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Here are a few examples how the HP-Prime reacts on different inputs -

everything entered in CAS mode and with mode Entry:'Algebraic'.

Entry:            Prime result:

================================================================================

2x          --->  2*x

2*x         --->  2*x

2 x         --->  2*x

2(x)        --->  2*x

(2)x        --->  Error message  ... why???

(2)(x)      --->  2*x

2(3)        --->  6

(2)3        --->  Error message  ... why???

(2)(3)      --->  6

                   1

1/2x        --->  ---            ... OMG, 'implicite' multiplication has

                  2*x                priority over the division :-(

(1/2)x      --->  Error message  ... why no implicite multiplication here???

(1/2)(x)    --->  1/2(x)         ... is neither 1/(2x) nor (1/2)*x, seems to be

                                     a function f(x) with the name '1/2' ???

                   1

1/2(x)      --->  ---

                  2*x

                   1

1/2x^3      --->  ----

                     3

                  2*x

                    1

1/2(x)^3    --->  ------         ... although () around x, it puts 2 into the

                       3             exponentiation (wrong precedence!!!)

                  (2*x)

                       3

2(x)^3      --->  (2*x)          ... same bug as above (even worse)

                       3

(2)(x)^3    --->  (2*x)          ... same as above (even with () around 2)

                      1

1/2(x+3)^4  --->  ----------     ... same as above!

                           4

                  (2*(x+3))

That's definitely enough for me to stay with my good old (reliable!) TI-92+ ... ;-)

Franz

Edited: 28 Sept 2013, 8:57 a.m.

Hi, just my opinion but all these :

(2)x

(2)3

(2)(x)^3

1/2(x+3)^4

means absolutly nothing for me

Edit : carriage return

Edited: 28 Sept 2013, 9:01 a.m.

Quote:

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Hi, just my opinion but all these :

(2)x

(2)3

(2)(x)^3

1/2(x+3)^4

means absolutly nothing for me

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Franz

It appears that trying to handle "do what I mean, not what I say" has introduced a bunch of new errors. In my opinion, it's better to state some simple rules and let the user deal with incorrect input than to make some really complicated rules and let the user deal with incorrect input. If the rules are simple then the user will have some confidence that they have input the right thing.

With that said, I do see one change to "normal" precedence that might make sense: In an expression like a/2b, the implicit multiplication might take precedence over normal multiplication. So a/2b is a/(2*b) but a/2*b is (a/2)*b.

As I said , it's just my opinion and _I_ prefer to use explicit multiplication

All of this is ambigous for me. For example :

1/y(x+3)^4

xy

a/bc

etc.

By the way, I agree that if implicit multiplication is allowed, the result must be predictable with an explicit logic

Edited: 28 Sept 2013, 9:20 a.m. after one or more responses were posted

Quote:

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With that said, I do see one change to "normal" precedence that might make sense: In an expression like a/2b, the implicit multiplication might take precedence over normal multiplication. So a/2b is a/(2*b) but a/2*b is (a/2)*b.

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It's absolutely unacceptable that an implicit multiplication takes even precedence over exponentiation in the HP-Prime as in my last example:

                      1

1/2(x+3)^4  --->  ----------

                           4

                  (2*(x+3))

Franz

Quote:

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All of this is ambigous for me. For example :

1/y(x+3)^4

xy

a/bc

etc.

---

Franz

But it's a strange idea to write someting like (2)X

By the way it works in HOME view

(2)X -> (2)*X

(X)5X -> (X)*5*X

(X)(Y)XY -> (X)*(Y)*X*Y if XY doesn't exist
(X)(Y)XY -> (X)*(Y)*XY If XY exists

I hope that the difference of behavior between HOME and CAS will be reduce in the future. In my opinion ( ;) ) this is more annoying

Edited: 28 Sept 2013, 9:29 a.m.

In HOME you get the expected result

I prefer to use unambigous 2D (texbook) entry but I agree the CAS behavior is curious here...

XCAS has the same behavior.

