Integrate question

[roadrunner]

I agree that they are both correct. The issue is that CAS is inconsistent because:

∫(sin(x),x)

returns -cos(x)

and not -cos(x) -1/48

which are also both correct.

-road

[parisse]

(10-20-2017 04:43 PM)DrD Wrote:  If the difference is not zero, and the complexity of the problem is already confusing enough to someone trying to make sense of all this, frustration has just been added to the poor soul who wants a simple answer to a simple question, "is my hand calculation correct?" Well ... no, not according to CAS/xcas.

As I have already commented, if you want to check an antiderivative computed by hand, the best method is to derive the expression, precisely to avoid the constant problem. Using a CAS properly requires some training, this is unavoidable.
I would really appreciate if people not trained to use a CAS could ask questions when they do not understand something instead of writing sentences like "the CAS is inconsistent". Sometimes you will find bugs, I don't contest that and I try to fix bugs as soon as possible. But I find plain wrong to persist in an error, it shows no respect for my work and expertise in the CAS area.
(Sorry for my bad English, imagine if you had to discuss in French)

[toshk]

input matters ....you want answer in all sine(s) as in you textbook
∫(sin('2*x+(π/2)')^3*sin(2*x)^5,x)

[DrD]

(10-20-2017 05:58 PM)parisse Wrote:  

(10-20-2017 04:43 PM)DrD Wrote:  ... frustration has just been added to the poor soul who wants a simple answer to a simple question, "is my hand calculation correct?" Well ... no, not according to CAS/xcas.

As I have already commented, if you want to check an antiderivative computed by hand, the best method is to derive the expression, precisely to avoid the constant problem. Using a CAS properly requires some training, this is unavoidable.
(Sorry for my bad English, imagine if you had to discuss in French)

... frustration has just been added to the poor soul who wants a simple answer to a simple question, "is my wxMaxima calculation correct?" Well ... no, not according to CAS/xcas.

... frustration has just been added to the poor soul who wants a simple answer to a simple question, "is my Wolfram Alpha calculation correct?" Well ... no, not according to CAS/xcas.

And so forth .... Et ainsi de suite ... (Excusez mon français)

You don't need to repeat your comments, we all are saying that we understood your explanations. We all understood that CAS/xcas isn't wrong. The issue isn't that CAS is inconsistent. We respect your work and expertise.

I don't think I could make a better case for this, even if I was fluent in French. I have encountered a few things in CAS now, that don't play well with real world examples. That's just the way it is. Software is not "God" to paraphrase an admirable man, whose work and expertise is quite remarkable!

Judge Judy:

Quote:We're done here.

[toshk]

Too many/much times comparing...and the word here is "inconsistent"
CAS is CAS...why doubt CAS but not the others; which of them is your gold standard?
if you do want to compare with any other software.
Do so with some work....
trigcos(((-1/2)*sin(2*x)^8/8)+((1/2)*sin(2*x)^6/6)) had +1/48.

[webmasterpdx]

If the difference is a constant, your CAS answer is correct.
In fact, you could write the answer down and put +10.5 at the end, and it'd be still correct.
ALL constant terms are irrellevant as you have to write the text "+ constant" at the end and this constant is NOT DEFINED. The f(x) portion is only relevant when you define the interval, in which case, all constant terms will be cancelled out.
Note that neither answer is "less accurate" than the other.

[DrD]

(10-20-2017 09:41 PM)webmasterpdx Wrote:  Note that neither answer is "less accurate" than the other.

Totally disagree. A single specified constant is less accurate, because a whole family of constants are allowable. To restrict the result to just the one value, is to ignore all the others including 0. The proof is the comparison between hand / similar technologies, when compared with CAS/xcas. Just focus on the difference, which is NOT 0.

[webmasterpdx]

Accuracy means closer to the exact value. Neither answer is any closer than the other, so neither is less accurate.
it'd be like defining lim(as x->0) 1/x, and saying 1000000 is more accurate than 1000. It isn't...

