tomleslie

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10 years, 177 days

MaplePrimes Activity


These are answers submitted by tomleslie

Just becuase there's always more than one way to it!

f1:=1/2*(-8*R*d1^2*r^2*C+10*d1*r^2*C*R+5*d1*r^3*C+2*r*L*d1^2-2*C*r^3+2*R*L*d1^2-R*L*d1^3-r*L*d1^3-4*C*r^2*R+2*R*d1^3*r^2*C-4*r^3*d1^2*C+r^3*d1^3*C+sqrt(26*r^6*d1^4*C^2+41*r^6*d1^2*C^2-44*r^6*d1^3*C^2-20*C^2*r^6*d1+16*C^2*r^5*R-16*C*r^4*L-176*r^5*d1^3*C^2*R+164*r^5*d1^2*C^2*R-74*r^4*d1^4*C*L+136*r^4*d1^3*C*L-136*r^4*d1^2*C*L-80*C^2*r^5*d1*R+72*C*r^4*L*d1-64*C*r^3*R*L+104*R^2*d1^4*r^4*C^2-176*R^2*d1^3*r^4*C^2+164*R^2*d1^2*r^4*C^2-8*r^6*d1^5*C^2+r^2*L^2*d1^6-4*R^2*L^2*d1^5+104*r^5*d1^4*C^2*R+40*r*L*R^3*d1^5*C-72*r*L*R^3*d1^4*C+56*r*L*R^3*d1^3*C-16*r*L*R^3*d1^2*C+R^2*L^2*d1^6+20*r^4*L*C*d1^5-32*r^4*d1^5*C^2*R^2+2*R*L^2*d1^6*r-2*r^4*L*d1^6*C+4*R^2*d1^6*r^4*C^2+4*R*d1^6*r^5*C^2-306*r^3*d1^4*C*R*L+548*r^3*d1^3*C*L*R-544*r^3*d1^2*C*R*L+288*C*r^3*L*d1*R+16*C^2*r^4*R^2+4*R^2*L^2*d1^4-16*R^2*L*d1^6*r^2*C-10*R*L*d1^6*r^3*C+r^6*d1^6*C^2-32*r^5*d1^5*C^2*R-4*r^2*d1^5*L^2-352*R^2*d1^4*r^2*C*L+580*R^2*d1^3*r^2*C*L-552*R^2*d1^2*r^2*C*L-80*d1*r^4*C^2*R^2-8*R^3*d1^6*L*C*r+88*r^3*L*C*d1^5*R+116*r^2*L*R^2*d1^5*C+4*C^2*r^6-8*r*R*L^2*d1^5+288*d1*r^2*C*R^2*L-64*C*r^2*R^2*L+8*r*L^2*d1^4*R+4*r^2*L^2*d1^4)^(1/2))/(-3*r^2*d1*L*C-6*R*d1*L*C*r+2*L*C*r^2+r^2*d1^2*L*C+4*L*C*r*R+2*R*d1^2*L*C*r);
#
# The expression form is
#
#  k*(A+B)
#
# where 'k' is a ratio, A is a sum of terms
# and B is a fourth root, these can be extracted
# as
#
  k:= op(1,f1)*op(3,f1);
  A:= add(op([2,1..-2],f1));
  B:= op([2,-1],f1);

Well if I fix syntax errors and typos using more-or-less guesswork (some of which) may be wrong, I can come with the attached worksheet

badplot.mw

Suggest you read the comments in this to determine whether or not my guesses were correct.

This takes about a minute to execute on my machine, and the final plots are not really very interesting :-(

I didn't really understand your question, but luckily the Wikipedai page at

https://en.wikipedia.org/wiki/Four-bar_linkage

seems to have a pretty clear description.

The attached worksheet implements the 'Classification' section of that Wikipedia entry. I suggest you check it very carefully, becuase with this many conditions, it would be very easy for typos to occur

Grashof.mw

Maple can only numerically solve PDEs with two (or fewer) independent variables. You have three.

The attached will compute the solution over the range of time specified by tRange, and steps of tStep. Since I have no idea what these values are I just used

tRange:=0..10

tStep:=0.1

You can change these settings in the attached to anything you want and everything should still work.