Quote:

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By the way it works in HOME view

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Franz

You guys have me totally confused by now. I checked Wikipedia for "Order of operations math" and it seems that calculator producers change the rules even between their own editions; there is surprisingly no firm universally accepted norm.

I have always believed in explicitly and laboriously entering my expressions with full use of parentheses which the calculator then resolves correctly always, as far as I know. Now, explicit entry seems to be the only responsible thing to do upon reading this Wikipedia article and this Forum. So what doctrine exactly does the Prime stipulate? Are you guys implying it has more than one? Home vs. CAS? Some say that it works in Home, but how can you assume that your Home view conveniently is the (yet-to-be ) established norm?

Chris

Edited: 29 Sept 2013, 1:19 a.m.

Implicit multiplication is accepted only in the following situation: a number followed by a symbol, or a number followed by a symbol to a power, i.e. you can use implicit multiplication for 2x or 3x^2, and that's all. If implicit multiplication is recognized, then no precedence rule apply, i.e. the number times the symbol is considered like if inside parentheses. Therefore 1/2x is parsed like 1/(2*x).
In all other situation, you must use *.
Professional CAS generally do not accept implicit multiplication at all, try 2x in maple for example.
to fhub: Xcas was designed to compete with CAS like maple, not with CAS mainly designed for highschools. It's not a hobby CAS, it's really competitive, for example Xcas is as fast or faster than maple for multivariate polynomial operations (multiplication, gcd, factorization, Groebner basis...).
If you are used to the TI92, right, you will have to change a few things like implicit multiplication. In exchange you will have access to more advanced maths.

Parisse,

Many thanks for the heads up. My Prime is a fantastic learning tool and I am discovering new things all the time. Like if one puts a negative sign in front of the base; and unexpectedly to me with parentheses the exponents starts operating on each other and give a huge net result. Like:

-2^(2^(2^2)) gives -65536 while

(((-2)exp2)exp2)exp2 gives +256.

I wish I could send you a screen shot. But in essence I do -2 to the two to the 2 to the 2 without parentheses in the first case, and with parentheses in the second case. I am sure the Prime is correct but it certainly was a surprise to me. And here I thought parentheses always protected me. Bummer. My Prime is doing exactly what I expected: teach me new stuff!

Chris

Here is what's wrong with allowing implicit multiplication:

1. Create a program with the following code:

EXPORT NEWT()

BEGIN

  F0:="X-F1(X)/" + diff(F1(X),X);

END;

2. Enter in 'X^3-8' into F1.

3. Run the program and then check F0 in Symb view.

The code above should have worked -- but it doesn't because diff does not return the result with an unnecessary extra set of parentheses. In order to properly form F0, one has to do:

EXPORT NEWT()

BEGIN

  F0:="X-F1(X)/(" + diff(F1(X),X) + ")";

END;

The trailing +")" can be left off if we want to do some lazy coding. The benefit of now being able to leave off ()'s in 1 or 2 minor cases does not warrant leaving many users frustrated that they are getting "unexpected" results when pretty much every other similar system DOES NOT allow this sort of implicit multiplication. In fact, it flies in the face of the order of operations. Based on

Also, from a pedagogical point of view, we are NOT helping students AT ALL by enabling them to lazily type 1/2x and get 1/(2x). If the HP Prime is really supposed to help students learn mathematics, then this minor "feature" is actually a step backward insofar as helping them learn order of operations.

I can appreciate that Xcas may be faster than commercial alternatives. However, if it means that users are going to have to always keep an extra set of manuals lying around because it's the one system that does not behave anything like the other ones, I would wager many would simply forgo using Xcas. Because let's face it -- even if Maple were slower, it's cheaper to buy a faster machine and run a familiar piece of software than to spend that extra time having to learn the idiosyncrasies of a competing software. The time saved by faster computations is completely nullified by the time it takes to learn the nuances of Xcas. One need only look at how poorly the RPN graphing calcs have done in the US classrooms. I wholeheartedly believe that the HP50G is still the best calc -- but you won't win over the education market in the US by forcing RPN down everyone's throats. Even more telling is the fact that the HP Prime has put RPN as a secondary option ever since the HP 50G. My point is, Xcas may be superior in many ways -- but unless it is as easy to use as the current commercial offerings with little to no learning curve, it will always play catch up in terms of market share.