[Didier Lachieze]

(10-20-2017 10:41 PM)DrD Wrote:  

(10-20-2017 09:41 PM)webmasterpdx Wrote:  Note that neither answer is "less accurate" than the other.

Totally disagree. A single specified constant is less accurate, because a whole family of constants are allowable. To restrict the result to just the one value, is to ignore all the others including 0. The proof is the comparison between hand / similar technologies, when compared with CAS/xcas. Just focus on the difference, which is NOT 0.

Hi DrD, I've followed this discussion with a great interest because I've always found such discussions on the hpmuseum forum are a great way to learn from great people and I'm learning everyday.
However, with my limited math capabilities I don't understand how the difference can tell you that one of the two operand is more restricted than the other, or that one is more accurate.

The Prime CAS returns a result expressed with cos functions, the hand method a result expressed with sin functions ;
CAS : (-3*cos(2*x)^8+8*cos(2*x)^6-6*cos(2*x)^4)/48
Hand: -(3*sin(2*x)^8-4*sin(2*x)^6)/48

Both are correct and none includes an explicit constant.
If you rewrite the CAS result to use sin functions you will get :
CAS = Hand -1/48

But you can also choose to rewrite the Hand result to use cos functions and then you get:
Hand = CAS +1/48

This doesn't tell anything about one solution being more accurate or less restrictive than the other.

Unless there is an elephant in the room... an assumption that was not explicitly stated: that the CAS should use the Hand method to get a matching result. But here there is not a single method to get a mathematical valid result and without explicitly telling to the CAS (either by design or as a parameter) which method you want it to use, I don't see how you can complain about the CAS result.

Personally, if I were expecting a student to solve by hand an indefinite integral, I would also expect him to be smart enough to understand what an indefinite integral is and that two solutions differing only by a constant are both equally valid. Your expectations may be different, and you may want a CAS tailored to a given textbook to provide literally the same results.

This may be due to the difference in how maths are teached in the U.S. and in France and may (or may not...) explain partially why with 1/5th of the population, France has almost the same number of Fields medals than the U.S.: List of countries by number of Fields Medallists.
This being said without any intention to launch a flame war, education in France is far from perfection and it's always good to look how things are done elsewhere to get good ideas for improvement.

[webmasterpdx]

10 of the field medalists came from the ENS school....that's the edge France has IMO.
I'm not from the US myself but am living here now...

[StephenG1CMZ]

(10-20-2017 05:58 PM)parisse Wrote:  ..
. Using a CAS properly requires some training, this is unavoidable.
I would really appreciate if people not trained to use a CAS could ask questions when they do not understand something instead of writing sentences like "the CAS is inconsistent". Sometimes you will find bugs, I don't contest that and I try to fix bugs as soon as possible. But I find plain wrong to persist in an error, it shows no respect for my work and expertise in the CAS area.
(Sorry for my bad English, imagine if you had to discuss in French)

As a complete novice at CAS I would be interested in some CAS training.
My maths tuition was before calculators were commonplace.

For my own needs an online/downloadable/free course in English,.would be useful.
Mon francais est peu.

Is there anywhere listing the courses/training that are available?

[Arno K]

Just my 2 pence, aren't you discussing different things? The one is integration by CAS machines and by hand where some obviously identical but different looking antiderivatives were produced, here any constant added would not change the result, to fulfill anybodies needs CAS could add something like @Cn add the end.
The other is then transforming one antiderivative into another, transformations using identities wth trig functions always involve constants being added or subtracted, these cannot be omitted, otherwise the functions written would be different.
But, and this is my point of view, anybody using a machine to perform some task for him should know what he/she is doing, be able to do it by hand and to check different looking results for equivalence.

