f:=((1/24)*sqrt(1/11*(819+210*sqrt(5)-126*sqrt(11)-
90*sqrt(55)))*cos(sqrt(2/5*(7-2*sqrt(11)))*t*tau/h)+
(1/8)*sqrt(1/33*(273+70*sqrt(5)+42*sqrt(11)+
30*sqrt(55)))*cos(sqrt(2/5*(7+2*sqrt(11)))*t*tau/h))^2+
(-(1/8)*sqrt(1/11*(91+39*sqrt(5)-2*sqrt(22*(47+21*sqrt(5)))))*
sin(sqrt(2/5*(7-2*sqrt(11)))*t*tau/h)+(1/8)*sqrt(1/11*
(91+39*sqrt(5)+2*sqrt(22*(47+21*sqrt(5)))))*
sin(sqrt(2/5*(7+2*sqrt(11)))*t*tau/h))^2 - 1;

g:=evalf(combine(eval(f,[t=x*h/tau])));

  g := -0.1080787779 cos(-1.952215567 x)

         + 0.3273257083 cos(2.718244725 x)

         - 0.04594923692 cos(0.7660291588 x)

         - 0.00381174552 cos(4.670460292 x) - 0.5434920872

`+`(map2(abs@op,1,[op([1..-2],g)])[])+op(-1,g);

                            -0.0583266186

So, no - the maximal value of f for real t, h, and tau can not be greater than that, so there are no real solutions.

Complex solutions can be found in Maple, for example, by replacing cos with cosh, sin with sinh, and t with x*h/tau.

Alec

Instead of using Re and Im, you could just use a normal quadratic formula, and add complex if you need it, in the ouput manally either in front, or after float or double.

Maple uses the converted code with Open Watcom compiler version 1.3, which is a part of Maple distribution, and while it includes complex.h, but support for it is far from complete, see C99 compliance note.

I think that help pages should mention that by ANSI C they mean "ANSI C without C99 additions".

Alec

PS For me, it is much easier to write code directly in C or C++ than convert it from Maple to C -Alec

assign(op([7,2],eval(f)), 24);
f();
                                  24

what's wrong with that? Or, say,

assign(op(op(f))[-1], 71);
f();
                                  71

Alec

The site seems to be operational now (since noon, I think - things worked out even faster than I expected). I didn't have time to work on it today. Perhaps, I'll add something during weekend. If somebody is interested, contact me - alec at my last name.com. I can provide FTP (and, maybe, even SSH) access, as well as basic info about Perl, Python, PHP, MySQL etc. that can be used. The site is hosted in standard LAMP configuration. At this time, the site is almost empty - except a very simple first page, a chat room, a very basic forum, and a mailing list.

Certainly, I can do the basic setup myself, but I'd like to see at least some other people wishing to work on it as well. I don't want it to be my own project.

Alec

jsmath seems to be a good idea for math content, and can be simply implemented. It can be added to MoinMoin.

Alec

OK, I've just registered the domain, mapleadvisor.com (since there were no other suggestions.) It will take about 2 days to propagate it to all the DNS servers and then we can start working on it.

And people involved in the project, as a bonus, will get an email address ending at that domain name (and starting with your name or whatever.)

Alec

Robert Israel explained that in his post above. For f - there are 2 cases, either f=0, or not. If it is not 0, then both numerator and denominator can be divided by f that makes it 1. For c - it can be made 0 by changing variables from x to x+t1 and from y to y+t2 for come constants t1 and t2.

Another way of solving this equation is the same as was outlined in this thread, writing the solution in form F(x,y)=C with some constant C. Then, differentiating with respect to t, we get dF/dx*dx/dt + dF/dy*dy/dt =0. So F can be found from this partial differential equation.

pde:=diff(F(x,y),x)*(a+b*x+c*y+d*x*y+f*x^2)+diff(F(x,y),y)*e*(a+b*y+c*x+d*x*y+f*y^2);

In this case,

pdsolve(pde);

takes again too long, but for some particular values of constants it gives the answer rather fast. For example, for

pdsolve(eval(pde,[d=0,f=0]));

and in the opposite case, for

pdsolve(eval(pde,[a=0,b=0,c=0]));

Alec

Robert Israel explained that in his post above. For f - there are 2 cases, either f=0, or not. If it is not 0, then both numerator and denominator can be divided by f that makes it 1. For c - it can be made 0 by changing variables from x to x+t1 and from y to y+t2 for come constants t1 and t2.

Another way of solving this equation is the same as was outlined in this thread, writing the solution in form F(x,y)=C with some constant C. Then, differentiating with respect to t, we get dF/dx*dx/dt + dF/dy*dy/dt =0. So F can be found from this partial differential equation.

pde:=diff(F(x,y),x)*(a+b*x+c*y+d*x*y+f*x^2)+diff(F(x,y),y)*e*(a+b*y+c*x+d*x*y+f*y^2);

In this case,

pdsolve(pde);

takes again too long, but for some particular values of constants it gives the answer rather fast. For example, for

pdsolve(eval(pde,[d=0,f=0]));

and in the opposite case, for

pdsolve(eval(pde,[a=0,b=0,c=0]));

Alec

Well done, Paulina!

That, probably, could be put in one of the Books (on this site), in addition to this blog.

Alec

The best that I know in this direction is Robert Israel's Maple Advisor Database.

Perhaps, people interested in adding something to it, could just post suggested additions in their blogs here.

Personally, I don't like sourceforge (their advertising system is disgusting, even worse than Google - and it is not that easy to achieve).

If there were people interested in that, I could, probably, host a website (up to say 50 GB, and reasonable bandwidth), advertising free,  on my webspace (something like mapleadvisor.com - that would be my choice, .org, or .net - I'd prefer not to use .us or .info - because of some known issues).

It may have a wiki as well (MoinMoin preferably.)

Alec

I have a procedure for pattern based transforms in my blog, written in 2005. It worked in many cases. I didn't continue working on it for 2 reasons. First - there were too many bugs in patmatch related procedures (such as matching regular parentheses with square brackets and inverse), and second - I had stopped using Maple myself at that time.

Alec

I never used them myself, except just for some quick reference, mostly in the Advanced Programming Guide, but some people recommend guides that come with Maple and available for downloading from here.

Help pages often useful. For example, if you checked ?piecewise , you would see an example with and.

Alec

PS I am not sure whether I can post that here, or not, but the best advice is to use SAGE instead and Python, as I do -Alec

I never used them myself, except just for some quick reference, mostly in the Advanced Programming Guide, but some people recommend guides that come with Maple and available for downloading from here.

Help pages often useful. For example, if you checked ?piecewise , you would see an example with and.

Alec

PS I am not sure whether I can post that here, or not, but the best advice is to use SAGE instead and Python, as I do -Alec

That seems to be another "design flaw".

Why not to define lasterror that way instead of deprecating it? It would be so much easier to remember, and it would work in the older code - that is even better than backward compatibility.

Alec

Here are the commands including Robert Israel's suggestion, and starting from eq in his post above, I didn't copy it here,

eq1:=convert(eq,FirstKind);
eq2:=eval(eq1[1],[f=1,c=0]);
dsolve(eq2);

But again, as Robert Israel said above, Maple won't give a general solution, because it doesn't exist for some particular choices of constants.

Alec