mint is nice, for what it does, but it's does not help in the situations I described. I agree that it is nice to get mint's information about declared and unused variables and undeclared variables. But, I find mint of almost no use for SYNTAX checking. For managing large projects I, too, like the $include functionality. I wish it could be used within the user interface as well. Doug

---------------------------------------------------------------------
Douglas B. Meade
Math, USC, Columbia, SC 29208  E-mail: mailto:meade@math.sc.edu       
Phone:  (803) 777-6183         URL:    http://www.math.sc.edu/~meade/

Seriously. Thanks, Jacques, for your excellent explanation. While I, too, could have set a high printlevel I could not have made as much sense as you did from the output. This is about what I expected. I saw that Maple made the equation homogeneous (moved the infinity to the left as a constant). I could then see that working with infinity as a coefficient in the polynomial was going to lead to some interesting results. While it is disappointing to learn about all of the places that Maple trips up on this, it is comforting to be able to "look under the hood" in times like this. Thanks again, Jacques! Doug

---------------------------------------------------------------------
Douglas B. Meade
Math, USC, Columbia, SC 29208  E-mail: mailto:meade@math.sc.edu       
Phone:  (803) 777-6183         URL:    http://www.math.sc.edu/~meade/

Seriously. Thanks, Jacques, for your excellent explanation. While I, too, could have set a high printlevel I could not have made as much sense as you did from the output. This is about what I expected. I saw that Maple made the equation homogeneous (moved the infinity to the left as a constant). I could then see that working with infinity as a coefficient in the polynomial was going to lead to some interesting results. While it is disappointing to learn about all of the places that Maple trips up on this, it is comforting to be able to "look under the hood" in times like this. Thanks again, Jacques! Doug

---------------------------------------------------------------------
Douglas B. Meade
Math, USC, Columbia, SC 29208  E-mail: mailto:meade@math.sc.edu       
Phone:  (803) 777-6183         URL:    http://www.math.sc.edu/~meade/

I agree with Jacques that the optimal response to the command solve( eq=infinity, x ); should be that this is a mathematically meaningless request. I agree that asking about discontinuities, or poles, or other types of singularities is much more meangingful. Still, the question remains, what exactly is Maple doing when it tries to solve an equation that involves infinity? Here is some trace output from solve [see note below]:

debug( solve ):
solve( (x-1)/expand((x^2-1)*(x-2))=infinity, x );
{--> enter solve, args = `/`(`*`(`+`(x, `-`(1))), `*`(`+`(`*`(`^`(x, 3)), `-`(`*`(2, `*`(`^`(x, 2)))), `-`(x), 2))) = infinity, x
                      [      x - 1                    ]
                      [----------------- = infinity, x]
                      [ 3      2                      ]
                      [x  - 2 x  - x + 2              ]
                                    false
                                    false
                                  infinity
                             _SolutionsMayBeLost
                                     {x}
                                    false
                                     {}
                                     {}
                                     {}
                      [      x - 1                    ]
                      [----------------- = infinity, x]
                      [ 3      2                      ]
                      [x  - 2 x  - x + 2              ]
                              x - 1                 
                        ----------------- = infinity
                         3      2                   
                        x  - 2 x  - x + 2           
                              x - 1                 
                        ----------------- - infinity
                         3      2                   
                        x  - 2 x  - x + 2           
                                      x
                             solve/rec/remember
proc(oeqns, ineqs, vars)  ...  end;
                                    false
                                    true
x -> evalb(normal(SolveTools:-CancelInverses(x)) = 0)
                             [{x = 1}, {x = -1}]
                             [{x = 1}, {x = -1}]
                             [{x = 1}, {x = -1}]
                             [{x = 1}, {x = -1}]
                             [{x = 1}, {x = -1}]
                             [{x = 1}, {x = -1}]
                             [{x = 1}, {x = -1}]
                             [{x = 1}, {x = -1}]
                                      x
<-- exit solve (now at top level) = 1, 1}
                                    1, -1

While it was not my original intent, I think this is related to my recent posting about the fact that infinity is considered a real-valued constant (realcons) by Maple. NOTE: Has anyone else noticed that output copied from a Maple (11.01) worksheet cannot be copied to other applications. In this example, each line of output produced by debugging solve appears as an assignment in the Maple worksheet, but only the RHS of the assignment can be copied. I find this frustrating! Doug

---------------------------------------------------------------------
Douglas B. Meade
Math, USC, Columbia, SC 29208  E-mail: mailto:meade@math.sc.edu       
Phone:  (803) 777-6183         URL:    http://www.math.sc.edu/~meade/

