## dharr

Dr. David Harrington

## 6416 Reputation

20 years, 22 days
University of Victoria
Professor or university staff

## Social Networks and Content at Maplesoft.com

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.

## Accessing the help worksheets...

@Earl I loaded the DirectSearch  version 2 files DirectSearch.mla and DirectSearch.hdb (from the application centre) to "C:/MapleLibs".  I get the same warning as Markian Hirnyk and a small non-functioning DirectSearch.help **see edit** (but not the error message) when I use HelpTools:-Database:-ConvertAll(); in Maple 2015.2. But I can see the help contents as worksheets when I use

c:=HelpTools:-Database:-ExtractContentsFromHDB("C:/MapleLibs", "C:/MapleLibs/DirectSearch.hdb"):

So I'm guessing that if you follow the manual instructions in ?HelpTools,Migrate (assuming it is still there in 2016), you can probably migrate in a more laborious fashion.

Edit: Actually the .help file was functional if it and the .mla file were moved to the current directory.

## using exact arithmetic...

@Majmaj If you really want Maple to do exact arithmetic, you want to just avoid floating point numbers (with a ".") and Digits altogether, and use rationals. So you could convert to rationals, do all your calculations and then convert back. The answers above effectively do that, but it seems simpler to use convert( ,rational,exact) and then evalf to the appropriate number of digits at the end. In the case of multiplication we can get the appropriate number of digits from the log of the denominator of the rationals, but as the others have pointed out, the general case is far from simple.

 > a:=convert(0.123456789,rational,exact);
 (1)
 > b:=a^2;
 (2)
 > evalf[18](b);
 (3)
 > evalf[ilog10(denom(b))](b);
 (4)
 > tofloat:=x->evalf[ilog10(denom(x))](x);
 (5)
 > tofloat(b);
 (6)
 >

## nuisance indeed...

@Carl Love Good point. I always used to use just indets with a single argument, which would not consider Pi an indeterminate, then changed to indets( ,name) so I missed things like exp(a*d). (My recollection may be faulty, but I think very early Maple versions wouldn't have considered exp(a*d) an indeterminant.) If one has to give a very specific type specification, one wonders about the usefulness of indets, which is probably mainly used just for what the OP wanted.

Regards,
David.

## signum better than AllSolutions...

@acer Interesting that the original answer with signum(t)^6 covers the t=0 case but the AllSolutions option does not.

## finite integrals with infinite integrand...

@tomleslie I had in mind here that some integrals with infinite integrands are nonetheless finite, e.g., int(ln(x),x=0..1) = -1.

Regards,

David.

## Parametric plot?...

Well if you want phiB on the x axis and qB on the y axis then use

plot([phiB1,qB,qB=0..20]);

You still specify the range for qB, not phiB1, because you have phiB1 in terms of qB. If you want to know what value of qB corresponds to a value of phiB1, then you can look at the plot or use fsolve. Your intention for phi is still unclear.

## I avoid numerical assignments...

I typically solve this problem by never assigning numerical values to variables, but using eval on a set of numerical parameters, as in the following:

Model 1

 > params:={a=1,b=2,c=1,d=3}; q:=a*b+c; r:=b+d; eval(q,params); eval(r,params);
 (1)

Model 2

 > params:={a=1,b=3,c=2,d=1}; q:=a*b^2+c; r:=b+2*d; eval(q,params); eval(r,params);
 (2)

I often put all the parameter sets at the top of the worksheet (but with different names: params1, params2 etc), so I can redo with different parameters by just changing the sets and then running the worksheet.

## Angular region...

@Carl Love Possibly. I was going by his sketch.

## Efficient list building...

@Carl Love The dynamic vector method of building lists is fastest,followed by the remember table method, but the other methods given do not give ordered lists. "entries" requires the 'indexorder' option to be ordered, but that slows it down, and there is a similar problem with the extracted remember table method.

