but rather have many simplified forms of varying usefulness in varying situations. Prime and the 50g are designed to teach students to distinguish between these different types of simplification, and to use whichever one is appropriate to their current situation.

The most common mistake students make is thinking that "simplified form" means "shortest form". But that's often not true. Easy example: both of the following expressions are equivalent. Which is the simplified form?

A: (x+1)^5
B: x^5+5*x^4+10*x^3+10*x^2+5*x+1

Answer: B, even though it's much longer.

[Gene]

Copied and submitted Joe's posting to the original link as a comment. We will see if it gets published.

Any examples that could be posted there where the nSpire CAS fails and the PRIME works fine?

[JDW]

(08-13-2018 09:07 PM)Joe Horn Wrote:  Many math expressions do NOT have a single correct "fully simplified" form, but rather have many simplified forms of varying usefulness in varying situations. Prime and the 50g are designed to teach students to distinguish between these different types of simplification, and to use whichever one is appropriate to their current situation.

I appreciate the math instruction! :-) Nevertheless, the fact remains that the Nspire simplifies the aforementioned expression in a single step using its most basic "Simply" command. That may not provide an "excellent education for students," but it does get one from Point A to Point B in the shortest possible time. One can call me a buffoon all day for not having thought to use "trigsin" to simply that expression, but again, the Nspire does it without one having to ponder the "method of simplification" so deeply.

This boils down to "what is a calculator really for?" And that depends on who is using it. We want students to learn, but we also want powerful tools. I must admit that I have a bad memory. I love it when my electronic tools help me to avoid having to remember the nitty gritty details and get me to the final answer/solution as quickly as possible. One may argue, "you clearly are no mathematician." And my answer to that is, "Yes, you are correct."

Anyway...

The second "simplification" example put forth in that article is this (Nspire at left, Prime at right):



What is the proper method of simplification on the Prime such that the Prime can achieve the same result in the above simplification example?

Lastly, I do not think that article is "biased toward the Nspire." If anything, it praises the Prime. It says the build quality of the Prime is better, makes less noise when rattled, makes less noise when buttons are pressed, has stable buttons, is easier to use, has a cleaner UI, and gives the buyer his money's worth. Wow! The only area where the article author gives the nod to the Nspire is in terms of Simplification, in that the user needs not know "special simplification methods" in order to get the expected simplified result.

[roadrunner]

(08-13-2018 09:36 PM)Gene Wrote:  Any examples that could be posted there where the nSpire CAS fails and the PRIME works fine?

Here's two:

   

mentioned by Mr. Parisse in this thread:

http://www.hpmuseum.org/forum/thread-10801.html

-road

[Gene]

ty.

Put those on the original site.

[toml_12953]

(08-13-2018 08:24 PM)JDW Wrote:  

(08-13-2018 05:09 PM)roadrunner Wrote:  

That "Simplify" setting changes nothing that I can see. Here is one of the simplification examples put forth in that article:



As you can clearly see, the Nspire simplifies it down to (sin(x))^2 but the Prime "simplifies" to -(1/2)*COS(2*x)+(1/2).

This is true with the CAS Setting "Simplify" set to None or Minimum or Maximum.

If you can get your Prime to simplify the said expression down to (sin(x))^2 in a single step, please provide the procedure.

Maybe the Prime considers a linear expression simpler than a parabolic one. I might not be using the terminology right but you should get the idea.

[roadrunner]

(08-13-2018 09:54 PM)JDW Wrote:  What is the proper method of simplification on the Prime such that the Prime can achieve the same result in the above simplification example?

Set your angle to degrees, set simplify to minimum, type or copy this:

2*sqrt(3)*tan(85)/(sqrt(59)+16*cos(5))

into the command line, and tap enter.

-road

edit: I just noticed, in the example above they had the nspire set to degrees and the prime set to radians. The nspire won't simplify that if set to radians either.

[Joe Horn]

(08-13-2018 09:54 PM)JDW Wrote:  Nevertheless, the fact remains that the Nspire simplifies the aforementioned expression in a single step using its most basic "Simply" command.

So does Prime, and both Prime and Nspire return perfectly correct simplifications with their SIMPLIFY commands. Why are you are assuming that the Nspire's output is THE correct one? It's not. Yes, it's ONE of the many possible correct results, but it's not THE ONLY correct one. Its rules for simplification are not the only possible rules for simplification. Prime happens to have an alternate set of rules which are just as "correct" as Nspire's.

[JDW]

(08-14-2018 01:45 AM)Joe Horn Wrote:  So does Prime, and both Prime and Nspire return perfectly correct simplifications with their SIMPLIFY commands. Why are you are assuming that the Nspire's output is THE correct one?

I never said the word "correct" regarding simplifications. I only said "simplify." There's a difference. And yes, I am aware that a "simplified form" is not always the "shortest" form. But reconsider one of the two article examples, and let's use Roadrunner's suggestion of changing Radians to Degrees to make the Prime simplify the following expression that was mentioned in the article:

2*sqrt(3)*tan(85)/(sqrt(59)+16*cos(5))

The Prime simplifies is thusly:

2*sqrt(3)/(sqrt(59)*tan(5)+16*cos(5)*tan(5))

The Nspire simplifies thusly:

2*sqrt(3)/(tan(5)*(16*cos(5)+sqrt(59)))

Both are correct, but the Nspire's simplification in this one case is shorter than the Prime's, however minor that shorter simplification may be. But in this particular example, the shorter of the two simplifications is the simpler of the two.

