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These are questions asked by ctomkins

I am solving a constrained maximization problem using the Lagrangian and getting back an empty set of solutions, i.e.: solns_LSW:= How do I go about diagnosing why Maple is having difficulty finding solutions? (Once I know that, I would of course also like to know how, if possible, to change the set-up so that Maple might actually find the solution(s)!) I can see that the Lagrangian becomes non-concave for cases where lambda2>p (p is one of the variables I am solving for: there are two, s and p -- see attached worksheet). This would clearly be the case for, say, p=0 optimal (which I have reason to believe it is, based on some numerical simulations I ran).
Hi -- I am trying to plot a (fairly basic) procedure, Q_plot, which defines a piecewise function (three pieces). Q_plot evaluates no problem at the command prompt for all three regions -- but only plots for two of the three regions. Resulting in a big hole in the middle of my graph! Hmm? I've uploaded a copy of the worksheet, with the plot (and the aformentioned hole in the middle). Thanks Here's the link to the worksheet: http://www.mapleprimes.com/files/5475_Diagnostic-proc-Q.mw
Hi -- I want to check the sign of a polynomial. Here's the polynomial expression (1/16)*(9*s^5-3*s^4*m-34*s^4*pa+12*s^3*m*pa+46*s^3*pa^2-18*s^2*m*pa^2-24*s^2*pa^3 +12*s*m*pa^3+s*pa^4-3*m*pa^4+2*pa^5-16*s^4+64*s^3*pa -96*s^2*pa^2+64*s*pa^3-16*pa^4+16*p^2*s+48*p^2*m-64*p^2*pa)/(s-pa)^4 and here's the parameterization: pa>s and pa>m. Generally checking the sign of the polynomial involves checking the signs of the factors...so, I'd like to factor the above expression. I haven't worked with "factor" much in Maple. Applying it as just factor(expr) with expr equal to the above expression does nothing. So not sure the best approach.
How do I get Maple 11 to show the symbol instead of the text when using textplot and labels=[ ] in plot? For example, I want my labels to have the symbol lambda, but when I try labels=[\lambda,x] I just get the text "lambda." Likewise, I'd like to be able to plot text with subscripts, i.e. text1:=textplot(0.6,0.8,"p_gt^*") gives me that exact text on the graph when what I really want to show up is the label p* with the subscript "gt." Thanks!
I am getting such odd results from plotting a procedure that I call Q_opt1. When I plot the procedure at a specified set of points, the values produced and shown by plot look correct, i.e. my procedure Q_opt is *decreasing* in the parameter s.

This can be seen in the link below to the plot Q_opt1_Diagnostic1, in which I plotted the following:

>plot([Q_opt(0.4,0.01,0.5),Q_opt(0.3,0.01,0.5),Q_opt(0.2,0.01,0.5),Q_opt(0.1,0.01,0.5)],s=0..0.5,legend=["Actual value s=0.4","Actual value s=0.3","Actual value s=0.2","Actual value s=0.1"]);

HOWEVER, when I plot the procedure with s as the input variable in plot, i.e.
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