In article ,
Dave Seaman wrote:

By the definition of unary minus, -x^2 is the number such that
x^2 + (-x^2) = 0.

Without a citation to "the definition" you're using, this is not
persuasive.

Your statement begs the question of operator precedence, and using it to
argue for a particular order of precedence is therefore a tautology.

In article , "Harlan Grove"
wrote:

PITA to use if you cling to any preconceived notions of left-to-right
evaluation, but NEVER ambiguous.

Yup - had to learn APL for my high school math classes. To be
successful, it was hard to avoid learning the math, rather than just the
formulae.

"fred" wrote in message
...
Do any of you SCI.MATH whizes want to weigh in on this?

MS Excel calculates "=-5^2" as 25, not as -25.
This is because 'negation' is handled first in Excel. (!?)
If you put a zero in the equation,
as in "=0-5^2", your answer changes to -25.

Is this in line with standard math rules?
Is negation different than subtraction?

I'm getting a lot of comments in the Excel NG
basically saying that "it's in the help section, so too bad".

I've had lots of math and as far as I know
negation and subtraction are the same thing.

Hmm, judging by the other posts, I seem to be the odd man
out! When I went to (primary) school,

-5 to the power of two = -5 * -5 = 25
-5 to the power of three = -5 * -5 * -5 = -125
...and so on.

The minus in "=0-5^2" is an operator, so zero less 5 to the
power of two = -25.

--
Mail sent to this email address is automatically deleted
(unread) on the server. Send replies to the newsgroup.

On Tue, 03 Aug 2004 08:31:45 -0600, JE McGimpsey wrote:
In article ,
Dave Seaman wrote:

By the definition of unary minus, -x^2 is the number such that
x^2 + (-x^2) = 0.

Without a citation to "the definition" you're using, this is not
persuasive.

Your statement begs the question of operator precedence, and using it to
argue for a particular order of precedence is therefore a tautology.

Let A be a commutative ring with unity. Then A[X] is the ring of
polynomials in X over A. It consists of all linear combinations of the
primitive monomials, which have the form

a * X^k

for a in A and k in N. Thus, -X^2 is the primitive monomial (-1) * X^2,
where -1 is the inverse of the identity 1 in A.

Here I have followed the treatment in Lang, simplified by considering
only the case of polynomials in a single symbol X rather than a set of
symbols S.


--
Dave Seaman
Judge Yohn's mistakes revealed in Mumia Abu-Jamal ruling.
<http://www.commoncouragepress.com/index.cfm?action=book&bookid=228

"fred" wrote in message ...
Do any of you SCI.MATH whizes want to weigh in on this?

MS Excel calculates "=-5^2" as 25, not as -25.
This is because 'negation' is handled first in Excel. (!?)
If you put a zero in the equation,
as in "=0-5^2", your answer changes to -25.

Is this in line with standard math rules?
Is negation different than subtraction?

I'm getting a lot of comments in the Excel NG
basically saying that "it's in the help section, so too bad".

I've had lots of math and as far as I know
negation and subtraction are the same thing.



Negation and subtraction are not the same thing. Subtraction has TWO
operands. As I learned in second-grade math, minuend minus subtrahend
equals difference.
Perhaps that's not in the grade-school math books anymore.

David Ames

Dave Seaman writes:
By the definition of unary minus, -x^2 is the number such that
x^2 + (-x^2) = 0.

Begging the question.

Phil

--
1st bug in MS win2k source code found after 20 minutes: scanline.cpp
2nd and 3rd bug found after 10 more minutes: gethost.c
Both non-exploitable. (The 2nd/3rd ones might be, depending on the CRTL)

In article ,
Dave Seaman wrote:

Let A be a commutative ring with unity. Then A[X] is the ring of
polynomials in X over A. It consists of all linear combinations of the
primitive monomials, which have the form

a * X^k

for a in A and k in N. Thus, -X^2 is the primitive monomial (-1) * X^2,
where -1 is the inverse of the identity 1 in A.

Here I have followed the treatment in Lang, simplified by considering
only the case of polynomials in a single symbol X rather than a set of
symbols S.

Still a tautology...<g

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

"Negation" should be regarded as multiplication in the order-of-operation
rules of arithmetic because, for all real x

- x = (-1)x .

Kevin O'Neill

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


"fred" wrote in message ...
Do any of you SCI.MATH whizes want to weigh in on this?

MS Excel calculates "=-5^2" as 25, not as -25.
This is because 'negation' is handled first in Excel. (!?)
If you put a zero in the equation,
as in "=0-5^2", your answer changes to -25.

Is this in line with standard math rules?
Is negation different than subtraction?

I'm getting a lot of comments in the Excel NG
basically saying that "it's in the help section, so too bad".

I've had lots of math and as far as I know
negation and subtraction are the same thing.




"JE McGimpsey" wrote in message
...
That's clearly explained in the XL Help topic "The order in which
Microsoft Excel performs operations in formulas".

In all the math I've ever done, from grade school on, negation and
subtraction have been separate operations (often, but not always, using
separate symbols, such as a hyphen for negation and an n-dash for
subtraction), so that -5^2 has always been interpreted to equal 25.

Personally, I'd take it up with your consultant, assuming that he/she
was working on the Excel model. That problem should have been a piece of
cake for someone with even moderate expertise to identify, from the sign
change alone! There's no way you should have to pay for 20 hours of
troubleshooting (at my rates, at least).

In article ,
"fred" wrote:

I did in another sub-thread. Dana was familiar with it already.

If you lead off with a negative sign it uses the negative value inside
the
exponentiation.
So, instead of =-5^2 equalling -25 it equals 25.
but, =0-5^2 is calculated correctly as -25 even though it's
mathematically
the same.

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


No break is needed if the reason for the existence of order-of-operation
rules is understood.


Kevin O'Neill

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


"fred" wrote in message ...
So if a physicist writes an equation he has to include the 'rules of
calculation' for others to use it? Give me a break.



