An XCas question....
10-14-2017, 06:58 AM
Post: #1
 webmasterpdx Senior Member Posts: 541 Joined: Sep 2015
An XCas question....
I notice that the HP Prime CAS and XCas behave similarly (obviously) towards the following integral....
integrate(e^(-a*x),x,0,+infinity)
in that it only gives a defined answer if you run assume(RE(a)>0) beforehand, as 1/a result.

However, if using Mathematica (Wolfram Alpha) when you give it the problem:

integrate(e^(-a*x),x,0,infiinity)

it gives the result as 1/a for RE(a)>0

i.e. It figures out the conditions for a defined answer and presents them. I don't have to figure out that I need to use +infinity or RE(a)>0. The CAS system figures out the boundaries, instead of me having to know them in advance. The Wolfram Alpha system is a better system in that respect.
I'm wondering is it a big deal for it to figure that out...i.e. I'd love for our CAS system to behave that way....

Here is what I'm talking about...
http://www.wolframalpha.com/input/?i=int...,infinity)

Thx
-Donald
10-14-2017, 10:25 AM
Post: #2
 DrD Senior Member Posts: 1,048 Joined: Feb 2014
RE: An XCas question....
You have heard about signature analysis, no doubt. As a very broad generality, it's a "signature" of the CAS on the prime, that various functions return results the way they do.

The more you use the prime CAS, the more this becomes an obvious truism. If more talent/expertise were spread across the CAS product, I'm pretty sure you would see the CAS become more like competitive products. Similarly, if the marketing scope was widened.

Wolfram, (and similar products), are designed using a different business model than Bernard Parisse methods. French math versus American math educational methods are not a core concern. I have been using the prime very extensively, most everyday, for the last few years. A some point, being frustrated with displayed results, even though usually correct, gives way to understanding this general signature characteristic, and I try to spend less time understanding the displayed result than I do on the underlying problem attempting to be solved.

I don't know if you will understand what I mean with this "in general" opinion, but the more you use the CAS, the more likely your experience will recognize this signature. I'm not suggesting anything less than great respect for Bernard's expertise, diligence, willingness to resolve issues, etc. CAS is not a simple product, but my feeling is that we could be further ahead of the product curve, than we currently are. How you would measure that, I cannot say. I just get the feeling that the technology demand 'out there' is ahead of the market on this one.

(Specific examples show up in this forum and elsewhere, if needed for clarity. I understand the marketing constraints).

The prime is a great product, though. Suffice to say: wish_list ≠ {};

-Dale-
10-14-2017, 10:42 AM
Post: #3
 webmasterpdx Senior Member Posts: 541 Joined: Sep 2015
RE: An XCas question....
Oh, I understand. In fact as I'm learning the Prime CAS, I'm becoming more and more familiar with the signature, as you call it. In fact, I'd say, becoming familiar with this signature should be the first thing anyone using it should learn, as how you specify the problems and interpret the results is very much dependent on this. In fact, I've started to update a page that I hooked up to the Prime wiki with these kinds of tips to help newbies to get up to speed with the "signature" quickly, and I'll continue to add things as I discover them myself.....here...
http://www.wiki4hp.com/doku.php?id=prime:cashome
I understand how complex CAS is, and it's one of the forefront fields of computing. I was around when this stuff was first being explored, as CAS allows many supercomputing solutions to problems to be done using CAS instead, which was one of the reasons it was being explored by the supercomputing gurus back in the 80's.
WolframAlpha/Mathematica is a product that to get the full product license would cost you something like $7000, so having results comparable to a$7000 solution in a $100 calculator is pretty impressive, so I'm pretty impressed with the Prime so far. I'm sure XCas will evolve and improve with time, and the HP Prime's version will follow that curve. 10-14-2017, 10:53 AM Post: #4  DrD Senior Member Posts: 1,048 Joined: Feb 2014 RE: An XCas question.... Lets hope that HP's business paradigm allows for that! 10-14-2017, 01:55 PM Post: #5  webmasterpdx Senior Member Posts: 541 Joined: Sep 2015 RE: An XCas question.... That's one of my biggest fears. I love doing this stuff on a calculator as opposed to a laptop or a phone/ipad. Many people think the calculator is obsolete, but when you use a small tool like a calculator you become very intimate with it. When I use octave or matlab, I'm not as intimate as it's not right there at my fingertips. I'm hoping that HP keeps supporting high end calculators. I really like the new numworks calculator. https://www.engadget.com/2017/08/28/numw...alculator/ It's open source and supports python. The only problem is it doesn't have a full Cas system on it, and it's only a 100MHz processor. I'd love to see something like the numworks calculator with full CAS support, and running on a 1GHz (actually, I'd like the clock to be programmable to save battery life) CPU.....and with it's open source and python paradigm. Now that'd be a kickass calculator! :-) Too bad HP won't support that, as they have to do this exam mode thing....and I understand this, as without that they lose a lot of the student market which is a big part of their market. It is possible to develop a calculator that could support exam mode and still allow a certain degree of hacking. Properly programming the MMU can protect any part you want to, including the MMU tables themselves. 10-14-2017, 03:03 PM Post: #6  DrD Senior Member Posts: 1,048 Joined: Feb 2014 RE: An XCas question.... [quote='webmasterpdx' pid='81471' dateline='1507989318'] python paradigm. Now that'd be a kickass calculator! :-) Too bad HP won't support that [/quote Well, you can't rule that out. How about a$7000 handheld calculator with Wolfram pro, or one of it's contemporaries?
10-14-2017, 03:35 PM
Post: #7
 webmasterpdx Senior Member Posts: 541 Joined: Sep 2015
RE: An XCas question....
Nah...too expensive :-)
....but maybe someone could convert the Numworks code to run on the HP Prime as an alternative firmware package and add the SymPy library to it (SymPy is the python CAS library). Now that'd be interesting.....
10-14-2017, 03:41 PM (This post was last modified: 10-14-2017 07:10 PM by StephenG1CMZ.)
Post: #8
 StephenG1CMZ Senior Member Posts: 705 Joined: May 2015
RE: An XCas question....
(10-14-2017 03:03 PM)DrD Wrote:  [quote='webmasterpdx' pid='81471' dateline='1507989318']
python paradigm. Now that'd be a kickass calculator! :-)

