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???