[webmasterpdx]

Stephen....check out the Hp Prime wiki....there are some good cas documents....if you know french, there is one for the prime, and plenty of good xcas ones....
http://www.wiki4hp.com/doku.php?id=prime:start

[DrD]

(10-21-2017 06:59 AM)StephenG1CMZ Wrote:  As a complete novice at CAS I would be interested in some CAS training.
My maths tuition was before calculators were commonplace.

For my own needs an online/downloadable/free course in English,.would be useful.
Mon francais est peu.

Is there anywhere listing the courses/training that are available?

Stephen:

If you are asking for CAS training as it relates to the prime specifically, there are various documents around, which you probably already know.

If you are asking about CAS training, in general, there aren't any official courses, that I know of. I don't think the subject matter has evolved to a state of the art that it can actually become a trainable topic, since there are a variety of CAS systems.

If you are not asking a loaded question (in which you already knew the answer), look into wxMaxima. https://en.wikipedia.org/wiki/Maxima_(software)
As a free CAS system, with roots at MIT, there are lots of on line resources to help navigate the learning curve. (and I have no connection to this product, just a reference, for a fellow ham!)

The prime is a great hand held device. Bernard Parisse is an excellent master of the technology that underpins it. I am but a lowly consumer of a product I purchased to use as a tool to make my math tasks easier, in much the same way as one who purchases an electric saw might, to cut material. I imagine many of us, (with all due respect for its progenitors), buy products without even a second thought who the originator, or it's development team, might be. If the usefulness of the product meets, or exceeds, the tasks encountered, then mission accomplished! Surely, success can't hurt future sales ... I probably would look to that company for future needs.

Of course, I know there are a LOT of hp groupies around. They buy hp calcs, just for the logo! I might have a little of that in me, too. The first hp calc I bought was an hp 25, and I haven't missed too many of its siblings to date! During my work career I even wore a few of them out! I think I still have an hp-48 that I used for telemetry SCADA system maintenance. It has a lot of battle scars, but probably still works. So handy to have had that serial port ....

[webmasterpdx]

Stephen again, I'm presuming you have an HP Prime (which is why you are on this forum). The Prime's CAS system is converted from XCas, so the best PC program to get info on the Prime's CAS would be XCas. While there are many other CAS systems like wxMaxima or Maple or Mathematica, they'll only serve to confuse as they'll do things just enough differently than the Prime to frustrate you. On the wiki there is a document called Symbolic Algebra and Mathematics with XCas. This is the best english document apart from the XCas online reference (which is also linked to). The best manual period, is written in French only and is also linked to from the wiki (search the page for "French")....and it's specifically for the HP Prime. Apart from that there are numerous tutorials and tips documents pointed to from the wiki that can introduce you to the Prime's CAS system....mostly under the Programming Documentation section.
Note that you don't have to leave your browser to use XCas (while there is a Windows version)....though Firefox works best with the MathML it uses. SmartCas is another one worth looking at in the browser for XCas....is linked to from the XCAS homepage (linked to also from the wiki).
Enjoy :-)
-Donald

[pier4r]

(10-21-2017 06:59 AM)StephenG1CMZ Wrote:  As a complete novice at CAS I would be interested in some CAS training.
My maths tuition was before calculators were commonplace.

For my own needs an online/downloadable/free course in English,.would be useful.
Mon francais est peu.

Is there anywhere listing the courses/training that are available?

I believe training not in "CAS", but how to do symbolic manipulations by hand and then give the CAS the right direction or being able to understand its limits.

So the courses would be:
Derivatives
limits
integrals
etc.

The "standard" ones for a course in Engineering.

And I understand Mr. Parisse. I mean even a numerical computation requires some skills with numbers to not trust blindly the calculator.

if someone types 360/4 and gets 90 back , how does someone know that it is correct? Comparing it to other calculators? Really? We are at this point?
(note: I fail too, sometimes, to care about the numbers/symbolic computation returned by a computer. Trusting is good but having an idea that the result is correct is better)

Seven times seven: https://www.cs.utexas.edu/users/vl/notes/asimov.html