You will also have to adjust the fileName in the

ExcelTools:-Export()

command to something appropriate for your machine

odeToExcel.mw

If you change the colon at the end of the line

Eff:=[seq([k1z[i],alpha0[i]],i=1..t)]:

to a semicolon, you will see that each entry in Eff, has three components - you should only have two! See below

Eff := [[-1.566422551*10^20, 1.566422551*10^20, 30[1]], [-1.566422551*10^20, 1.566422551*10^20, 30[2]], [-1.566422551*10^20, 1.566422551*10^20, 30[3]], [-1.566422551*10^20, 1.566422551*10^20, 30[4]], [-1.566422551*10^20, 1.566422551*10^20, 30[5]], [-1.566422551*10^20, 1.566422551*10^20, 30[6]]]

No idea what you mean by 30[1], 30[2], 30[3] etc

There is no Neural Network "package" in Maple. There are a couple of worksheets, with implementations of specific Neural Networks posted by users. at the Maple Application Centre

There are two Maple processes you have to consider - 'automatic simplification' and 'evaluation'. It is relatively easy to suspend the latter using unevalution quotes, as in

a:=''2*x-5''>''3*x-6''; not a double quote but two forward single quotes

which will return

a := '3*x-6' < '2*x-5'

Notice however that if one subsequently enters 'a' in your worksheet, then 'a' will be 'evaluated' again, and 3*x<2*x-1 will be returned

Notice also that this approach does not prevent automatic simplification. Contrast the above with

a:=''2*x-5''>''3*x-6+1'';

The 'automatic simplification' process will 'simplify' the 6+1 part on the rhs, but the expression is otherwise unevaluated so this one returns

a := '3*x-5' < '2*x-5'

If you want to avoid both automatic simplification and evalutation then you best bet is probably the InertForm package.

The command

a:=InertForm:-MakeInert(2*x-5) > InertForm:-MakeInert(3*x-6+1); #Note the 6+1 which will be 'simplified'

will return an inert form which (unlike evaluation quotes) will remain inert in subsequent evaluations, until/unless one uses the command

InertForm:-Value(a);

If you really, really want to kill the automatic simplification process as well, you can use the construct

use InertForm:-NoSimpl in 2*x-5>3*x-6+1; end;

 

 

Carl is correct (as usual).

I think this is primarily a lexicographic issue.

arctan() is an odd function, so arctan(a-b)=-arctan(b-a) except Maple will never "prefer" the latter. On the other hand arctan(b-a) will always be returned as -arctan(a-b), presumably because in the latter case Maple "prefers" the arguments to the arctan() function to be lexicographically ordered.

However it begs the obvious question - what happens with more than two arguments? Just for amusement, try

arctan(a-b+c);

arctan(b-a+c);

and see if you can come with a "logical" reason for the resulting argument ordering/sign selection - because I can't!! - and I have therefore invalidated my own lexicograhic argument:-(

1 + floor(n/2), n=0..;

OEIS Sequence A008619

OEIS provides no name, just "Positive integers repeated."

You need to understand the difference between an equation and an assignment.

The following code provides the solution you require

eqns:=[ x[1]=R__S-C,
             x[2]=K__p*x[1],
             x[3]=x[2]-x[4]-x[5],
             x[4]=K*C,
             x[5]=K__d*x[6],
             x[6]=x[3]/(M*s+B),
             C=x[6]/s
          ];
sols:=solve(eqns, [x[1], x[2], x[3], x[4], x[5], x[6], C]);
sols[1][7]/R__S;

Debugging your 2D code is almost impossible. I have converted it line-by-line to 1-D input, then made a guess, at what you intended for each line and corrected it according to my guess

Are all of my guesses correct - almost certainly not!!

However the attached does execute, and finally produces a plot.

I suggest you read it very, very carefully in order to determine whether or not it is what you expect.

corrPlot.mw

 

 

If you use the menu entries

File->Export As

and select latex as the fileType, then this ought to export pretty much everythiing.

Suggest you check the help pages

?Export as LaTeX

and

?Translation of Maple Worksheets to LaTeX

The first explains the process, and the second explains the details.

On the toolbar try

Format->Numeric Formatting

and I reckon you need the engineering category. Then just set the options the way you want them

Check the help at ?simplify/siderels

For your specific case

simplify(-x^(a)+x^n, {a=n});

will return zero

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