"Dik T. Winter" wrote in message
...
In article "fred"
writes:
Do any of you SCI.MATH whizes want to weigh in on this?

Well, contrary to some responders I do not read this in an excel newsgroup
(I have no reason to read such a newsgroup...).

MS Excel calculates "=-5^2" as 25, not as -25.

Yes, that is one of the possibilities.

This is because 'negation' is handled first in Excel. (!?)

Right, there are quite a few programming languages that do the same.

If you put a zero in the equation,
as in "=0-5^2", your answer changes to -25.

Indeed.

Is this in line with standard math rules?

Yup, both are in line with standard math rules. There are no standard
rules about how unary operators are handled.

Is negation different than subtraction?

Yes, indeed.

I've had lots of math and as far as I know
negation and subtraction are the same thing.

When you look at the definition for rings, and stuff like that, you will
find that they are very different. If you look you will find that
a - b
is just shorthand for
a + b'.
where b' is the negative of b. So
0 - 5^2
is shorthand for
0 + (5^2)'

There are more places where some programming languages do not give you
what you thought they should do. Exponentiaton is an example. What is:
a ^ b ^ c?
There is not strict left to right rule in mathematics...

You may wonder, why should I do
a - b + c
from left to right? Well, actually you have to transform it to something
that is basic mathematics:
a + (-b) + c
and now it does not matter what way you do the operations.
where (5^2)' is the negative of 5^2.
--
dik t. winter, cwi, kruislaan 413, 1098 sj amsterdam, nederland,
+31205924131
home: bovenover 215, 1025 jn amsterdam, nederland;
http://www.cwi.nl/~dik/

Plot the curve y = -x^2.

Solve the equation -x^2 -18x + 5 = 0.

The standard normal density is f(x) = 1/sqrt(2 pi) exp(-x^2 / 2).

What is the value of -16^(1/4)?

The standard is not peculiar to those of us who are bemoaning the bug
here. It is as universal as spelling rules. The only individuals
claiming this to be an ambiguity appear to be computer professionals
exclusively. There are thousands of end users of this product who are
not programmers, nor should one need to be to use a spreadsheet. Nor
should they be expected to comb the documentation to discover this
peculiar "feature." This is a very flawed design.

--
Stephen J. Herschkorn

On Tue, 03 Aug 2004 10:54:54 -0600, JE McGimpsey wrote:
In article ,
Dave Seaman wrote:

Let A be a commutative ring with unity. Then A[X] is the ring of
polynomials in X over A. It consists of all linear combinations of the
primitive monomials, which have the form

a * X^k

for a in A and k in N. Thus, -X^2 is the primitive monomial (-1) * X^2,
where -1 is the inverse of the identity 1 in A.

Here I have followed the treatment in Lang, simplified by considering
only the case of polynomials in a single symbol X rather than a set of
symbols S.

Still a tautology...<g

You don't know what a tautology is.

You asked for a citation. I provided one[1]. Moreover, the definition
shows why polynomials are defined the way they are. They are linear
combinations of the primitive monomials X^k.

[1] Lang, _Algebra_, 1965. I haven't checked the later editions.


--
Dave Seaman
Judge Yohn's mistakes revealed in Mumia Abu-Jamal ruling.
<http://www.commoncouragepress.com/index.cfm?action=book&bookid=228

On 03 Aug 2004 19:31:00 +0300, Phil Carmody wrote:
Dave Seaman writes:
By the definition of unary minus, -x^2 is the number such that
x^2 + (-x^2) = 0.

Begging the question.

See my followup elsewhere.



--
Dave Seaman
Judge Yohn's mistakes revealed in Mumia Abu-Jamal ruling.
<http://www.commoncouragepress.com/index.cfm?action=book&bookid=228

In article ,
"Stephen J. Herschkorn" wrote:

The standard is not peculiar to those of us who are bemoaning the bug
here. It is as universal as spelling rules.

Repetition doesn't make it so...

Nor is what you'd write by hand fundamentally relevant to using a
spreadsheet, either. You didn't learn to add numbers using =SUM(A1:A10)
in grade school.

The only individuals claiming this to be an ambiguity appear to be
computer professionals exclusively.

Not me. I was trained as a chemist.

There are thousands of end users of this product who are not
programmers, nor should one need to be to use a spreadsheet.

Absolutely correct. OTOH, they should be able to verify that they know
how to use *any* tool before they rely on it.

Nor should they be expected to comb the documentation to discover
this peculiar "feature."

What documentation does one need to enter =-5^2 into a cell to verify
(or in this case, refute) one's assumption?!?

This is a very flawed design.

Perhaps (I could use it either way, but then I do check the
documentation before I rely on the result), but it's been in existence
for 20 years now. That makes it a *standard* for spreadsheets. It's not
going to change.

"fred" wrote in message .. .

BOULDERDASH!!! This is a horrible bug in Excel (whereof I was
previously unaware). It is very standard that exponentiaion takes
precedence over negation. Ask any semi-decent high school student to
draw a graph of y = -x^2, and what will you get?


Thank you sir!

As another poster noted, M.P.E.P is a programming forum, but told that it
violates math convention, they still argue. They probably just didn't
believe me.

Another said "much ado about nothing", but I think this is a horrible bug
too. Excel should at least follow regular math conventions. What other
surprizes await?!

Wel, try this... Start up the Calculator that comes with WindowsXP.
Enter the keystrokes: 2 + 3 * 5 =

Try it in BOTH standard and scientific "Views"

Compare, and reconcile, the answers.

And don't forget, the programmers for Lotus 123 thought that 1900 was
a leap-year

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

I've seen some high-level arguments including reference to algebraic structures
(rings, groups, etc.) and "unary operations" in this and nearby threads that yield
the correct result for the evaluation of an expression such as -3^2 (which is -9).

