Domain not checked out, please see inside...

[Aries]

P.S. Firmware v8151 ;-)

[Nigel (UK)]

(08-12-2015 11:36 AM)Aries Wrote:  

P.S. Firmware v8151 ;-)

I've looked at this several times and I'm not sure what you are saying. The answer looks correct to me. . .

Nigel (UK)

[Nigel (UK)]

(08-12-2015 01:31 PM)Nigel (UK) Wrote:  

(08-12-2015 11:36 AM)Aries Wrote:  

P.S. Firmware v8151 ;-)

I've looked at this several times and I'm not sure what you are saying. The answer looks correct to me. . .

Nigel (UK)

. . . unless you consider the function to be undefined at x=1 and that x=1 should therefore be excluded from the domain. But that seems a little harsh!

Nigel (UK)

[Aries]

The domain of the fractional inequality is D=R-{1}, hence x=1 MUST be excluded from its domain.
The answer is not correct at all, that's a serious mistake in fact !

[Arno K]

(08-12-2015 02:31 PM)Aries Wrote:  The domain of the fractional inequality is D=R-{1}, hence x=1 MUST be excluded from its domain.
The answer is not correct at all, that's a serious mistake in fact !

Well, I do not think that it is not correct as I tend to simplify first, then we have (x-1)*(x+3)>=0 and the Primes answer is ok. But a real bug is the fact that it even does that with simplify set to "None", here it should exclude 1.
Arno

[DrD]

The trusty Wolfram Alpha seems to agree with Aries, and if X=1, the denominator would be difficult to understand.

[Aries]

(08-12-2015 02:46 PM)Arno K Wrote:  

(08-12-2015 02:31 PM)Aries Wrote:  The domain of the fractional inequality is D=R-{1}, hence x=1 MUST be excluded from its domain.
The answer is not correct at all, that's a serious mistake in fact !

Well, I do not think that it is not correct as I tend to simplify first, then we have (x-1)*(x+3)>=0 and the Primes answer is ok. But a real bug is the fact that it even does that with simplify set to "None", here it should exclude 1.
Arno

You may simplify first but the fraction remains, its domain is still there, it can't be ignored ;-)

[Tim Wessman]

Yup, I'd agree that it isn't correct. Interesting enough, not a single calculator I've just tested (casio, 2-TIs, 50g, prime) return a >1. Doesn't seem to be a unique issue.

Bernard?

[EDIT]
Not unique for calcs either.

Checked maxima (doesn't handle inequalities of this type at all as far as I can tell).

Sage spits out [[x <= -3], [x >= 1]].

[Arno K]

(08-12-2015 04:03 PM)Aries Wrote:  

(08-12-2015 02:46 PM)Arno K Wrote:  Well, I do not think that it is not correct as I tend to simplify first, then we have (x-1)*(x+3)>=0 and the Primes answer is ok. But a real bug is the fact that it even does that with simplify set to "None", here it should exclude 1.
Arno

You may simplify first but the fraction remains, its domain is still there, it can't be ignored ;-)

Ok, clearly the domain stays the same, but this is a removable discontinuity, usually all further calculation is then done after a sentence explaining that and then using the simplified function. Here, as I explained above its a bug in the Prime and not only there, as Tim found out.
Arno

[retoa]

Also the Advanced Graphing app seems to have some problem finding the edge at -1, very slow...

Reto

[Aries]

(08-12-2015 06:44 PM)Arno K Wrote:  

(08-12-2015 04:03 PM)Aries Wrote:  You may simplify first but the fraction remains, its domain is still there, it can't be ignored ;-)

Ok, clearly the domain stays the same, but this is a removable discontinuity, usually all further calculation is then done after a sentence explaining that and then using the simplified function. Here, as I explained above its a bug in the Prime and not only there, as Tim found out.
Arno

I know the function f(x) has a "hole" that can be removed by properly "redefining" a new function F(x) in such a way it's continuous in R but it's not necessary and besides we're talking about different and separated functions, one discontinuous and the other continuous ;-)
By the way Wolfram Alpha takes only the primary f(x) into account, giving the right answer.
Discontinuity is discontinuity, what I'm interested in are the intervals where the inequality is "satisfied" and concerning to this the calculator shows the incorrect answer :-)

[Stefan]

My guess is that the CAS first calculates the upper and lower limit at the singularity which equals 0 in both cases and then calculates the solutions for the function with the singularity removed.

[Aries]

Ok, Stefan, let's suppose the Prime CAS "expands" the primary function f(x) in order to remove, as you said, the discontinuity, apart from the fact we have two different functions, now the question is, is there a way to keep the CAS from removing the "hole" and giving the wrong result ?
We have seen before that setting "simplify" to "None" is useless.

[Hlib]

(08-14-2015 11:00 AM)Aries Wrote:  ...now the question is, is there a way to keep the CAS from removing the "hole"...

http://www.hpmuseum.org/cgi-sys/cgiwrap/...ead=227504

Re: HP39GII and local functions
Message #13 Posted by Tim Wessman on 24 July 2012, 1:10 p.m.,
in response to message #12 by Gilles Carpentier:

==As for type...yeah, oops. We kind of forgot to include that. :-(
Nice thing is it only takes a short time to code it (probably an hour or so for something this simple) and it is fully integrated into the system. To define a system function/variable you provide: a name, getter/evaluator, setter (if a variable), min args, max args, algebraic priority, enabling of automatic input processing including list processing for specific agrumnts, whether it requires full qualification (C1 versus Statistics_2Var.C1 - eg. global or not), special printing if needed, Help, Menu id, and special printing for 2d mode (sigma or the like).
Then you have a new function that will work properly everywhere - including the help interface, placement in the appropriate menu location and even will handle special printing in 2d display mode!
Contrast that with adding a built in function to the 50g ROM. Might take anywhere from a week to much more depending on quite a few factors.
TW==

The best way - it is good to know mathematics and not to wait for implementation of promises of Prime "developers". The mathematical part is realized in Prime at the high level. Don't carp at trifles. If Prime holds on in the market of 5 years, then I too will buy it.

[parisse]

Please do not post pictures, post commandlines instead, because that will spare time to all people who would like to try in the emulator since one can copy/paste commandlines.
The CAS *is* correct. Polynomial removable singularities are removed by efficient CAS, because otherwise you would never be able to do anything useful, you would loose all the time in special case handling (with combinatoric explosion of the number of special cases), and for nothing except perhaps for exercices that make math teachers happy to say to their student "You're wrong, it's not defined" :-)

[DrD]

A counter example, perhaps?

solve((1/(x-1))≥0); ==> {x>1}

[parisse]

There is no polynomial removable singularity in 1/(x-1), therefore it's not a counterexample.

[Aries]

Another example: solve(((x-4)^2*(x+3))/(x^2+5*x+6)>=0), the intervals are:



x=-3 is not part of the domain (domain is R-{-3,-2}), the result is incorrect.
Setting SIMPLIFY to "NONE" doesn't do anything.
Best,

Aries ;-)

[parisse]

Actually, -3 is part of the domain because a CAS considers rational fraction as equivalent to their irreducible representation. But it should not be part of the answer (maybe because solving a/b>0 is equivalent to a*b>0, I'll have a look). But anyway CAS are not implemented to solve particular cases (that would be too costly), you should not be surprised to see things like that. In other words, answers are expected to be generically correct.

[Aries]

I perfectly see the logic and thank you for your patience, parisse, but please take a look at that, I'm begging you !
Best,

Aries ;-)