I agree with Jacques that the optimal response to the command solve( eq=infinity, x ); should be that this is a mathematically meaningless request. I agree that asking about discontinuities, or poles, or other types of singularities is much more meangingful. Still, the question remains, what exactly is Maple doing when it tries to solve an equation that involves infinity? Here is some trace output from solve [see note below]:

debug( solve ):
solve( (x-1)/expand((x^2-1)*(x-2))=infinity, x );
{--> enter solve, args = `/`(`*`(`+`(x, `-`(1))), `*`(`+`(`*`(`^`(x, 3)), `-`(`*`(2, `*`(`^`(x, 2)))), `-`(x), 2))) = infinity, x
                      [      x - 1                    ]
                      [----------------- = infinity, x]
                      [ 3      2                      ]
                      [x  - 2 x  - x + 2              ]
                                    false
                                    false
                                  infinity
                             _SolutionsMayBeLost
                                     {x}
                                    false
                                     {}
                                     {}
                                     {}
                      [      x - 1                    ]
                      [----------------- = infinity, x]
                      [ 3      2                      ]
                      [x  - 2 x  - x + 2              ]
                              x - 1                 
                        ----------------- = infinity
                         3      2                   
                        x  - 2 x  - x + 2           
                              x - 1                 
                        ----------------- - infinity
                         3      2                   
                        x  - 2 x  - x + 2           
                                      x
                             solve/rec/remember
proc(oeqns, ineqs, vars)  ...  end;
                                    false
                                    true
x -> evalb(normal(SolveTools:-CancelInverses(x)) = 0)
                             [{x = 1}, {x = -1}]
                             [{x = 1}, {x = -1}]
                             [{x = 1}, {x = -1}]
                             [{x = 1}, {x = -1}]
                             [{x = 1}, {x = -1}]
                             [{x = 1}, {x = -1}]
                             [{x = 1}, {x = -1}]
                             [{x = 1}, {x = -1}]
                                      x
<-- exit solve (now at top level) = 1, 1}
                                    1, -1

While it was not my original intent, I think this is related to my recent posting about the fact that infinity is considered a real-valued constant (realcons) by Maple. NOTE: Has anyone else noticed that output copied from a Maple (11.01) worksheet cannot be copied to other applications. In this example, each line of output produced by debugging solve appears as an assignment in the Maple worksheet, but only the RHS of the assignment can be copied. I find this frustrating! Doug

---------------------------------------------------------------------
Douglas B. Meade
Math, USC, Columbia, SC 29208  E-mail: mailto:meade@math.sc.edu       
Phone:  (803) 777-6183         URL:    http://www.math.sc.edu/~meade/

I don't understand your request. The help for seq (?seq) does include examples with both {} and []. Moreover, both ?[] and ?list give information about forming lists. You do have to have some idea of what you are trying to do before you would come up with any of these. I don't believe it's unreasonable to expect a user to come up with at least one of these. You can't expect any system to provide a meaningful response to the question: Tell me what I need to know. Doug

---------------------------------------------------------------------
Douglas B. Meade
Math, USC, Columbia, SC 29208  E-mail: mailto:meade@math.sc.edu       
Phone:  (803) 777-6183         URL:    http://www.math.sc.edu/~meade/

I can see some problems with your code, but need more information to completely resolve your problems. The main information I need is the definition of eqn. From the error message you included it appears to me that you did not execute the definition of plot1. The only outright error I see in your code is that plot2 is not a plot, it's just a function. You probably want something like:

plot2 := plot( 1/2*x^2, x=-0.25..0.25 ):

Here's a template for you to use.

restart;
with( plots ):
with( DEtools ):
eqn := diff(y(x),x)=y(x);  # replace with the correct ODE
plot1 := phaseportrait(eqn, y(x), x=-0.25..0.25,
                       [[y(-1/2)=2],[y(3/2)=0]],
                       titlefont=[TIMES,ROMAN,18],
                       title=`Sec 2.1 #17`,
                       color=grey, linecolor=[red,blue]):
plot2 := plot( (1/2)*x^2, x=-0.25..0.25, color=green ):
display([plot1,plot2]);

I hope this is helpful. Doug

---------------------------------------------------------------------
Douglas B. Meade
Math, USC, Columbia, SC 29208  E-mail: mailto:meade@math.sc.edu       
Phone:  (803) 777-6183         URL:    http://www.math.sc.edu/~meade/

The discussion of differing interpretations has been interesting. Let me add another dimension to this. Mathematically, infinity is not a real number. It's used to represent the "endpoints" of the real line. Also, recall, tha the set of real numbers is both open and closed. Contrast this with Maple's response to the following:

is( infinity, realcons );
              true

This response is clearly documented in the help pages (?type,realcons). Moreover, I have used this feature on many occasions. (There have been a few times when I wished Maple did know infinity is not a real number, but there are other ways to deal with this.) My point in making this observation is that it is important to look at the definitions and not to transfer meanings from other (albeit related) uses. Doug

---------------------------------------------------------------------
Douglas B. Meade
Math, USC, Columbia, SC 29208  E-mail: mailto:meade@math.sc.edu       
Phone:  (803) 777-6183         URL:    http://www.math.sc.edu/~meade/

The discussion of differing interpretations has been interesting. Let me add another dimension to this. Mathematically, infinity is not a real number. It's used to represent the "endpoints" of the real line. Also, recall, tha the set of real numbers is both open and closed. Contrast this with Maple's response to the following:

is( infinity, realcons );
              true

This response is clearly documented in the help pages (?type,realcons). Moreover, I have used this feature on many occasions. (There have been a few times when I wished Maple did know infinity is not a real number, but there are other ways to deal with this.) My point in making this observation is that it is important to look at the definitions and not to transfer meanings from other (albeit related) uses. Doug