The issue is far simpler than most other posts/responses seem to indicate: it
comes from the order-of-operation rules of arithmetic, and "negation" should
be regarded as multiplication under these rules because, for any real number x

- x = (-1)x .
Consequently,

-3^2 = (-1)*3^2 = (-1)*9 = -9.

The order-of-operation rules are sometimes seen as something cooked up
by pedants. Anyone should consider reason for the existence of the rules
by considering what values the following might assume when "simplified" if
there were no rules.

2 + 3*4 (24 or 14 ?)

9 - 5 - 3 (1 or 7 ?)

-3^2 (9 or -9 ?)

Having the rules is better than needing to say, "Well . . . ya' know what I mean,"
frequently, and are far more important than most people realize -- they are how
expressions (and consequently, equations) are read (and understood) even
when the expressions contain variables.

It is mildly interesting that some exceptions to the rules (specific cases in which
the rules don't matter, e.g., a + b + c ) are listed among the field properties of
the real numbers.

It is truly unfortunate that ANY computer languages or programs would not
conform to the order-of-operation rules.


Kevin O'Neill

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



"Alan Beban" wrote in message ...
Stephen J. Herschkorn wrote:
fred wrote:

Do any of you SCI.MATH whizes want to weigh in on this?

MS Excel calculates "=-5^2" as 25, not as -25.
This is because 'negation' is handled first in Excel. (!?)
If you put a zero in the equation,
as in "=0-5^2", your answer changes to -25.

Is this in line with standard math rules?
Is negation different than subtraction?

I'm getting a lot of comments in the Excel NG
basically saying that "it's in the help section, so too bad".

I've had lots of math and as far as I know
negation and subtraction are the same thing.


Alan Beban wrote:

Well, this is an Excel forum, so one should expect a programming point
of view. But if you search on mathematical notation generally, I
think negation is viewed as a unary operator, while subtraction is
viewed as a binary operator; and the discussions are not much clearer
in that context. My own view, not as a mathematician, is that the
issue revolving around how to evaluate -1^2 depends on some *order of
precedence*, and is totally conventional as to negation and
exponientation.




BOULDERDASH!!! This is a horrible bug in Excel (whereof I was
previously unaware). It is very standard that exponentiaion takes
precedence over negation. Ask any semi-decent high school student to
draw a graph of y = -x^2, and what will you get?

Stating it is a documented convention is not a legitimate argument.
What if Microsoft(R) buried in its documentation that addition takes
precedence over multiplication? That the spell checker would always
change word "friend" to "freind"? That the sum function adds only every
other term? That using a "q" in one of its products would cause the
system to reboot? These effects would be just as valid by this logic.

I have sent this comment to Microsoft(R), though I expect no good to
come of it.


Pounding on the desk about it being "very standard that exponientation
takes precedence over negation" is much less persuasive than would be
citing the "standard" order of precedence rules applicable in
mathematics. I don't find what "a semi-decent high school student" would
do to be very compelling. Why can't the people who are so emotional
about the issue (which, incidentally, seems to have been resolved in C
the same way as it is in Excel, which is hard to blame Microsoft for)
cite some persuasive authority besides the fact that their grandmother
taught them to Please Excuse My Dear Aunt Sally, which my limited Google
search suggests is applicable to only the binary operators listed and
not to unary operators? Maybe we could all learn something if we were
directed to an authoritative source of the convention in ordinary
mathematics without regard to programming.

Alan Beban

Stephen J. Herschkorn wrote:

Plot the curve y = -x^2.

I can't until someone gives me the convention to determine whether it is
to be interpreted as y=-(x)^2 or y=(-x)^2

Solve the equation -x^2 -18x + 5 = 0.

I can't until someone gives me the convention to determine whether it is
to be interpreted as -(x)^2 -18 + 5 = 0 or (-x)^2 -18x + 5 = 0
. . .

What is the value of -16^(1/4)?

I don't know until someone gives me the convention to determine whether
it is to be interpreted as -(16)^(1/4)) or ((-16)^(1/4))

The standard is not peculiar to those of us who are bemoaning the bug
here. It is as universal as spelling rules.

Unless the inquiry gets sufficiantly sophisticated, I can usually
resolve "spelling rules" by resort to a decent unabridged dictionary,
like to resolve the correct spelling of "balderdash". If the order of
precedence is so universal, please cite a "universal" authority (i.e.,
the analog of the unabridged dictionary for spelling).

The only individuals
claiming this to be an ambiguity appear to be computer professionals
exclusively.

I'm not a computer professional; in the absence of some persuasive
authority, I find it ambiguous.

Alan Beban

By the definition of unary minus, -x^2 is the number such that
x^2 + (-x^2) = 0.

Without a citation to "the definition" you're using, this is not
persuasive.

Your statement begs the question of operator precedence, and using it to
argue for a particular order of precedence is therefore a tautology.

Pick *any* algebra text, calculus text, etc. The expression -x^2 means
the negative of x^2 throughout mathematics. If you want the negation
to have priority, you write (-x)^2. For example, if you see the expression
-x^2 +3x-2 in any math book, it means (-1)*x^2 +3*x -2 and is certainly
not the same as x^2 +3x-2 (unless you are in a field of characteristic 2).
This is absolutely standard notation.

--Dan Grubb

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

See my previous post(s).


Kevin O'Neill

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

"Alan Beban" wrote in message ...
Stephen J. Herschkorn wrote:

Plot the curve y = -x^2.

I can't until someone gives me the convention to determine whether it is
to be interpreted as y=-(x)^2 or y=(-x)^2

Solve the equation -x^2 -18x + 5 = 0.

I can't until someone gives me the convention to determine whether it is
to be interpreted as -(x)^2 -18 + 5 = 0 or (-x)^2 -18x + 5 = 0
. . .

What is the value of -16^(1/4)?

