Robert Israel

6577 Reputation

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18 years, 214 days
University of British Columbia
Associate Professor Emeritus
North York, Ontario, Canada

MaplePrimes Activity


These are replies submitted by Robert Israel

Click on the red Maple leaf button in the tool br above this editor window.  A little "Maple Tag" box appears.  Copy the Maple output from the worksheet, paste it in to the  "Maple Math Expression" field.  Press OK.  Use "Preview comment" to check that it works.  Results are not always good, but often it works.


Click on the red Maple leaf button in the tool br above this editor window.  A little "Maple Tag" box appears.  Copy the Maple output from the worksheet, paste it in to the  "Maple Math Expression" field.  Press OK.  Use "Preview comment" to check that it works.  Results are not always good, but often it works.


Actually, forward slashes can be used in Maple under Windows as well. 

So "c:/my_data_files/bits.dat" should work (again, assuming there is a top-level directory "my_data_files" in drive c:).

Actually, forward slashes can be used in Maple under Windows as well. 

So "c:/my_data_files/bits.dat" should work (again, assuming there is a top-level directory "my_data_files" in drive c:).

Try it and see.

Try it and see.

Ctrl-m switches you to Maple input (for that particular input region) .  That's a good thing, though it's even better to change the default using Tools, Options, Display.  But there's more to the Standard vs Classic issue than just 2D vs 1D input.

Ctrl-m switches you to Maple input (for that particular input region) .  That's a good thing, though it's even better to change the default using Tools, Options, Display.  But there's more to the Standard vs Classic issue than just 2D vs 1D input.

You also want to add some initial zeros.   This procedure will give you the binary digits of x in a list of length n (if possible):


> makebin:= proc(x::nonnegint, n::posint)
    local L, m;
    L:= ListTools:-Reverse(convert(x,base,2));
    m:= nops(L);
    if m > n then error "This needs %d digits", m end if;
    [0 $ (n-m), op(L)];
    end proc;
    
For example:
> makebin(6, 8);

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

You also want to add some initial zeros.   This procedure will give you the binary digits of x in a list of length n (if possible):


> makebin:= proc(x::nonnegint, n::posint)
    local L, m;
    L:= ListTools:-Reverse(convert(x,base,2));
    m:= nops(L);
    if m > n then error "This needs %d digits", m end if;
    [0 $ (n-m), op(L)];
    end proc;
    
For example:
> makebin(6, 8);

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

I don't know what model you are using, but clearly there's something wrong with it if it's supposed to be a number of particles, because the result is certainly negative.

polylog(3/2, t) (which in Extended typesetting level is written as Li[3/2](t), is defined as

sum(t^j/j^(3/2),j=1..infinity) for |t| <= 1. 

If -1 <= t < 0 this is an alternating series whose first term is negative, and the result is negative.

For t < -1 the series diverges, but the function is defined by analytic continuation.  The result still seems to be negative: try e.g. plotting.

 

I don't know what model you are using, but clearly there's something wrong with it if it's supposed to be a number of particles, because the result is certainly negative.

polylog(3/2, t) (which in Extended typesetting level is written as Li[3/2](t), is defined as

sum(t^j/j^(3/2),j=1..infinity) for |t| <= 1. 

If -1 <= t < 0 this is an alternating series whose first term is negative, and the result is negative.

For t < -1 the series diverges, but the function is defined by analytic continuation.  The result still seems to be negative: try e.g. plotting.

 

For A^2 = A where A is n x n (and n is a given positive integer), you could try this:

> A:= Matrix(n,n, symbol=a);
  R:= A^2;
  eqs:= {seq(seq(R[i,j] = A[i,j], i=1..n), j=1..n)};

 

 

For A^2 = A where A is n x n (and n is a given positive integer), you could try this:

> A:= Matrix(n,n, symbol=a);
  R:= A^2;
  eqs:= {seq(seq(R[i,j] = A[i,j], i=1..n), j=1..n)};

 

 

You're missing a multiplication symbol "*" after the last a.  However, even after correcting that, solve finds no solution for B,g,a.  The fact is that equations such as these with variables appearing both in exponents and outside them are very unlikely to have closed-form solutions. Given numerical values of the parameters b,k,t,w, you might get numerical solutions using fsolve.  For example:

 

> eqs:= {B*(B-1)*t^B+3*a*B*t^B-6*a+12*a^2 = 0,
    g*(g-1)*t^g+3*a*g*t^g+(6*a-12*a^2)*b*t^(B*(b-1)) = 0,
    -3*a^2/t^2-3*a*t^(B*b-2)*(a+B*b)+3*a*t^(g-2)*(a+g)+1/2*g*B*t^(g+B-2)+k^2*t^(-3*a*(1+w)) = 0};
> fsolve(eval(eqs, {b=1,t=2,k=3,w=4}));

{B = -11.70443667, a = .4933504884, g = -.1179980646}

 

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