Lastly, I also find it hard to believe that students in high school or even college would require calculations such that the speed difference given by using Xcas on a calculator would even be noticeable. Most of the problems they will ever face in a class tend to be easily handled by basic programming. If speed were ever really a factor, then even if they used Xcas it would be done on a much more powerful computer and not a handheld.

Edited: 29 Sept 2013, 10:20 p.m.

Han, I'm not sure I understand all you said.
For your program, I'm sorry but it's not the CAS that is involved here. In the CAS, you can do:
f1(x):=x^2-2;
f0:=id-f1/f1';
(f0@@4)(1.0);
For implicit multiplication, I'm essentially against it, but I find also convenient not to write * when writing polynomials : it's a tradeoff. I always tell my students to write an explicit * (unless there is really no doubt like for 2x). Unfortunately I don't know how to tell bison/yacc how to change the priority of the few rules where I have added implicit multiplication to be like an explicit *, that's why 1/2x is parsed like 1/(2*x). If someone knows how to do that I'd be happy to modify the rules (it's in the input_parser.yy file from giac source, line 201 to 204), adding %prec T_FOIS does not work.

Regarding the software choice, I agree that ease of use is very important. When I spoke of speed, it was in response to fhub who believes Xcas is just a hobby software. But ease of use is not something intrinsic, it depends on previous knowledge of people, and for a CAS, on math teacher knowledge.
I have no idea how it is in the US, but here in France, Xcas has now a real marketshare in highschools. I can insure you that having something free really makes a difference, because you can tell your students to download the software and use it on their computer (and that's probably why I get about 50 000 downloads per year). Moreover, maple was by far the marketleader in French "classes preparatoires" (CAS are not used anymore there from this year, but that's another discussion topic), therefore many math teachers know maple and Xcas compatibility with maple makes the change very easy. In addition, we have really good French documentation for Xcas. You don't need a manual with Xcas, everything is available online and accessed with a few clicks. Unfortunately, we can't say the same for English documentation. What is really lacking in my opinion is a good English Xcas/Prime CAS manual, written by an US math teacher who can read French and adapt our French documentation.

Quote:

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...the few rules where I have added implicit multiplication to be like an explicit *, that's why 1/2x is parsed like 1/(2*x). If someone knows how to do that I'd be happy to modify the rules...

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First, implicit multiplication is ok if it's ONLY an abbreviation for a missing (or omitted) multiplication char (*), but it should definitely NOT change the usual precedence rules at all. That means if the parser discovers such an implicit multiplication, then it should simply insert a * character into the expression, but nothing else, i.e. no extra (...) at all.

Example: the parser should replace 1/2x by 1/2*x, BUT NOT by 1/(2*x) because this is a violation of the precedence rules.

Thus 1/2x should be evaluated as (1/2)*x, and if the user really wants the complete 2x in the denominator, then he should explcitely enter 1/(2x).

Ok, so far about implicit multiplication in principle - and now about WHERE or WHEN such an implicit multiplication should be allowed:

I would say only in the following situations:

1) number followed by a variable: for example 2x --> 2*x

2) number followed by left round bracket: for example 2(expr) --> 2*(expr)

3) right round bracket followed by left round bracket: for example (expr1)(expr2) --> (expr1)*(expr2)

4) right round bracket followed by a variable or a number: for example (expr)x --> (expr)*x, and also (expr)2 --> (expr)*2, although the last case isn't very usual/important.

A variable followed by a left round bracket - for example x(expr) - can't be treated as implicit multiplication, because that's usually a function call. So only the 4 situations above make sense to interpret them as implicit multiplication.

