dharr

Dr. David Harrington

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20 years, 335 days
University of Victoria
Professor or university staff
Victoria, British Columbia, Canada

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I am a retired professor of chemistry at the University of Victoria, BC, Canada. 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

indets(eq[1],name); gives the indeterminates: {a, b, c, d, HRa[1, 0], SR[1, 1], W[1, 0], ga[1, 0]}

If you add "assuming t>0", then you will get just (+) infinity, which seems to the the correct answer since the denominator approaches zero as s approaches t. This assumes you wanted s real - not sure what answer you expected here.

_z1 is a dummy integration variable. You asked for an analytic solution (the default) and it contains an integral that can't be evaluated analytically.

Probably you only want an numerical solution, so add the numeric option to dsolve. Then you can use the returned procedure to find values of Vc at different times, or use odeplot to look at the solution as a function of time.

How about putting the whole thing in a procedure? Then your "quitting the search" can be

return i[1], ...i[10];

Put the cursor in the execution group, then use edit/select execution group (or ctrl-alt-shift-E) to select the group. Then you can copy it. This copies the input and output.

In Maple 2015, you can fudge it like:

with(plots):with(plottools):

p1:=display(parallelepiped([0, 0, 1], [0, 2, 2], [2, 2, 2], transparency=0.5),shading=xyz):

p2:=display(parallelepiped([0, 0, 1], [0, 1, 1], [1, 1, 1], transparency=0.5),shading=zhue):

display([p1,p2]);

 

(I think in earlier versions, color functions and shading schemes weren't available for all plot structures, like the POLYGON structure that parallelopiped produces. So I think the warning from plottools is perhaps a leftover from earlier versions, and I'm not sure this workaround can solve the problem in Maple 15)

Set each of your plots into a variable, then combine them with plots:-display. You may want to add extra options to the display that override the ones in the individual plots:

p1:=plots:-pointplot([seq([x,0],x=[-sqrt(16),-2,-3/4,0,exp(1),Pi])],view=[-4..4,0..0.01],symbolsize=20,symbol=solidcircle,colour=blue,scaling=constrained);

p2:=plots:-textplot([-4,.7,typeset("-sqr 16")],font=[TIMES,BOLD,12]);

plots:-display(p1,p2,view=[-4..4,0..1],scaling=constrained);

Use Digits:=40; before plotting. I'm guessing you need more digits to combine the very large 10^1390 with the very small exp(-1.597924898*2000)

I'd select the text, copy it and then paste in into a text file such as code.txt. Then read it into maple using the read command, something like read(cat(currentdir(),"/code.txt")); (assumes your maple worksheet and code.txt are in the same directory). You may have to edit the text file slightly, e.g., what look like backquotes don't seem to be, so replace them with actual backquotes (according to the syntax error).

Also conformal in the plots package will do the grids in to new curves as you wanted. See also conformal3d.

After creating two plots, e.g. by

p1:=plot(x,x=0..1,color=blue);p2:=plot([[0.5,0.5]],style=point,symbol=solidcircle,symbolsize=30,color=red);

 

then plots:-display(p1,p2) plots p2 on top of p1, and plots:-display(p2,p1) plots p1 on top of p2.

Simplest way is

polarplot(sin(t)/cos(t)^2,t=-Pi/2..Pi/2, coordinateview=[0..2,-Pi..Pi]);

 

This may not be as efficient since it generates 256 matrices and then eliminates the zero matrices. But it does the conversion to the required notation at the same time.

M:=Matrix(4,4,(i,j)->E||i||j);

M := Matrix(4, 4, {(1, 1) = E11, (1, 2) = E12, (1, 3) = E13, (1, 4) = E14, (2, 1) = E21, (2, 2) = E22, (2, 3) = E23, (2, 4) = E24, (3, 1) = E31, (3, 2) = E32, (3, 3) = E33, (3, 4) = E34, (4, 1) = E41, (4, 2) = E42, (4, 3) = E43, (4, 4) = E44})

(1)

nums:=map(Bits:-Split,[$0..15],1,bits=4); #all binary numbers from 0 to 15 in bit reversed order

[[0, 0, 0, 0], [1, 0, 0, 0], [0, 1, 0, 0], [1, 1, 0, 0], [0, 0, 1, 0], [1, 0, 1, 0], [0, 1, 1, 0], [1, 1, 1, 0], [0, 0, 0, 1], [1, 0, 0, 1], [0, 1, 0, 1], [1, 1, 0, 1], [0, 0, 1, 1], [1, 0, 1, 1], [0, 1, 1, 1], [1, 1, 1, 1]]

(2)

M.~(Vector(nums[7]).Vector(nums[8])^%T);  # how it works
add(k,k=%);

Matrix([[0, 0, 0, 0], [E21, E22, E23, 0], [E31, E32, E33, 0], [0, 0, 0, 0]])

 

E21+E31+E22+E32+E23+E33

(3)

S:=table();
for i to nops(nums) do for j to nops(nums) do   #generate all 256 possibilities
S[i,j]:=add(k,k=M.~(Vector(nums[i]).Vector(nums[j])^%T));
end do end do;
S:=convert(S,set) minus {0}:   #remove the ones that are the zero matrix

table( [ ] )

(4)

nops(S);

225

(5)

S;


 Full output of S is removed but starts
{E11, E12, E13, E14, E21, E22, E23, E24, E31, E32, E33, E34, E41, E42, E43, E44, E11+E12...

Download bits.mw

Edited: I realize I should have just gone from 1 to 15 (not 0 to 15) and then I woudn't have to remove the zero matrices.

The returned module pds has routines to plot the solution, e.g., pds:-plot(...). For details and examples see the pdsolve/numeric help page ?pdsolve,numeric

Most of Maple (including the plot3d command) uses the "Math" convention as on the ?coords help page, i.e., the azimuthal angle second.

But the VectorCalculus package uses the "Physics" convention as on the ?VectorCalculus,Coordinates help page, i.e., azimuthal angle third. I believe the Physics package also uses this convention, though a quick glance at the help pages did not clarify this.

This is a definite problem for Maple, and I have seen some commentary about improving the situation, though I don't recall where. A first step would obviously be to put some warnings on each of these help pages!

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