You have shown me the usefulness of the RootOf
expression for solving values of x for given
values of t and shown the plot of f(x) and it's
inverse g(t) thus x values can be determined for
t values without an expression other than the
RootOf expression and I guess an explicit
expression of x as a function of t is not
possible which is what I think Acer was trying
to tell me. One last question. Acer mentioned
the terms "closed form solution." Could someone
define that for me in easy to understand terms
with a simple example please. Thank you.

Sometimes RootOf solutions are more compact and
easy to produce compared to symbolic answers or
approximate answers, but they are of no value when
a symbolic or numerical approximation is needed.
In other words, when Maple returns a RootOf
solution and cannot back it up with allvalues()
answers the RootOf solution for all practical
purposes is meaningless. So the key is knowing
when Maple can back up RootOf solutions with
solutions containing the roots and when it can
not. That is what I am trying to find out.
You raise anothe question for me. By closed
form are you speaking of exact symbolic solutions
as opposed to numeric approximations and do you
call numeric approximations open forms?

Sometimes RootOf solutions are more compact and
easy to produce compared to symbolic answers or
approximate answers, but they are of no value when
a symbolic or numerical approximation is needed.
In other words, when Maple returns a RootOf
solution and cannot back it up with allvalues()
answers the RootOf solution for all practical
purposes is meaningless. So the key is knowing
when Maple can back up RootOf solutions with
solutions containing the roots and when it can
not. That is what I am trying to find out.
You raise anothe question for me. By closed
form are you speaking of exact symbolic solutions
as opposed to numeric approximations and do you
call numeric approximations open forms?

Awha, I had no idea that the labels at the right
side were just GUI creations. Thus the necessity
for the label as you have so clearly explained.
I really do appreciate the time and effort you
took to explain that to me. Now I have a polar
graphing question but I will post that separately.
Again, thanks.

Awha, I had no idea that the labels at the right
side were just GUI creations. Thus the necessity
for the label as you have so clearly explained.
I really do appreciate the time and effort you
took to explain that to me. Now I have a polar
graphing question but I will post that separately.
Again, thanks.

Jacques, problem 1 in not the same problem as
problem 2 so for your examle the answers are
different for different problems. That is not
the same as generating different labels for the
same problem worked twice but I do understand
what you are saying which I think is that there
needs to be some way of back tracking to a set
of answers when all roots are appropriate, which
apparently is what the label is for. Having said
that, for the user, the line labels at the right
side of the answer and in parentheses would seem
to be sufficient for the user. So I guess the
understanding I am seeking is that the RootOf labels
is used in lieu of index numbers when all
roots satisfy the equation, and the label= number
provides a unique identifier should one ever
need it. How does that sound?
are

Jacques, problem 1 in not the same problem as
problem 2 so for your examle the answers are
different for different problems. That is not
the same as generating different labels for the
same problem worked twice but I do understand
what you are saying which I think is that there
needs to be some way of back tracking to a set
of answers when all roots are appropriate, which
apparently is what the label is for. Having said
that, for the user, the line labels at the right
side of the answer and in parentheses would seem
to be sufficient for the user. So I guess the
understanding I am seeking is that the RootOf labels
is used in lieu of index numbers when all
roots satisfy the equation, and the label= number
provides a unique identifier should one ever
need it. How does that sound?
are

JacquesC, Although I am not interested in being
argumentative, I couldn't resist replying to
your questions. "is that so surprising? Of course ot.
Says who? Says I. I may not be a skilled programmer,
but mathmatics I know and if I were your boss, you
would agree or be out of a job. Moving on to the
real issues, I don't understand the purpose of
treating two identical RootOfs as independent nor
what that has to do with a the problem of
solve({x^2=2,y^2=2},{x,y})
not returning the correct number of solutions
and if somehow that is a required fix, why show
it to the user which serves no apparent perpose.
Just for fun, I replied to your post on the
previous thread.

JacquesC, Although I am not interested in being
argumentative, I couldn't resist replying to
your questions. "is that so surprising? Of course ot.
Says who? Says I. I may not be a skilled programmer,
but mathmatics I know and if I were your boss, you
would agree or be out of a job. Moving on to the
real issues, I don't understand the purpose of
treating two identical RootOfs as independent nor
what that has to do with a the problem of
solve({x^2=2,y^2=2},{x,y})
not returning the correct number of solutions
and if somehow that is a required fix, why show
it to the user which serves no apparent perpose.
Just for fun, I replied to your post on the
previous thread.

Dear JacquesC,
You might want to also teach your students to
keep their resume updated. I think that most
bosses will not tolerate such a hostile and
uncooperative additude. As a teacher you can
dictate such terms to your students but as an
employee in the corporate world you cheerfully
do what you are told to do or you get replaced
by someone that will, and when the boss says I
need you to fix this bug, it really doesn't
matter what the spec says. I might add that as
a Maple customer, I need the program to return
mathematically correct answers and don't care
what the spec says. If maple doesn't return
correct answers and some other program does, then
maple looses business and that is as it should bu.

Dear JacquesC,
You might want to also teach your students to
keep their resume updated. I think that most
bosses will not tolerate such a hostile and
uncooperative additude. As a teacher you can
dictate such terms to your students but as an
employee in the corporate world you cheerfully
do what you are told to do or you get replaced
by someone that will, and when the boss says I
need you to fix this bug, it really doesn't
matter what the spec says. I might add that as
a Maple customer, I need the program to return
mathematically correct answers and don't care
what the spec says. If maple doesn't return
correct answers and some other program does, then
maple looses business and that is as it should bu.

Correction, I meant to say plus or minus the
square root of three.

Correction, I meant to say plus or minus the
square root of three.

Still more info:
With a new worksheet, entering
solve(x=RootOf(_Z^2-3,label=_L2),x) returns the
correct answers of plus or minus three as previously
indicated. BUT entering
solve(x=RootOf(_Z^2-3,label=_Crap),x) does also!
So apparently if only one of the roots is the
correct answer, index= is used but if all roots
are the correct answer, label=whatever is used
as a device to fill in the field that could have
been used for an index number, again suggesting
that labels used in association with RootOf answers
are just a programming kluge that has no practical
mathematical purpose. Am I wrong about this Maple???

Still more info:
With a new worksheet, entering
solve(x=RootOf(_Z^2-3,label=_L2),x) returns the
correct answers of plus or minus three as previously
indicated. BUT entering
solve(x=RootOf(_Z^2-3,label=_Crap),x) does also!
So apparently if only one of the roots is the
correct answer, index= is used but if all roots
are the correct answer, label=whatever is used
as a device to fill in the field that could have
been used for an index number, again suggesting
that labels used in association with RootOf answers
are just a programming kluge that has no practical
mathematical purpose. Am I wrong about this Maple???