I don't know until someone gives me the convention to determine whether
it is to be interpreted as -(16)^(1/4)) or ((-16)^(1/4))

~~~~~~~ SNIP

Unless the inquiry gets sufficiantly sophisticated, I can usually
resolve "spelling rules" by resort to a decent unabridged dictionary,
like to resolve the correct spelling of "balderdash". If the order of
precedence is so universal, please cite a "universal" authority (i.e.,
the analog of the unabridged dictionary for spelling).

The only individuals
claiming this to be an ambiguity appear to be computer professionals
exclusively.

I'm not a computer professional; in the absence of some persuasive
authority, I find it ambiguous.

Alan Beban

(Daniel Grubb) writes:

By the definition of unary minus, -x^2 is the number such that
x^2 + (-x^2) = 0.

Without a citation to "the definition" you're using, this is not
persuasive.

Your statement begs the question of operator precedence, and using it to
argue for a particular order of precedence is therefore a tautology.

Pick *any* algebra text, calculus text, etc. The expression -x^2 means
the negative of x^2 throughout mathematics. If you want the negation
to have priority, you write (-x)^2. For example, if you see the expression
-x^2 +3x-2 in any math book, it means (-1)*x^2 +3*x -2 and is certainly
not the same as x^2 +3x-2 (unless you are in a field of characteristic 2).
This is absolutely standard notation.

Uh, no. -x² + 3x - 2 would be standard notation. Little ^ characters
have no standard notational meaning.

But the same argument would hold here as well.

--
David Kastrup, Kriemhildstr. 15, 44793 Bochum

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



so that -5^2 has always been interpreted to equal 25.


Absolutely not!

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


I've had lots of math and as far as I know
negation and subtraction are the same thing.


This statement is too vague to have meaning.


Check posts from Kevin O'Neil for a simple explanation


_______________________________________________



"fred" wrote in message ...
Do any of you SCI.MATH whizes want to weigh in on this?

MS Excel calculates "=-5^2" as 25, not as -25.
This is because 'negation' is handled first in Excel. (!?)
If you put a zero in the equation,
as in "=0-5^2", your answer changes to -25.

Is this in line with standard math rules?
Is negation different than subtraction?

I'm getting a lot of comments in the Excel NG
basically saying that "it's in the help section, so too bad".

I've had lots of math and as far as I know
negation and subtraction are the same thing.




"JE McGimpsey" wrote in message
...
That's clearly explained in the XL Help topic "The order in which
Microsoft Excel performs operations in formulas".

In all the math I've ever done, from grade school on, negation and
subtraction have been separate operations (often, but not always, using
separate symbols, such as a hyphen for negation and an n-dash for
subtraction), so that -5^2 has always been interpreted to equal 25.

Personally, I'd take it up with your consultant, assuming that he/she
was working on the Excel model. That problem should have been a piece of
cake for someone with even moderate expertise to identify, from the sign
change alone! There's no way you should have to pay for 20 hours of
troubleshooting (at my rates, at least).

In article ,
"fred" wrote:

I did in another sub-thread. Dana was familiar with it already.

If you lead off with a negative sign it uses the negative value inside
the
exponentiation.
So, instead of =-5^2 equalling -25 it equals 25.
but, =0-5^2 is calculated correctly as -25 even though it's
mathematically
the same.

"Rainer Rosenthal" wrote in message ...

"fred" wrote

MS Excel calculates "=-5^2" as 25, not as -25.

Is this in line with standard math rules?

No. If all were OK, they'd call this program

Excellent

but since it lacks something it's just called

Excel

--
Rainer Rosenthal, _____________________


__________________________________________________ _________________________

@@ . . . . . . WHISTLE . . . . . . @@

Stick mit triangles, dudenkopf.

Ari

BOULDERDASH!!!



Is this a suburb of Boulder, Colorado? If not, it should be.



This is a horrible bug in Excel



Anyone with a modicum of literacy must agree.

Ari
__________________________________________________ _______


"Stephen J. Herschkorn" wrote in message ...
fred wrote:

Do any of you SCI.MATH whizes want to weigh in on this?

MS Excel calculates "=-5^2" as 25, not as -25.
This is because 'negation' is handled first in Excel. (!?)
If you put a zero in the equation,
as in "=0-5^2", your answer changes to -25.

Is this in line with standard math rules?
Is negation different than subtraction?

I'm getting a lot of comments in the Excel NG
basically saying that "it's in the help section, so too bad".

I've had lots of math and as far as I know
negation and subtraction are the same thing.


Alan Beban wrote:

Well, this is an Excel forum, so one should expect a programming point
of view. But if you search on mathematical notation generally, I
think negation is viewed as a unary operator, while subtraction is
viewed as a binary operator; and the discussions are not much clearer
in that context. My own view, not as a mathematician, is that the
issue revolving around how to evaluate -1^2 depends on some *order of
precedence*, and is totally conventional as to negation and
exponientation.

draw a graph of y = -x^2, and what will you get?

Stating it is a documented convention is not a legitimate argument.
What if Microsoft(R) buried in its documentation that addition takes
precedence over multiplication? That the spell checker would always
change word "friend" to "freind"? That the sum function adds only every
other term? That using a "q" in one of its products would cause the
system to reboot? These effects would be just as valid by this logic.

I have sent this comment to Microsoft(R), though I expect no good to
come of it.


--
Stephen J. Herschkorn

"Aristotle Polonium" wrote

Stick mit triangles, dudenkopf.


| ' . |
| ' ' |
| . ' |
| |
| \ / | PLONK!
| -|- |
| (_) |
| A. P. |
|__________|


--
Rainer Rosenthal, _____________________
| _ | |
| (_) | Given A, P and a circle. Find B, C on the |
| A P | circle with P on BC and area(ABC)=maximum. |
|__________|___(Ingmar Rubin in de.sci.mathematik) ________|

Alan Beban wrote:

Stephen J. Herschkorn wrote:

Plot the curve y = -x^2.


I can't until someone gives me the convention to determine whether it
is to be interpreted as y=-(x)^2 or y=(-x)^2