BUT, as I already mentioned: the only action should be to insert a * character, but not change anything else (i.e. not changing any precedence rules).

Franz

I consider myself that 1/2x should not be used because it's ambiguous.
If you omit the * sign, then I find it more intuitive to consider that you meant to group the number and the following symbol who are closed together (2 and x here) than to add a * and apply precedence rules. Especially since according to my own experience, students do not know the precedence rules for / and * : ask students what a/b*c or a/b/c means. It's much better to tell them to add parenthesis
(a/b)*c and (a/b)/c.
Now, writing rules in a forum is one thing, implementing is another thing (talk is cheap). As I already said, the only alternative I know how to implement is to disable implicit multiplication. I don't think that's what people want.

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As I already said, the only alternative I know how to implement is to disable implicit multiplication. I don't think that's what people want.

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Ambiguity is too high a price to pay for this, IMHO.

WolframAlpha/Mathematica make a distinction between 1/2x and 1/(2x). If this cannot be done on the Prime, it is better to have implicit multiplication disabled. This is just my opinion, though.

Edited: 30 Sept 2013, 10:48 a.m.

Quote:

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Ambiguity is too high a price to pay for this, IMHO.

WolframAlpha/Mathematica make a distinction between 1/2x and 1/(2x). If this cannot be done on the Prime, it is better to have implicit multiplication disabled. This is just my opinion, though.

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I agree -- disable it until it gets worked out. Disabling on the HP Prime will help reinforce the order of operations. There are really only two outcomes:

1. If implicit mult. is disabled:

The students who don't have the order of operations mastered (or occasionally forget to account for them) will now have to explicitly multiply. They might not like it, but at least they will be given reinforcement that these rules matter -- and for those who forget, they will be more likely to appreciate the reminder. I remind my students when they use their TI calculators and they always smile at themselves while saying "oh yeah..." or "aha!"

Edit: Given that there is also textbook entry now, this group of users would likely never go back to algebraic entry anyway.

2. If implicit mult. is left as it currently is:

The students and teachers who DO recognize the order of operations will undoubtedly find this not only annoying, but also consider this "feature" a bug. Regardless of the documentation and the ease of input, the "feature" is a complete contradiction of what has become mathematically and universally accepted (referring to order of operations). And those who do not have this concept mastered -- all it does is now further enable them to think that it's "ok."

Edited: 30 Sept 2013, 12:02 p.m.

Quote:

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But it's a strange idea to write someting like (2)X

By the way it works in HOME view

(2)X -> (2)*X

(X)5X -> (X)*5*X

(X)(Y)XY -> (X)*(Y)*X*Y if XY doesn't exist
(X)(Y)XY -> (X)*(Y)*XY If XY exists

I hope that the difference of behavior between HOME and CAS will be reduce in the future. In my opinion ( ;) ) this is more annoying

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(2)X is not strange. In fact, it comes up often in calculus for students who first learn about shortcuts to computing derivatives. When first learning the derivative rules, all the explicit steps are often shown until students become comfortable enough to do some of the simplification in their head. But leaving in the intermediate steps helps them visualize the application of a particular derivative rule (or several).

f(x) = e^(2x)*x ===> f'(x) = e^(2x-1)(2-0)*x + e^(2x)*1

As for (X)(Y)XY -- this should always mean X*Y*XY if the system is going to allow for variables of several letters. On the lower-end TI-84 models in which only single-letter variables are allowed, then the implicit multiplication would make sense (that is, XY means X*Y). However, XY must always be treated as a single variable on systems which accept more-than-one-letter names. Otherwise, having XY interpreted as possibly X*Y or XY depending on the existence of a variable 'XY' is just asking for a lot of headache.

Quote:

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I consider myself that 1/2x should not be used because it's ambiguous.
If you omit the * sign, then I find it more intuitive to consider that you meant to group the number and the following symbol who are closed together (2 and x here) than to add a * and apply precedence rules. Especially since according to my own experience, students do not know the precedence rules for / and * :

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Quote:

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Now, writing rules in a forum is one thing, implementing is another thing (talk is cheap). As I already said, the only alternative I know how to implement is to disable implicit multiplication. I don't think that's what people want.