restart:
#List building using regular table - result is not ordered
P:= proc(n)
local T,k;
for k to n do T[k]:= k end do;
[entries(T, 'nolist')]
end proc:
CodeTools:-Usage(P(2^22)):
P(5);

memory used=196.15MiB, alloc change=476.01MiB, cpu time=3.98s, real time=3.67s, gc time=624.00ms
[1, 2, 3, 5, 4]

restart:
#List building using regular table - use of indexoder option to order slows things down
P:= proc(n)
local T,k;
for k to n do T[k]:= k end do;
[entries(T, 'nolist','indexorder')]
end proc:
CodeTools:-Usage(P(2^22)):
P(5);

memory used=308.15MiB, alloc change=0.53GiB, cpu time=10.75s, real time=10.47s, gc time=670.80ms
[1, 2, 3, 4, 5]

restart:
#List building using regular table - convert to list slows things down more
P:= proc(n)
local T,k;
for k to n do T[k]:= k end do;
convert(T,list)
end proc:
CodeTools:-Usage(P(2^22)):
P(5);

memory used=388.16MiB, alloc change=0.67GiB, cpu time=17.46s, real time=12.08s, gc time=7.64s
[1, 2, 3, 4, 5]

restart:
#List building using remember table
P:= proc(n)
local R,k;
for k to n do R(k):= k end do;
[seq(R(k),k=1..n)];
end proc:
CodeTools:-Usage(P(2^22)):
P(5);

memory used=243.97MiB, alloc change=508.01MiB, cpu time=6.19s, real time=5.82s, gc time=826.81ms
[1, 2, 3, 4, 5]

restart:
#List building using extracted remember table - not ordered
P:= proc(n)
local R,k;
for k to n do R(k):= k end do;
[seq(k,k=op(4,eval(R)))];
end proc:
CodeTools:-Usage(P(2^22)):
P(5);

memory used=211.96MiB, alloc change=492.02MiB, cpu time=4.48s, real time=4.07s, gc time=873.61ms
[1, 2, 3, 5, 4]

restart:
#List building using dynamic vector
P:= proc(n)
local R:=Vector(),k;
for k to n do R(k):= k end do;
[seq(k, k= R)]
end proc:
CodeTools:-Usage(P(2^22)):
P(5);

memory used=174.03MiB, alloc change=82.03MiB, cpu time=3.34s, real time=3.21s, gc time=421.20ms
[1, 2, 3, 4, 5]

## Need an approximate solution...

I have had success in the past with providing an approximate solution. Something like 'approxsoln' = [F(eta) = 1+eta-(1/6)*eta^2, G(eta) = 0, H(eta) = 1-(1/3)*eta]. Presumably you know something about what the solution looks like roughly. Particularly there is not much information about G, only that it is zero at both boundaries.

## Coloured contours...

It's not really an answer, but I do this with a coloured 3-D contour plot where I specify the exact contours I want and then colour the plot according to height using shading =zhue. For example

plot3d(S(X, Y), X = 0 .. X3, Y = 0 .. 1, axes = boxed, orientation = [-90, 0], scaling = constrained, style = surfacecontour, contours = [seq(i/(10.)+0.5e-1, i = 0 .. 9)], shading = zhue, thickness = 3, tickmarks = [6, 4, 3], labels = ["", "", ""], grid = [150, 50]);

You can then have a colour key using

plot3d(X, X = 0 .. 1, Y = 0 .. .2, axes = boxed, orientation = [-90, 0], scaling = constrained, thickness = 2, font = [Times, normal, 20], style = surfacecontour, shading = zhue,thickness=2, tickmarks = [0, 0, 0], labels = [" ", " ", " "],contours=[seq(0.1*i+0.05,i=0..9)]);

## syntax problems...

I can't see the right-hand side of your screen, but two problems come to mind. To define a1 as a function, you need a1:=(r,theta)->sum( etc And for plotting a function you need either plot(a1,0..infinity,0..Pi/2) or plot(a1(r,theta),r=0..infinity,theta=0..Pi/2)

## the worksheet...

I didn't save yesterday, but did it again, with a smaller number of solutions this time (263), though I believe I entered the equations identically. Many of the solutions have many variables zero, so there is a lot of structure here.

## the worksheet...

I didn't save yesterday, but did it again, with a smaller number of solutions this time (263), though I believe I entered the equations identically. Many of the solutions have many variables zero, so there is a lot of structure here.

## changing source...

I found this also. Specifically after entering with the maple button, the code previewed with an image (but not well). When I made the post, the image wasn't there. Looking at the source showed the text had been moved out of the maple tags and put after the closing one. I moved it back in source mode, but it ended up outside again. This behavior was different I think from a few days earlier. Definitely strange.

David

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