Solve the equation -x^2 -18x + 5 = 0.


I can't until someone gives me the convention to determine whether it
is to be interpreted as -(x)^2 -18 + 5 = 0 or (-x)^2 -18x + 5 = 0

. . .

What is the value of -16^(1/4)?


I don't know until someone gives me the convention to determine
whether it is to be interpreted as -(16)^(1/4)) or ((-16)^(1/4))


I suspect you are being highly disingenous here. Either that, or you
must have had a terrible time getting through high-school level
algebra. The onus is on *you* to provide one reputable source, outside
of computer manuals, where these expressions are not interpreted as I
have been maintaining.

Interesting that you left ouf my example of the Gaussian (or error
function). Have you *ever* seen it written
with extra parentheses as in exp(-(t^2))?

--
Stephen J. Herschkorn

"Stephen J. Herschkorn" wrote:

fred wrote:

Do any of you SCI.MATH whizes want to weigh in on this?

MS Excel calculates "=-5^2" as 25, not as -25.
This is because 'negation' is handled first in Excel. (!?)
If you put a zero in the equation,
as in "=0-5^2", your answer changes to -25.

Is this in line with standard math rules?
Is negation different than subtraction?

I'm getting a lot of comments in the Excel NG
basically saying that "it's in the help section, so too bad".

I've had lots of math and as far as I know
negation and subtraction are the same thing.


Alan Beban wrote:

Well, this is an Excel forum, so one should expect a programming point
of view. But if you search on mathematical notation generally, I
think negation is viewed as a unary operator, while subtraction is
viewed as a binary operator; and the discussions are not much clearer
in that context. My own view, not as a mathematician, is that the
issue revolving around how to evaluate -1^2 depends on some *order of
precedence*, and is totally conventional as to negation and
exponientation.

BOULDERDASH!!! This is a horrible bug in Excel (whereof I was
previously unaware). It is very standard that exponentiaion takes
precedence over negation. Ask any semi-decent high school student to
draw a graph of y = -x^2, and what will you get?

Stating it is a documented convention is not a legitimate argument.
What if Microsoft(R) buried in its documentation that addition takes
precedence over multiplication? That the spell checker would always
change word "friend" to "freind"? That the sum function adds only every
other term? That using a "q" in one of its products would cause the
system to reboot? These effects would be just as valid by this logic.

I have sent this comment to Microsoft(R), though I expect no good to
come of it.

--
Stephen J. Herschkorn


I real enjoy some of the funny answers to that bug
(it is a well known one). What i enjoy most: some
may never looked inside a Math text book.

To keep it running: the following VBA code in Excel
2000 returns -4 as answer:

Sub tst()
MsgBox (-2 ^ 2)
End Sub

Which of course should be wrong if the spraed sheet
answer is right. Or am i wrong? Or is every funny
justification for that MS nonsense to be taken as a
correct argument only if i do not want to apply it
for the coding within Excel? Sorry for being childish.

--

use mail not nonail for mail

"Jerry W. Lewis" wrote...
Harlan Grove wrote:
"Jerry W. Lewis" wrote...
....
. . . I do not have access to a version of
Lotus, but I presume that they utilized the same order of operator
precedence . . .

And you'd be wrong! In 123, -3^2 returns -9.

Interesting and surprising. Thanks for the information.

Purely for the sake of argumentativeness, why surprising? It had to
return -9 or +9, and given the precedence in most programming
languages that provide both unary minus and exponentiation operators
-9 would be more common. Indeed, in VBA -3^2 returns -9.

Conformity with VisiCalc wasn't a good idea. VisiCalc was APL in
reverse - all left to right evaluation. For example, 2*3^4 = (2*3)^4
rather than 2*(3^4), and 2+3*4 = (2+3)*4 rather than 2+(3*4). Just as
in APL, and for the same reason, this is UNAMBIGUOUS.
Counterintuitive, perhaps, but unambiguous. If Excel also enforced
left to right evaluation with no operator precedence and only
parentheses to change evaluation order, then Excel could claim
consistency with VisiCalc, FWLIW. It doesn't, so Microsoft can't claim
conformity with either VisiCalc or 123 to support their choice of
operator precedence. They came up with this all on their own.

That Lotus chose to have 123 behave differently than VisiCalc was a
good thing, IMO. OTOH, Microsoft Excel is aking to COBOL rather than
FORTRAN. How nice!

That said, at least in the context of programming languages, in which
various spreadsheets' formulas are functional languages, there's no
consistent convention for operator precedence. Whether or not this
is/was a mistake is irrelevant to the extent that changing it would be
worse. In any case, this is *not* a bug in Excel, it's a feature
arising from a possibly obtuse design decision.

So far 4 different parsing approaches in spreadsheets and programming
languages have been described: APL's no precedence, strict right to
left; VisiCalc's no precedence, strict left to right; the mainstream's
(123, FORTRAN, BASIC including VBA, Perl, Python, etc.) exponentiation
taking higher precedence than negation; and the fringe's (Excel,
COBOL, apparently AppleScript, REXX and a few others) negation taking
higher precedence than exponentiation.

At the very least, no matter what may be correct in textbooks, there's
ample variety in programming languages, so anyone attempting to use
any programming language to perform calculations on a digital computer
had better check their programming language's operator precedence.
Bitching, whining and moaning about how this is wrong, wrong, terribly
wrong is wasted time, breath and effort.

Phil Carmody wrote...
....
He probably means that unary minus has a significantly higher
precedence
than subtraction, so much so that it has a strictly higher precedence
than at least one operator that one would commonly view as being of a
strictly higher precdence than subtraction.

No kidding! Gee, I'd never have guessed. How odd that this makes C
just like FORTRAN. I've been involved in a few back & forth
discussions with Alan, and I have little doubt he misconstrued C's ^
operator.

FWLIW, the precedence of unary minus/negation and multiplication,
division and remainder operators just doesn't matter. Considering C's
*,

(a * b) == (-a) * (-b) == -(a * (-b))
(-a * b) == (-a) * b == -(a * b)
(a * -b) == a * (-b) [b's - can't be parsed otherwise]