---------------------------------------------------------------------
Douglas B. Meade
Math, USC, Columbia, SC 29208  E-mail: mailto:meade@math.sc.edu       
Phone:  (803) 777-6183         URL:    http://www.math.sc.edu/~meade/

Due to a recent problem with Firefox, I am using IE to access MaplePrimes. Even after refreshing (repeatedly), I still have the problem with the input box being shifted to the right. (This means I'm typing about half of each row blind. I can see what I actually typed by previewing, but then it's a challenge to fix any errors by counting keystrokes.) I'll add that when this page is first loaded the input box does appear where it should. But, only for a flash. The page is immediately redrawn and the box shifts to the right.) I hope this extra information will be useful when fixing this problem once and forall. Doug P.S. Congratulations, Will, on your recent entry to married life.

---------------------------------------------------------------------
Douglas B. Meade
Math, USC, Columbia, SC 29208  E-mail: mailto:meade@math.sc.edu       
Phone:  (803) 777-6183         URL:    http://www.math.sc.edu/~meade/

Curious, Please re-read the earlier responses to your question. When you enter (with or without the explicit multiplication)

int( sec^2*x, x );

Maple sees the integrand as a constant times x, for which a correct antiderivative is one-half the constant times x-squared. The integrand needs to be the square of the value of the secant function evaluated at x:

int( sec(x)^2, x );

I know this input is slightly different from how the problem is typically typeset. The reality is that visual appearance does not always carry any mathematical meaning. Maple, like any software, has to be able to infer a meaning from the input. It is essential that users provide input that conveys mathematical content. Doug

---------------------------------------------------------------------
Douglas B. Meade
Math, USC, Columbia, SC 29208  E-mail: mailto:meade@math.sc.edu       
Phone:  (803) 777-6183         URL:    http://www.math.sc.edu/~meade/

Curious, Please re-read the earlier responses to your question. When you enter (with or without the explicit multiplication)

int( sec^2*x, x );

Maple sees the integrand as a constant times x, for which a correct antiderivative is one-half the constant times x-squared. The integrand needs to be the square of the value of the secant function evaluated at x:

int( sec(x)^2, x );

I know this input is slightly different from how the problem is typically typeset. The reality is that visual appearance does not always carry any mathematical meaning. Maple, like any software, has to be able to infer a meaning from the input. It is essential that users provide input that conveys mathematical content. Doug

---------------------------------------------------------------------
Douglas B. Meade
Math, USC, Columbia, SC 29208  E-mail: mailto:meade@math.sc.edu       
Phone:  (803) 777-6183         URL:    http://www.math.sc.edu/~meade/

Pat, I'm glad my responses have been useful for you. I remember how much I learned from reading the postings of the masters on the USENET's sci.math.symbolic newsgroup. Before long, if it's not already happened, I'll bet you will start to see some questions posted on MaplePrimes that you can answer. When you see a chance to add to an exchange, do not hesitate to offer your input. Your questions have been well-worded and nicely reduced to the real essence of the issue at hand. My responses have come from my own experiences, so it's not a problem to respond. To not respond would be tantamount to being selfish with my knowledge. Thanks again for the kind words. Doug

---------------------------------------------------------------------
Douglas B. Meade
Math, USC, Columbia, SC 29208  E-mail: mailto:meade@math.sc.edu       
Phone:  (803) 777-6183         URL:    http://www.math.sc.edu/~meade/

Pat, I'm glad my responses have been useful for you. I remember how much I learned from reading the postings of the masters on the USENET's sci.math.symbolic newsgroup. Before long, if it's not already happened, I'll bet you will start to see some questions posted on MaplePrimes that you can answer. When you see a chance to add to an exchange, do not hesitate to offer your input. Your questions have been well-worded and nicely reduced to the real essence of the issue at hand. My responses have come from my own experiences, so it's not a problem to respond. To not respond would be tantamount to being selfish with my knowledge. Thanks again for the kind words. Doug

---------------------------------------------------------------------
Douglas B. Meade
Math, USC, Columbia, SC 29208  E-mail: mailto:meade@math.sc.edu       
Phone:  (803) 777-6183         URL:    http://www.math.sc.edu/~meade/

Alex, Have you been able to set a system default of Maple Input for Maple 11 (11.01, actually) on a network? My system administrators tell me these choices are stored on a users profile locally. This means users have to reset this choice on each computer they use on our network. Prior to Maple 11, this was possible. Other threads on MaplePrimes have discussed this, with the general conclusion that it is not possible. I would be very happy to learn that this can be done NOW and that I don't have to wait for a future release. Doug

---------------------------------------------------------------------
Douglas B. Meade
Math, USC, Columbia, SC 29208  E-mail: mailto:meade@math.sc.edu       
Phone:  (803) 777-6183         URL:    http://www.math.sc.edu/~meade/