And as to using "trigsin()" to simplify the other expression given in the article, again, I honestly would never have thought to use that. I've noted it for future reference, however.

With that said, I'm not praising the Nspire, nor do I even have one or want one. I am just pondering the article and the two simplification examples. I appreciate your input and have found all the comments here insightful. Thank you.

[Aries]

(08-14-2018 12:18 AM)roadrunner Wrote:  

(08-13-2018 09:36 PM)Gene Wrote:  Any examples that could be posted there where the nSpire CAS fails and the PRIME works fine?

Here's two:



mentioned by Mr. Parisse in this thread:

http://www.hpmuseum.org/forum/thread-10801.html

-road

The first integral can be solved by ibp (u=sin(x)^2*cos(x)^2):



As for int((2*x^2+1)*e^(x^2)), basically Nspire CAS has no error function (erf(x), erf(z)), though this could be implemented by M. Beaudin libraries (ETS kit):
https://seg-apps.etsmtl.ca/nspire/ (see librairies)
So the TI Nspire stops to applying linearity.
int(e^(x^2)) can be "developed" by ibp (u=e^(x^2) and v'=1), achieving the correct result.
Anyway I dont think these are examples of a "simplification" process.
Best,

Aries

[roadrunner]

(08-14-2018 01:29 PM)Aries Wrote:  The first integral can be solved by ibp (u=sin(x)^2*cos(x)^2):

Aries,

Is ibp an integral by parts function on the nspire? Mine doesn't have that function. What version software do you have?

-road

[Gene]

Hi Aries, I agree these are not simplification examples... and I have no doubt that the nSpire can solve them by IBP as you show.

But, that requires more knowledge than merely the integration symbol... which parallels (it seems to me) the PRIME example of needing to do the special TRIG function to simplify some things instead of simply the simplify which works on the nSpire. The PRIME can apparently integrate the expressions shown without the need to use the IBP approach... so I think it has some parallels there.

I posted this to the other forum not at all trying to be a fan boy and argue that the PRIME is better than the nSPIRE. I suspect there are a number of problems where both provide solutions in the most straightforward way and other problems where the PRIME can solve them using a "less" straightforward or more detailed way... and similar but perhaps different problems where the nSpire requires a "less" straightforward approach.

Does not mean that one is better or worse than the other. They are simply tools. Use the one that is best for the problems you face.

That was my intent. :-)

[Joe Horn]

(08-14-2018 01:16 PM)JDW Wrote:  ... And yes, I am aware that a "simplified form" is not always the "shortest" form. ... But reconsider one of the two article examples, and let's use Roadrunner's suggestion of changing Radians to Degrees to make the Prime simplify the following expression that was mentioned in the article:

2*sqrt(3)*tan(85)/(sqrt(59)+16*cos(5))

The Prime simplifies is thusly:

2*sqrt(3)/(sqrt(59)*tan(5)+16*cos(5)*tan(5))

The Nspire simplifies thusly:

2*sqrt(3)/(tan(5)*(16*cos(5)+sqrt(59)))

Both are correct, but the Nspire's simplification in this one case is shorter than the Prime's, however minor that shorter simplification may be. But in this particular example, the shorter of the two simplifications is the simpler of the two.

I totally and strongly disagree with that last sentence, which essentially says that A*(B+C) is simpler than A*B+A*C. The fundamental concept in "simplification" is "perform all the indicated operations and collect like terms". Since distributing a multiplication over addition is performing an indicated operation, it's a kind of simplification. Factoring is NOT a kind of simplification, otherwise 2^3 would be the simplified form of 8.

Quote:I'm not praising the Nspire, nor do I even have one or want one. I am just pondering the article and the two simplification examples.

Understood. Please do me the favor of letting me know whenever my delight in debating gets obnoxious.

[Komanguy]

I’ve had a look into that comparison between the nspire and the prime.

Here my comments:

First, on the first example the nspire angles are set to degrees while the prime it’s in radians.
The prime doesn’t simplify automatically expressions, that’s why there’s a specialy « symplify » command to do that; the author just needed to hit that button.

On the second example, you should always use the appropriate function to simplify an expression. It’s a very important matter. For example, cos(x)*sin(x)*tan(x) instead of sin(x)ˆ2, I would have prefered 1-cos(x)ˆ2 depending on my needs.

[Aries]

(08-14-2018 02:26 PM)roadrunner Wrote:  

(08-14-2018 01:29 PM)Aries Wrote:  The first integral can be solved by ibp (u=sin(x)^2*cos(x)^2):

Aries,

Is ibp an integral by parts function on the nspire? Mine doesn't have that function. What version software do you have?

-road

Hi roadrunner,
ibp is not part of the basic functions on the Nspire CAS, take a look here:
https://tiplanet.org/forum/archives_voir.php?id=12390
And here:
https://tiplanet.org/forum/archives_voir.php?id=4481
Many "functions" are missing on the Nspire CAS (Laplace and Fourier transforms, PFE with complex numbers, etc.) but this is not a limitation as long as they can be programmed through libraries.
Best,

Aries