(-a * -b) == (-a) * (-b) == (-a * (-b)) == -(a * (-b))

Unary minus *could* have been given equal to or lower precedence than
*, / and %, and it wouldn't have mattered. I suspect the reason it's
higher is that it was supposed to be given the same as -- and ++, and
those are given higher precedence than *, / and %. Much, much easier
giving all unary operators the same precedence, so they'd be resolved
by the associativity rule alone.

Therefore there is a concrete example of an expression which is
interpretted
differently in C than it would be using people like you's
conventions.

First, what are my conventions? Second, if my favored conventions
exactly matched those of Excel, how would that matter vis-a-vis
negation/unary minus and *, / or %? While the machine may mechanically
parse unary minus earlier than *, / or %, the results would be the
same if it parsed unary minus after.

In C's case, the precedence inversion is with the multiplicative
family
of operators. e.g. compare C's interpretation of -2%3 as (-2)%3
rather than
-(2%3).

OK, it matters for remainder, but because there's residual ambiguity
about what (-2) % 3 should return. Is the answer -2 or +1? This is
also a matter of convention, and there are differences of opinion.
FWIW, C and Excel differ here, but it's due to the sign convention of
the remainder operator, not to operator precedence. In C, -2 % 3 ==
(-2) % 3 == -(2 % 3) == -2, but in Excel MOD(-2,3) == 1 != or <
-MOD(2,3) == -2. Note that because Excel uses a function for
remainder, unary minus's operator precedence is immaterial; the signs
of both arguments to the remainder function are necessarily obvious.

Stephen J. Herschkorn wrote:

I suspect you are being highly disingenous here. Either that, or you
must have had a terrible time getting through high-school level
algebra. The onus is on *you* to provide one reputable source, outside
of computer manuals, where these expressions are not interpreted as I
have been maintaining.

Whether I am being highly disingenuous and whether I had difficulty with
high-school level algebra are irrelevant. It seems to me self-evident
(accepting that ^2 is equivalent to a superscript 2) that -x^2, without
an adopted convention as to the order of precedence between negation and
exponentiation, can as readily be interpreted as -(x^2) or (-x)^2; that
is, without an adopted convention, it is ambiguous.

I'm simply asking for a citation to the order of preference convention
that you have indicated is universally accepted (outside of computer
programming). Unless you are claiming that its acceptance is (and
always has been?) so universal that it has never been authoritatively
declared--even in textbooks purporting to be the basis for teaching
unfamiliar students the fundamentals of the language to be used in
high-school algebra. Onus or not, I just find it odd that a thread can
have gone on this long with noone citing a source for a universally
accepted convention, other than assertions about broad usage.

In short, where can one learn about the order of precedence of negation
and exponentiation in mathematics without having to read a slew of
algebra books to measure up common usage.

Alan Beban

On Tue, 03 Aug 2004 14:26:52 -0700, Alan Beban wrote:
Stephen J. Herschkorn wrote:

I'm simply asking for a citation to the order of preference convention
that you have indicated is universally accepted (outside of computer
programming). Unless you are claiming that its acceptance is (and
always has been?) so universal that it has never been authoritatively
declared--even in textbooks purporting to be the basis for teaching
unfamiliar students the fundamentals of the language to be used in
high-school algebra. Onus or not, I just find it odd that a thread can
have gone on this long with noone citing a source for a universally
accepted convention, other than assertions about broad usage.

In short, where can one learn about the order of precedence of negation
and exponentiation in mathematics without having to read a slew of
algebra books to measure up common usage.

You evidently have not read my post in which I cited Lang on the
definition of polynomial rings.

You have seen a wealth of examples demonstrating that -x^2 is universally
understood to mean -(x^2), ranging from the application of the quadratic
formula to the definition of the normal density function, to the formulas
used for differentiation and antidifferentiation of polynomials.

There has been no evidence of a single example in any math book
demonstrating the opposite convention, despite repeated challenges to
produce such an example.


--
Dave Seaman
Judge Yohn's mistakes revealed in Mumia Abu-Jamal ruling.
<http://www.commoncouragepress.com/index.cfm?action=book&bookid=228

VB/VBA/Basic - different product, different rules.

VBA works with Excel as it works with other software packages. There are
many diffences in how they parse and interpret.

To ensure the highest probability of success, one must learn the rules
employed. When advertised behavior doesn't match assumed behavior, then who
is to blame? Personally, when I want to depend on some type of implicit
behavior, I either test it or consult the documentation (and then test it to
see if I understood it correctly).

--
Regards,
Tom Ogilvy



"Axel Vogt" wrote in message
...


"Stephen J. Herschkorn" wrote:

fred wrote:

Do any of you SCI.MATH whizes want to weigh in on this?

MS Excel calculates "=-5^2" as 25, not as -25.
This is because 'negation' is handled first in Excel. (!?)
If you put a zero in the equation,
as in "=0-5^2", your answer changes to -25.

Is this in line with standard math rules?
Is negation different than subtraction?

I'm getting a lot of comments in the Excel NG
basically saying that "it's in the help section, so too bad".

I've had lots of math and as far as I know
negation and subtraction are the same thing.


Alan Beban wrote:

Well, this is an Excel forum, so one should expect a programming point
of view. But if you search on mathematical notation generally, I
think negation is viewed as a unary operator, while subtraction is
viewed as a binary operator; and the discussions are not much clearer
in that context. My own view, not as a mathematician, is that the
issue revolving around how to evaluate -1^2 depends on some *order of
precedence*, and is totally conventional as to negation and
exponientation.

BOULDERDASH!!! This is a horrible bug in Excel (whereof I was
previously unaware). It is very standard that exponentiaion takes
precedence over negation. Ask any semi-decent high school student to
