dharr

Dr. David Harrington

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17 years, 146 days
University of Victoria
Professor or university staff
Victoria, British Columbia, Canada

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I am a professor of chemistry at the University of Victoria, BC, Canada, where my research areas are electrochemistry and surface science. I have been a user of Maple since about 1990.

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These are answers submitted by dharr

I'm not sure exactly what you are surprised about, since you don't say. The calculated dot product and its rationalized form are correct for the dot product assuming the variables are real. Perhaps you wanted an error message because the product isn't conformable and want the dot only to work for a row vector times a column vector. In regular maple, that does work <a,b,c>^%T.<d,e,f> gives a*d+b*c+c*f, but Maple assumes that for a non conformable product, you want a dot product and gives you that. I would have preferred a more strict adherance to confomability, but I think Maple is trying to help you out here.

The notation T^n does not iterate the function n times; for this you need T@@n. You got the right first spiral only by coincidence, because they are the same for z=1. You will have to do the iterates of the inverse function separately. For the double spirals I'm not sure about the z value, so I'll let you fix it up.

Indras_pearls_spirals.mw

Your Inits contains occurrences of "r", which need to be replaced by values.

If I understand you correctly, you want something unique to happen the first time the worksheet runs and something different the next time it is rerun with !!!. The following code does this:

if not assigned(k) then
    k:=1  # only run the first time
else
    k:=k+1;
end if:
k;

k increments each time the worksheet is run with !!!. To reset use the restart icon.

pointplot will do this, e.g., plots:-pointplot([[1,5],[2,3]]);

or just plot with style= point: plot([[1,5],[2,3]],style=point);

The help page for this mentions this variation, and since it mentions the introduction of the maxroots option in Maple 15, it has probably been around since before then

You asked "What is name of the integration technique that Maple is using in the first step?". This is usually just called change of variables, or sometimes integration by substitution, see wikipedia.

Edit: Your worksheet has both epsilon and varepsilon; this is the main problem.

I only partially understand the geometry you want. I find it easier to work from more negative to more positive x values. Note that the piecewise conditions work like successive else-if clauses.

piecewise.mw

 

evalc puts things in th a+I*b form assuming all variables are real.

 

Edit: normal will then put things over a common denominator. You can then use evalc on the numerator if you want to pretty it up.

evalc.mw

The infinity norm is the maximum of the elements, so if you do this on the difference of your two vectors, you get what you want.

Download Norm.mw

 

If you leave the epsilon[i] quantities unspecified you can solve the equations in about 300 s on my machine, but the answer(s) has a length of 10350686, i.e., too complicated to work with unless you just want numerical values. Perhaps there is some structure to that...

In principle, you could the substitute the complicated epsilon[i] quantities into the answer, but that makes the whole thing even more complicated.

test2.mw

Edit: there is only one answer, but has(ans,RootOf) returns true, so there is likely not a fully analytical solution, and only a numerical solution is feasible.

I'm not a mac user so this might not apply, but a new worksheet and saved one are in different folders. So a full path instead of "/VLA/library/" might work.

You probably know this already, but if you translate the problem to run from x=0 to x=L, then dsolve directly gives all the solutions, where they are all sine functions.

PIB.mw

The missing half of the solutions from eq (8), {A=0, B=B, k=Pi*(1+2*_Z1)/L}, are the cosine solutions that the parametric solver finds. The parametric solver only deals with polynomial equations, so I think it is treating cos(k*L/2) as a single variable. Then you had to use solve to get the k values. 

The "bug" is that solve didn't find these cosine solutions when allsolutions is specified. The help for allsolutions says "Return more solutions for non-algebraic equations" [my bold], so I think it was using a different algorithm, and did not view it as a two-step problem: polynonial solve while freezing cos(k*L/2) and sin(k*L/2), and then solving these for k.

Not really sure what you want, even after your answer to @Joe Riel. Look at the help for workbook - it can hold multiple worksheets and other sorts of data.

I think since Colours is not an export of the module, it can only be accessed by a procedure (export of) the module. A simple example is attached.

Edit: kernelopts(opaquemodules=false) can override this behaviour

module.mw

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