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Franz

Interesting, fhub, we do not have the same definition of implementation : I meant of course writing source code for bison/yacc that implement precedence rules. Describing precedence rules is easy, writing source code for that is another matter.
I'm of course ok to suppress these implicit multiplication rules for the HP prime if HP decides so, but I will certainly not do it for Xcas. In France, we don't care formally about implicit multiplication like you seem to do on this forum. Writing 2x instead of 2*x is just a convenient notation. And I reiterate, I really believe it's completly artificial to parse 1/2x as 1/2*x, since there is no operator that separates 2 and x, the 2 and x are implicitly grouped, I don't see any reason to apply precedence rules here. I think you just treat it as a bug because it is different from the software you are used to. If that prevents you from using Xcas without looking more closely to the features it provides for free, it's your choice, I will perhaps loose one user, but I believe I would loose more users by disabling 2x as a shortcut for 2*x.

Perhaps the following compromise would be better:

Introduce a flag / setting in which implicit multiplication is enabled or disabled and let the users decide. I would not even mind if the default setting was enabled.

The reality is that since we have textbook entry, most users will probably use that mode instead of algebraic input.

Quote:

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Perhaps the following compromise would be better:

Introduce a flag / setting in which implicit multiplication is enabled or disabled and let the users decide.

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And IF anyone enters such an expression as for example 2x, then it's definitely better to automatically (i.e. always) treat it as 2*x, because what would be the alternative? It could only be to give an error message, and that's also not really confortable.

Franz

Quote:

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I don't really see the need for such an extra flag or setting - even if implicit multiplication is implemented, nobody is forced to use it.

And IF anyone enters such an expression as for example 2x, then it's definitely better to automatically (i.e. always) treat it as 2*x, because what would be the alternative? It could only be to give an error message, and that's also not really confortable.

Franz

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Your hypothetical case in the second paragraph and the fact that some people find 1/2x (as a shortcut for 1/(2x)) useful is precisely why such a flag should be implemented. It is clear from the discussion that there are those who would prefer to have that shortcut. When enabled, then 1/2x gets interpreted as 1/(2x). When disabled, 1/2x becomes (1/2)*x. No error message needs to ever show up.

Quote:

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I really believe it's completly artificial to parse 1/2x as 1/2*x

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That's what I meant when I called XCAS a 'private hobby CAS' - it fulfills YOUR wishes/believes and standards but not the usual mathematical conventions.

Franz

Quote:

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Your hypothetical case in the second paragraph and the fact that some people find 1/2x (as a shortcut for 1/(2x)) useful is precisely why such a flag should be implemented. It is clear from the discussion that there are those who would prefer to have that shortcut. When enabled, then 1/2x gets interpreted as 1/(2x). When disabled, 1/2x becomes (1/2)*x. No error message needs to ever show up.

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;-)

But even this flag won't help against the wrong XCAS result for 1/2(x+3)^4 ... :-(

Franz

Quote:

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Well, then 95% of all calculators and ALL other serious CAS are 'completly artificial' in their expression parsing??

That's what I meant when I called XCAS a 'private hobby CAS' - it fulfills YOUR wishes/believes and standards but not the usual mathematical conventions.

Franz

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Quote:

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maple does not parse 2x, are you considering that maple is not a serious CAS?

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I don't care about users like you who dismiss the work of others like you do.

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Franz

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Han, I'm not sure I understand all you said.
For your program, I'm sorry but it's not the CAS that is involved here. In the CAS, you can do:

f1(x):=x^2-2;

f0:=id-f1/f1';

(f0@@4)(1.0);

---

Inside a program on the HP Prime this does not seem to work. Do you have an equivalent suggestion for use within a program?

You can create a CAS function, and then call that from the "normal" program.

TW