draw a graph of y = -x^2, and what will you get?

Stating it is a documented convention is not a legitimate argument.
What if Microsoft(R) buried in its documentation that addition takes
precedence over multiplication? That the spell checker would always
change word "friend" to "freind"? That the sum function adds only every
other term? That using a "q" in one of its products would cause the
system to reboot? These effects would be just as valid by this logic.

I have sent this comment to Microsoft(R), though I expect no good to
come of it.

--
Stephen J. Herschkorn


I real enjoy some of the funny answers to that bug
(it is a well known one). What i enjoy most: some
may never looked inside a Math text book.

To keep it running: the following VBA code in Excel
2000 returns -4 as answer:

Sub tst()
MsgBox (-2 ^ 2)
End Sub

Which of course should be wrong if the spraed sheet
answer is right. Or am i wrong? Or is every funny
justification for that MS nonsense to be taken as a
correct argument only if i do not want to apply it
for the coding within Excel? Sorry for being childish.

--

use mail not nonail for mail

"JE McGimpsey" wrote in message
...
In article ,
"Stephen J. Herschkorn" wrote:

Ask any semi-decent high school student to
draw a graph of y = -x^2, and what will you get?

If you asked someone competent, not just semi-decent, from my high
school, or college, or graduate school, you'd get the same curve as

y = x^2


I doubt that any U.S school, including yours, teaches a different convention
than that -z is the negation of z. With z=x^2 you have -x^2 is the negation
of x^2.

Perhaps you were thinking in terms of a plotting sequence:

y = -x
plot(y^2)

which indeed would plot a positive curve, because it is plotting (-x)^2,
which is NOT the same as -x^2.

KeithK

but it's a convention, not a law, so it wouldn't be surprising to see
the negation of

y = x^2

The flaw is in assuming that you have a lock on absolute truth, rather
than recognizing that when there's ambiguity you need context.

There's no ambiguity that negation and subtraction are different. The
fact that the typography is ambiguous means that you need to check your
assumptions.

Those who insist that a computer application must conform to *their*
standard have never programmed in APL.

In article <sYTPc.1888$Uh.1172@fed1read02, "KeithK"
wrote:

I doubt that any U.S school, including yours, teaches a different convention
-z is the negation of z.

Of course not. Nobody is disputing that...

With z=x^2 you have -x^2 is the negation of x^2

And of course you know that the second statement doesn't logically
follow from the first. Nor is it logically incorrect. It's simply an
assertion.

Doubt if you must, but the US high school I attended used the opposite
to the supposedly "universal" convention (though it was certainly
discussed as a convention, not "the universal truth", and I'm fluid
enough to accommodate whichever convention(s) are being used).

Since a significant portion of the curriculum for the Calc and DiffEQ
courses (algebra was 7th grade) included daily exercises on the material
using APL (as did my college math courses), that was, perhaps, a natural
consequence. It certainly emphasized the difference between negation and
subtraction, and the *formality* of order of precedence was made more
salient.

Typographically, the negation operator in our textbooks was different
than the subtraction operator, and parentheses were used when needed.

I no longer know what curriculum is used at that school, of course,
though at least one of the faculty members that taught me is still
there. Might be diverting to give her a call...

Stephen J. Herschkorn wrote:

as a follow up to Alan Beban's previous post, snippet:

SH
Plot the curve y = -x^2.
AB
I can't until someone gives me the convention to
determine whether it is to be interpreted as
y=-(x)^2 or y=(-x)^2


I suspect you are being highly disingenous here. Either
that, or you must have had a terrible time getting
through high-school level algebra. The onus is on *you*
to provide one reputable source, outside of computer
manuals, where these expressions are not interpreted as I
have been maintaining.


If you'll forgive me, and in the nicest way, you give the
impression of an academic stuck in narrow confinement. You
previously cited convention or notation that is in the
ever on going process of evolution. For readability,
brevity and generally understood it has until recently
served its purpose well. But a convention nonetheless, and
potentially ambiguous.

Alan's point is pertinent and helpful, you (and Dave
Seaman nearby) have missed it. The onus is not on him
to "to provide one reputable source", you may well be
correct that such does not exist. Surely, the point is
that the onus is on the user of a chosen app to explicitly
conform to "its" convention. If you don't like it
don't "chose" to use it. I would be very surprised if
there are any of today's maths students unaware of such
requirement, particularly with something as ubiquitous as
Excel.

My school days were long before the aid of a chip.
Fortunately I was taught to think like this:

+(+1) -(+1) +(-1)

1-1-1 is an abbreviation, partial evaluation or
conventional notation of the above, depending on your
point of view.

BTW, to conform with "another" Excel convention you need
to append the shorter version with an "=" before entering
into a cell. Optionally you may elect to switch to a
Lotus convention. It's one of those need to know things.

Regards,
Peter

PS, in another post Fred wrote along the lines that
negation and subtraction are the same. Maybe you can
correct me but I was taught negation may be considered as

A x (-1)
or, a double subtraction of itself as in
A - A - A

"Harlan Grove" wrote

in VBA -3^2 returns -9.

I agree with your attitude as stated below, but it sure seems like an
inconsistency when "Cells(1,1)=-3^2" in an Excel macro (VBA) makes the
cell-value -9, while typing "=-3^2" in the cell makes the cell-value 9.
It's the seeming *inconsistency* that's the problem.

At the very least, no matter what may be correct in textbooks, there's
ample variety in programming languages, so anyone attempting to use
any programming language to perform calculations on a digital computer
had better check their programming language's operator precedence.
Bitching, whining and moaning about how this is wrong, wrong, terribly
wrong is wasted time, breath and effort.

--r.e.s.

In article "Stephen J. Herschkorn" writes:
What is the value of -16^(1/4)?

The standard is not peculiar to those of us who are bemoaning the bug
