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These are questions asked by DJJerome1976

I am trying to customize the Venn Diagram generated by the VennDiagram command in the Statistics package. I would like to be able to shade just any of the regions. For example, if only two sets (A and B) are being displayed, I would like to be able to shade just A, just B, both A and B, or both A and/or B. Also, is it possible to have a rectangle surrounding the circles which represents the universal set? Could the circles be labeled with the letter "A" or "B" to be able to identify each set?

I am working with lines in 2- and 3-space, defined parametrically. In 2-space, how would I go about using Maple to determine if the lines are identical or parallel. For example, if L1:=<2-4*t,5+6*t>, L2:=<-6-12t,17+18t>, L3:=<20t,-30t>, I would like a procedure that would be able to determine that L1 and L2 are identical lines, and that L1 and L3 are parallel lines. Similarly, it would be able to determine if lines in 3-space, are identical, parallel, or skew. 


I was looking into the geometry package, but I don't think it allows me to do this.



I am trying to check to see if two equations are equivalent, subject to rearrangment and scalar multiplication. For example, I would to have a procedure that would determine that each of the following equations are the equivalent:

(a) (1/2)*y*exp(-y)+2*y^3 - x*ln(x) +x^2 = 10
(b) (1/2)*y*exp(-y)+2*y^3 +x^2 = 10 + x*ln(x)

(c) y*exp(-y)+4*y^3 - 2*x*ln(x) +2*x^2 = 20

Is there a systematic way to go about doing this? Thanks!

I'm doing some work with undirected and directed graphs, and I'm needing to find examples of longest paths and longest cycles.  How may this be done in Maple?


I am using A:=LinearAlgebra:-RandomMatrix(10,10,generator=-10..10) to generate a random matrix. How may I specify that every row of A has at least three non-zero entries? 


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