Too bad HP won't support that
[/quote

Well, you can't rule that out. How about a \$7000 handheld calculator with Wolfram pro, or one of it's contemporaries?

No thanks - I wouldn't dare open the box
But a Raspberry Pi running BASIC, C, Mathematica, Prime PPL, Python and XCas whilst also working as a Software Defined Radio for about £150 (packaged in a portable package with a touchscreen) would be nice for Xmas.

Stephen Lewkowicz (G1CMZ)
10-14-2017, 06:46 PM (This post was last modified: 10-14-2017 08:01 PM by compsystems.)
Post: #9
 compsystems Senior Member Posts: 1,101 Joined: Dec 2013
RE: An XCas question....
numWorks as its name says it is for numeric works, let's hope it launches a symbolic Works (SymWorks) calculator.

I think a calculator with only numerical power is a calculator that is not useful for secondary education, since algebra is the queen of all areas of mathematics.

The good enough is the enemy of the excellent.
10-15-2017, 06:35 AM (This post was last modified: 10-15-2017 06:36 AM by parisse.)
Post: #10
 parisse Senior Member Posts: 969 Joined: Dec 2013
RE: An XCas question....
(10-14-2017 03:35 PM)webmasterpdx Wrote:  Nah...too expensive :-)
....but maybe someone could convert the Numworks code to run on the HP Prime as an alternative firmware package and add the SymPy library to it (SymPy is the python CAS library). Now that'd be interesting.....
I don't think you really tried :
- the Numworks firmware : it is very incomplete compared to the HP Prime, for example the Calc application has about 50 commands. And if you define a function in the Python app, you can not use it in the Calc app.
- sympy: it's slow, especially if you like integrals. One second on your PC would be more than 1 minute on your calc.

Now a few words about the Wolfram Alpha comparison. As I understand it, Wolfram Alpha is designed to answer something on a few keywords, it is not designed to do a full computing session. At least in the free version, you can't assume something on a parameter as a first query and ask for something in a second query. In other words, it's easier if you want to do something that the system was designed to do but you can not easily do something that the system was not designed to do, unlike in a CAS where you can extend the system with your own programs.
It's not the same design as Giac/Xcas, a comparison with Mathematica (or Maple or Maxima ...) would be more meaningfull.
10-15-2017, 07:26 AM
Post: #11
 webmasterpdx Senior Member Posts: 541 Joined: Sep 2015
RE: An XCas question....
I thought wolfram alpha WAS mathematica....(not talking the free version).
10-15-2017, 10:50 AM
Post: #12
 DrD Senior Member Posts: 1,048 Joined: Feb 2014
RE: An XCas question....
I think Wolfram Alpha Pro is interactive from Wolfram's Mathematica, but I don't use either of them. Sometimes I do use the free online Alpha product, but I also do use wxMaxima, also free. For us seniors, justifying the very expensive products when there are so many other things chasing disposable income, doesn't rise very high on the list.