here. It is as universal as spelling rules.

Perhaps, but it is spelled out nearly nowhere. Certainly not at school.

The only individuals
claiming this to be an ambiguity appear to be computer professionals
exclusively.

So what?

There are thousands of end users of this product who are
not programmers, nor should one need to be to use a spreadsheet. Nor
should they be expected to comb the documentation to discover this
peculiar "feature." This is a very flawed design.

Would you care to pay a penny for each user that thinks "1 + 2 * 3 = 9"?
I have even seen professional physicians make that error (they enter it
as such on their calculator and get that answer).

Mathematics does not dictate that '*' precedes '+'; that is only
convention. A convention that is (alas) not spelled out in most books.
The Dutch saying for the convention is "Meneer Van Dale Wacht Op Antwoord"
implying the following order:
1. M Machtsverheffen = powering
2. V Vermenigvuldiging = multiplication
3. D Deling = division
4. O Optellen = addition
5. A Aftrekken = subtraction.
Using that rule there are quite a few people that thing that
8 - 3 + 4 = 1
Can you understand why?
--
dik t. winter, cwi, kruislaan 413, 1098 sj amsterdam, nederland, +31205924131
home: bovenover 215, 1025 jn amsterdam, nederland; http://www.cwi.nl/~dik/

"r.e.s." wrote...
....
I agree with your attitude as stated below, but it sure seems like an
inconsistency when "Cells(1,1)=-3^2" in an Excel macro (VBA) makes the
cell-value -9, while typing "=-3^2" in the cell makes the cell-value 9.
It's the seeming *inconsistency* that's the problem.

Agreed, it's a problem. However, it was unavoidable. BASIC existed long
before any spreadsheet, and BASIC had established operator precedence
(mainstream). Excel existed before VBA, a dialect of BASIC, was grafted onto
it, and the nice people at Microsoft made a bad (but irrevocable in
practical terms) design decision about operator precedence. (Does anyone
know how Multiplan handled -3^2?)

When the two, Excel and VBA, were merged, the inconsistency became truly
exquisite. Excel also uses a sign convention in its financial functions,
something none of the non-Excel clone spreadsheets (so few these days) do or
did. Indeed, there are a lot of questionable design decisions in Excel, but
at this point in time you have to live with them or use something else.



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JE McGimpsey wrote in message ...
In article ,
Dave Seaman wrote:

By the definition of unary minus, -x^2 is the number such that
x^2 + (-x^2) = 0.

Without a citation to "the definition" you're using, this is not
persuasive.

Your statement begs the question of operator precedence, and using it to
argue for a particular order of precedence is therefore a tautology.

Any introductory course on abstract algebra. -x is the additive
inverse of x: the number such that x + (-x) = 0.

'cid 'ooh

"Harlan Grove" wrote in message ...
"Dik T. Winter" wrote...
...
When you look at the definition for rings, and stuff like that, you will
find that they are very different. If you look you will find that
a - b
is just shorthand for
a + b'.
where b' is the negative of b. So
0 - 5^2
is shorthand for
0 + (5^2)'
...

I don't recall exponentiation being covered in the development of either
rings or fields. Just addition and multiplication and their respective
inverses. Exponentiation wasn't brought up until polynomials were
introduced.


Didn't you cover group theory? Exponential notation is quite common
for multiplicative groups, and multiplicative notation is quite common
in additive groups. Example:

In (Z_7, +), x + x defines 2x, x + x + x defines 3x, etc. In (Z_7,
*), x*x defines x^2, x*x*x defines x^3, etc. That's how you're
justified to use things like the least integer property and modular
arithmetic when working with abstract groups.

'cid 'ooh

"Acid Pooh" wrote in message
om...
JE McGimpsey wrote in message
...
In article ,
Dave Seaman wrote:

By the definition of unary minus, -x^2 is the number such that
x^2 + (-x^2) = 0.

Without a citation to "the definition" you're using, this is not
persuasive.

Your statement begs the question of operator precedence, and using it to
argue for a particular order of precedence is therefore a tautology.

Any introductory course on abstract algebra. -x is the additive
inverse of x: the number such that x + (-x) = 0.

'cid 'ooh

I do believe that most posters in this thread know that. However, while the
meaning of -x may be clear, the meaning of -x^2 is not.

--

Vasant

"Kevin O'Neill" wrote...
....
The issue is far simpler than most other posts/responses seem to
indicate: it comes from the order-of-operation rules of arithmetic,
and "negation" should be regarded as multiplication under these rules
because, for any real number x

- x = (-1)x .
....

True, but also - x = 0 - x. Which is the one to use?

It is truly unfortunate that ANY computer languages or programs would not
conform to the order-of-operation rules.

Agreed, but more than a few don't. As stated elsewhere in this thread,
VisiCalc, the first widely used spreadsheet, used simple left-to-right
evaluation with no operator precedence. APL, on the other hand, uses simple
right-to-left evaluation with no operator precedence. COBOL and it seems
also REXX in addition to Excel use standard operator associativity and
operator precedence *except* for negation having higher precedence than
exponentiation. Finally, there are the mainstream languages that adopted, to
the extent possible, standard math/science textbook operator precedence.

It's unfortunate COBOL, REXX and Excel do this, but they do exist and they
can't be changed without breaking existing applications. Also, the existence
of at least 4 different arithmetic evaluation procedures in programming
languages (broadly defined to include spreadsheets as a functional variety)
should give pause to anyone attempting to use any of them to program.

When programming computers, know your tools.

Is there any reason why it works this way? What I figure is that someone a
long time ago (maybe the COBOL designers) saw -3 ** 2 or something similar
in FORTRAN and decided that this 'naturally' read as negative three (as a
term in and of itself) raised to the second power. They generalized from
this, and -x ** 2 would be negative x (also as a term in and of itself)
raised to the second power. It may go counter to textbook convention, but
from the point of view of nonmathematicians it's not a completely
unreasonable approach.



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