A better approximation gives more digits of accuracy in the result per digit of precision used in the computation than a good approximation does.  I was wondering if anyone could come up with a better approximation to the MRB constant than 31/165, 

Hi,

I need to fit a complex function to some data points Couuld you please show me what Maple operations to use?

The function is:

pn := unapply(KT*bn*(sum((dWn[i](lambda)*(sum(c[i+r]*binomial(i+r, i)*(Lmbd0(lambda)/bn)^r, r = 0 .. nterm-i))+IWn[i](lambda)*(2*lambda^3-2)*(sum(r*c[i+r]*binomial(i+r, i)*(Lmbd0(lambda)/bn)^(r-1), r = 1 .. nterm-i))/(bn*(3*lambda^2)))/bn^i, i = 0 .. nterm)), lambda);

- 'IWn' and 'dWn' are known (and long) functions of lambda.

This is an important topic which is why I have labelled it as a post.  Many users would like to know how to implement a minor fix to versions where fixes have not been applied.

I will start with one example.

   pdsolve had an issue where the fourth order term was not evaluated in the pdsolve command.  The issue 
   works Maple 16.  To those users of earlier versions where the code didn't work, it was ...

   showstat(pdsolve)

Dear everyone,

  Hello,

  I have a question related to copy and paste in Maple 16.

 Consider an input like

**********************************

eq1:=4*x^n*y^m+3*x^2+5*y^2;

f1:=map(t -> `if`(match(t = c*y^d, y, 's'), subs(s,c), NULL),
      convert(eq1, list));


f2:=map(t -> `if`(match(t = c*y^d, y, 's'), subs(s,d), NULL),
      convert(eq1, list));

Sir/Madam

My Version of MAPLE is 13.02

I have the following expression on my worksheet:

(63/8) ((cos(Θ))^5)[G,H,L,P,T,U]^5 -(35/4)((cos(Θ))^3)[G,H,L,P,T,U]^3 + (15/8)(cos(Θ))[G,H,L,P,T,U]

I do not need the factors of [G,H,L,P,T,U] and I want to delete them, but all my efforts in the past few hours are in vain. I have tried to highlight those expressions and then use the EDIT -> DELETE ELEMENT...

Hi,

Is there a way to generate Java or C code to implement a general nth order linear ordinary differential equation?

I am looking to be able to send the coefficients and have it compute the time waveform given initial conditions.

Regards.

how can I solve memory used limitation problem on MAC OSX LION .After memory indicated on the bowwtom of the sheet reaches 57M it freezes.

I noticed the following behaviour in Maple 16:

x1 := (a)^(b):
eval(x1,[a=103/100]):
evalf[3](%);

                                 b
                             1.03

I wish to use the 'Numeric Formatting' feature on some results in Maple, to show the correct significant figures in the results. But when I apply Numeric Formatting to any result, the decimal seperator changes from the usual dot (.) to a comma (,). How can I keep the dot as decimal seperator while applying the correct significant figures?

Thanks. 

I entered the following code in Maple 15.  In one instance it plotted the correct graph with the "x" and "y" labels exactly where I wanted them.  The identical code, in another instance (and again in a separate tab) generates an error:

  "Error, (in plots:-display) cannot make plot structure from object with name textplot"

Of course, when I click the error above in Maple (it is a link), a Maple webpage comes up that says:

If anyone was interested Euro 2012 starts tomorrow.  Using the FIFA simulation created by Robert Israel one could enter the new values for the ELO ratings found here http://www.eloratings.net/euro_cup.html to create a similar simlation of Euro 2012.  Just for visual sakes here's the ELO ratings for the teams in the tournament.

mapletrig.mw

Hi all,

I need to solve a simple integration as shown in the attached work sheet.  But don't know how to obtain the required answer as shown.

I shall be very thank full if you guys could help me out with this.

Best Regards

A.Q

Please excuse me if this question is too basic or has been answered before, though I've spent a couple of hours searching for similar questions without any luck.

I have the following expression, which is given in terms of other expressions:

Dear Maple Users

I have been testing Maple 16 for some time now, and I am overall very pleased with it. There is however one issue, which is really annoying. In previous version of Maple, images inserted into Maple and plots were printed much bigger than they looked like in the Worksheet. Then me and other users have requested to have the printed output look more like it does in the Worksheet on the computerscreen. Maple has adressed those user complaints in the new...

Way back in Maple 6, the rtable was introduced. You might be more familiar with its three types: Array, Matrix, and Vector. The name rtable is named after "rectangular table", since its entries can be stored contiguously in memory which is important in the case of "hardware" datatypes. This is a key aspect of the external-calling mechanism which allows Maple to use functions from the NAG and CLAPACK external libraries. In essence, the contiguous data portion of a hardware datatype rtable can be passed to a compiled C or Fortran function without any need for copying or preliminary conversion. In such cases, the data structure in Maple is storing its numeric data portion in a format which is also directly accessible within external functions.

You might have noticed that Matrices and Arrays with hardware datatypes (eg. float[8], integer[4], etc) also have an order. The two orders, Fortran_order and C_order, correspond to column-major and row-major storage respectively. The Wikipedia page row-major  explains it nicely.

There is even a help-page which illustrates that the method of accessing entries can affect performance. Since Fortran_order means that the individual entries in any column are contiguous in memory then code which accesses those entries in the same order in which they are stored in memory can perform better. This relates to the fact that computers cache data: blocks of nearby data can be moved from slower main memory (RAM) to very fast cache memory, often as a speculative process which often has very real benefits.

What I'd like to show here is that the relatively small performance improvement (due to matching the entry access to the storage order) when using evalhf can be a more significant improvement when using Maple's Compile command. For procedures which walk all entries of a hardware datatype Matrix or multidimensional Array, to apply a simple operation upon each value, the improvement can involve a significant part of the total computation time.

What makes this more interesting is that in Maple the default order of a float[8] Matrix is Fortran_order, while the default order of a float[8] Array used with the ImageTools package is C_order. It can sometimes pay off, to write your for-do loops appropriately.

If you are walking through all entries of a Fortran_order float[8] Matrix, then it can be beneficial to access entries primarily by walking down each column. By this I mean accessing entries M[i,j] by changing i in ther innermost loop and j in the outermost loop. This means walking the data entries, one at a time as they are stored. Here is a worksheet which illustrates a performance difference of about 30-50% in a Compiled procedure (the precise benefit can vary with platform, size, and what else your machine might be doing that interferes with caching).

Matrixorder.mw

If you are walking through all entries of an m-by-n-by-3 C_order float[8] Array (which is a common structure for a color "image" used by the ImageTools package) then it can be beneficial to access entries A[i,j,k] by changing k in the innermost loop and i in the outermost loop. This means walking the data entries, one at a time as they are stored. Here is a worksheet which illustrates a performance difference of about 30-50% in a Compiled procedure (the precise benefit can vary with platform, size, and what else your machine might be doing that interferes with caching).

Arrayorder.mw