I've heard that Wolfram Alpha, "isn't God." So maybe there will be an open source, freely available, CAS product someday, that will become the gold standard among the pack. As online educational tools begin to proliferate, it seems likely this will emerge. Still, Wolfram Alpha IS useful to contrast other results from similar products, especially when results need confirmation.
10-15-2017, 11:11 AM
Post: #13
 webmasterpdx Senior Member Posts: 541 Joined: Sep 2015
RE: An XCas question....
Well, what I found nice about wolfram alpha is the fact that I didn't have to create assume() statements beforehand. It did that work for me. In my original post I put a link to an example...it did the integration and said for RE(a)>0. To get it to work on xcas, I had to do an assume(RE(a)>0) first. Often it's hard to know what assumptions to make beforehand....it's often trial and error.
10-15-2017, 01:31 PM (This post was last modified: 10-15-2017 01:48 PM by DrD.)
Post: #14
 DrD Senior Member Posts: 1,048 Joined: Feb 2014
RE: An XCas question....
Yes, I totally agree. From a user standpoint, the results are often not ready for practical use, in that simplified results still need to be further simplified. This is arguable, for sure, but I just encountered this one, as one quick example:

CAS leaves the derivative alone in the coth'() term. By hand, I get:

diff(coth(cosh(2*x)),x); ==> -2*csch(cosh(2*x))^2 * sinh(2*x)

(If I haven't introduced any typo's), the problem is difficult enough. The need for further work to match the CAS result with the hand result just adds another layer for potential mistakes. As only an example, I have encountered many similar distractions, and I think I understand the barriers that the CAS must overcome, i.e., by not using tables, French vs American approaches, and equivalent representations, etc.

The [a b/c] key is very useful for its current purpose. Perhaps, this key could be also used to re-state displayed function results as well. This is what I mean by, "the technology demand is ahead of the prime," yet, it is something that could be achieved, given sufficient priority.
10-15-2017, 01:43 PM
Post: #15
 Arno K Senior Member Posts: 431 Joined: Mar 2015
RE: An XCas question....
Perhaps there is a cas-version in which coth() is not implemented, then the result is clear.
Arno
10-15-2017, 02:10 PM
Post: #16
 DrD Senior Member Posts: 1,048 Joined: Feb 2014
RE: An XCas question....
I needed to edit that post, due to the image I inserted. I used this only as an example. The broader point is that some results are almost as difficult to resolve as the underlying problem being solved. This is an area where improvement is needed.

I sense there is a difference of opinion between educators, and students or other users. One point of view is that the user needs to be able to manipulate any process result, and a counterpoint is that the user wants to just USE the process result.

As a student, I would rarely need a calculator for these kind of problems. The advantage it can offer, is to confirm results that students obtain. For other users, the idea is often to move from the calculator to finished project, efficiently.
10-15-2017, 03:02 PM
Post: #17
 DrD Senior Member Posts: 1,048 Joined: Feb 2014
RE: An XCas question....
Well, my example isn't a valid one. I just learned that:

"The functions COTH, SECH, CSCH, ACOTH, ASECH, and ACSCH do not exist on the Prime"

So, I have to apologize for my example. There have been plenty of other ones, that could make a better case for improved simplifications. Since this is a general complaint, I'll just suggest this as an area needing improvement.
10-15-2017, 04:00 PM
Post: #18
 Arno K Senior Member Posts: 431 Joined: Mar 2015
RE: An XCas question....
Well, I think not every function has to be implemented. Using 1/tanh works fine.
Arno
10-15-2017, 04:44 PM
Post: #19
 DrD Senior Member Posts: 1,048 Joined: Feb 2014
RE: An XCas question....
There are lots of examples in which that point can be made, for sure. Things like SEC, CSC, COT, (and their inverses), aren't really necessary. There are plenty of other unneeded features. No need for radicals, use fractional powers. No need for the template key, or LOG/10^X. After the four basic functions, add, subtract, multiply and divide, perhaps a memory, what else is really needed? In fact, there isn't any need for a calculator at all. Especially in a math classroom. Completely unnecessary is a programming language that uses all this unnecessary math! ...

One reason to walk back up the evolutionary tree, is utility value. I was happy to pay for the convenience of the hp prime, and if a better one comes along, I'm interested.
10-15-2017, 05:23 PM
Post: #20
 Arno K Senior Member Posts: 431 Joined: Mar 2015
RE: An XCas question....
Wow, harsh words, but that is your opinion.
Arno
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