Annonymouse

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These are replies submitted by Annonymouse

@Carl Love yes, those assuptions are valid.

@Kitonum 

I get an error for line, does it belong to a package? (i also get an error when i try and take it from plots or geometry)

@Annonymouse I had started a new question, as i had worked on the problem for much of a day, and thought i could ask a much better question; whereas if I edit this, it makes everythign look confusing to new readers, either by making the replies at odds with the innitial question, or making the new reader read through the replies.

I'm happy to change my behaviour, would you rather I edit the question, or post extra information as a reply?

@Annonymouse aa_problem_MWE.mw

after quite a few hours of work I can now show you that the solution for t>1000 (the point where the variables become continuous rather than smooth) dsolve seems to give different results if its run from t=0, or if its run using variables at t=1000 as innitial conditions a second time.

So it appears to me that something weird is happening at the discontinuity. Once i get my head better around the problem i'll turn it into a seperate question - because when i asked this i still wasn't sure what i was asking!

@Preben Alsholm these equations don't behave like this in numerical integration methods outside maple - and the bizare behaviour seems to orignate at the place where they are continuous rather than smooth, the point that you've picked is after that point (t=1000). So its probably a maple issue. 

 

Thanks anyway

I was able to make it work by using Lists! (Solve_Problems_MWE2.mw)

Thanks

Also is there a simple way of finding the indexes for which AllNonZero returns true?

Download Solve_Problems_MWE2.mw

 

 

@acer 

Your skills with maple are too far ahead of mine for me to really fully get what your doing (i'm going to start googling your commands) but I can certianly show you my shortest solution and how i got it

calling the expresion eq
I observed that most of it was aquotient which i wanted to simplify, and a small part of it wasn't, so I simplified eq-small part and then added small part:

(simplify(rhs(eq)-(-2*k[d1]-2*k[d2])*B[2211], size)/(B[2211]*(k[d1]+k[d2]))+(-(2*(k[d1]+k[d2]))*B[2211])*(1/(B[2211]*(k[d1]+k[d2]))))*B[2211]*(k[d1]+k[d2])

this gives

(2*beta*(alpha*R[b]*(beta*k[a2]+k[d1])*k[a1]^2+(alpha*k[a2]^2*beta*R[b]+(k[d1]+k[d2])*(2*alpha*R[b]+beta)*k[a2]+2*k[d1]^2+k[d1]*k[d2])*k[a1]+k[a2]*k[d2]*(alpha*R[b]*k[a2]+k[d1]+2*k[d2]))/(alpha*beta*R[b]*(beta*k[a2]+k[d1]+k[d2])*k[a1]^2+(beta^2*alpha*R[b]*k[a2]^2+beta*(k[d1]+k[d2])*(3*alpha*R[b]+beta)*k[a2]+(2*(((1/2)*alpha*R[b]+beta)*k[d1]+(1/2)*k[d2]*(2*alpha*R[b]+beta)))*(k[d1]+k[d2]))*k[a1]+(k[d1]+k[d2])*(alpha*R[b]*k[a2]+k[d1]+2*k[d2])*(beta*k[a2]+2*k[d1]+k[d2]))-2)*B[2211]*(k[d1]+k[d2])

which has length 899
and your function F gives a value of 147

playing around with the numerator by hand (i am still more confident with paper than maple) i was able to find a form of it that I was happy with :

2*k[a1]*k[a2]*beta((k[a1]+k[a2])*R[b]*alpha+k[d1]+k[d2])^2+2*beta*(sum(k[ai]*k[di]((2*k[a1]-k[ai]+2*k[a2])*R[b]*alpha+k[d1]+k[di]+k[d2]), i = 1 .. 2))

and of the denominator:

 ((k[a1]^ + k[a2]^) R[b] alpha+ k[d1]+ k[d2])k[a1] k[a2]^ beta^2+(k[d1]+k[d2])*((k[a1]^2 +3 k[a1] k[a2] +k[a2]^2 k[d1]) R[b] alpha+(k[a1] (2 k[d1]^+ k[d2]^)+k[a2]( k[d1]^+2 k[d2]^)beta+((k[a1] (k[d1]^+2 k[d2]^)+k[a2](2 k[d1]^+k[d2]^)) R[b] alpha+(k[d1]+2 k[d2]) (k[d2]+2 k[d1]) ):

Visually they look shorter- I havent checked them yet with maple (I am not yet a computer whizz).
My intuition is that the equation should be symmetric in the sense that if all the 1s and 2s were swapped the expression would be the same. I feel like there should be a way of using that to help maple but I haven't worked it out yet.

:) thanks again for your responce!

@Preben Alsholm Thats useful - but it still puts everything over a single denominator which is unhelpful as there are some very simple terms outside the quotients that it is merging into the quotient, and making more complicated

I've moved over to plotting the results as transparent surfaces rather than wireframes, and setting them as different colours which eliminates the problem,although is less prety

@tomleslie 

I should be C[T] i had used it to represent an input variable before i realised this caused problems in maple.

Your code looks good - although you still havent succeeded in drawing the curve at the intersection. Thats also what i cant seem to do.

@tomleslie 

 

This doesn't seem to be mentioned on either help page.

Export puts this proc into an area that doesn't seem to show up when the document is compiled.

\mapleinline{inert}{2d}{lieDer := proc (H, F) local N, V, vars; N := nops(F); vars := [seq(x[t], t = 1 .. N)]; V := map(proc (a, b) options operator, arrow; diff(b, a) end proc, vars, H); DotProduct(Vector(F), Vector(V), conjugate = false) end proc; -1}{\[\displaystyle \]}

How do i make this show up?

@acer 

Thanks so much for your help!

is there any way to italicise the y?
(I want it to fit in with a Latex document)

@acer 

lowast looks perfect on my windows machine! You've completely solved my problem, thanks!

@acer
thanks,that was genuinely helpful; When i do keneralopts(version) it tells me it is the version before yours:

Maple 2015.1, X86 64 WINDOWS, Jul 23 2015, Build ID 1059989

I'll look at upgrading.

How would you include subscripts in the labels? currently i cant see a way of labeling something as y[1]* in the sense of y with a subscript of 1 and an asterisk.

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