Hello Maple-Primers!

I am trying to evaluate a system at many different points.  I would like to include an interpolation function in this system, but have thusfar been unsuccessful.

Usually, I solve a system symbolically by using eliminate and unapply:

eq[1] := A = M^3;
eq[2] := C = A*2;
eq[3] := D = N+3;
eq[4] := B = piecewise(A = 0, 0,C);
eq[5] := E = B*D;
elimsol:=eliminate(convert(eq,list),[A,B,C,D,E])[1];

unappsol:=unapply(elimsol,[N,M]);

unappsol(1,2);
{A = 8, B = 16, C = 16, D = 4, E = 64} <--- great!

Now, I want to include an interpolation function in the system of equations.  They look like this (see worksheet for actual interpolation function):

B_interp := (W,T) -> CurveFitting:-ArrayInterpolation([FC_Map_W,FC_Map_T],FC_Map,Array(1 .. 1, 1 .. 1, 1 .. 2, [[[W, T]]]),method=linear);

eq[5] := E = B_interp(N,M);

Error, (in CurveFitting:-ArrayInterpolation) invalid input: coordinates of xvalues must be of type numeric <-- bad!

Anyone have any ideas?  I've tried to use polynomials, but I can't seem to get a fit close enough for my purposes.

Maple_2D_Interpolate_FC.mw

Hello,

       How long can I expect Maple17 to take to algebraically solve a system of 14 nonlinear equations that has approximately 40% nonlinearity in its terms? I am running it on the machine right now, but have no idea what to expect. As mentioned before, I'm new to Maple...

Here is my code:

restart; eq1 := A*z-B*a*z-V*a*q-W*(b+d)*a = 0; eq2 := W*(b+d)*a-V*b*q-(F*G+B+D)*b*z = 0; eq3 := V*a*q-W*c*(b+d)-(B+C+E)*c*z = 0; eq4 := V*b*q+W*(b+d)*c-(B+C+D+F)*d*z = 0; eq5 := G*F*b*z-V*q*e-(B+H)*e*z = 0; eq6 := H*e*z-V*q*f-(B+S)*f*z = 0; eq7 := S*f*z-V*q*g-B*g*z = 0; eq8 := V*q*g+S*s*z-(B+C+E)*h*z = 0; eq9 := F*d*z+V*q*e-(B+C+H+T)*t*z = 0; eq10 := H*t*z+V*q*f-(U+B+C+2*S)*s*z = 0; eq11 := T*t*z-(B+H+Y)*u*z = 0; eq12 := U*s*z-(B+S)*v*z+H*u*z-Y*H*v*z/(H+S) = 0; eq13 := g-c-d-t-s-h = 0; eq14 := z-a-b-c-d-e-f-g-h-s-t-u-v = 0; soln := solve({eq1, eq10, eq11, eq12, eq13, eq14, eq2, eq3, eq4, eq5, eq6, eq7, eq8, eq9}, {a, b, c, d, e, f, g, h, q, s, t, u, v, z});

Thanks.

Greetings,

       I am new to Maple and this forum. I would like to obtain a Jacobian of a system of 12 ODEs. What have I done wrongly with my code?

eq_1 := -B*a+A-V*(c+d+t+s+h)*a/(a+b+c+d+e+f+g+h+s+t+u+v)-W*(b+d)*a/(a+b+c+d+e+f+g+h+s+t+u+v);
eq_2 := W*(b+d)*a/(a+b+c+d+e+f+g+h+s+t+u+v)-V*(c+d+t+s+h)*b/(a+b+c+d+e+f+g+h+s+t+u+v)-(F*G+B+D)*b;
eq_3 := V*(c+d+t+s+h)*a/(a+b+c+d+e+f+g+h+s+t+u+v)-W*(b+d)*c/(a+b+c+d+e+f+g+h+s+t+u+v)-(B+E+C)*c;
eq_4 := V*(c+d+t+s+h)*b/(a+b+c+d+e+f+g+h+s+t+u+v)+W*(b+d)*c/(a+b+c+d+e+f+g+h+s+t+u+v)-(B+C+D+F)*d;
eq_5 := G*F*b-V*(c+d+t+s+h)*e/(a+b+c+d+e+f+g+h+s+t+u+v)-(B+H)*e;
eq_6 := H*e-V*(c+d+t+s+h)*f/(a+b+c+d+e+f+g+h+s+t+u+v)-(B+S)*f;
eq_7 := S*f-V*(c+d+t+s+h)*g/(a+b+c+d+e+f+g+h+s+t+u+v)-B*g;
eq_8 := V*(c+d+t+s+h)*g/(a+b+c+d+e+f+g+h+s+t+u+v)+S*s-(B+E+C)*h;
eq_9 := F*d+V*(c+d+t+s+h)*e/(a+b+c+d+e+f+g+h+s+t+u+v)-(B+C+H+T)*t;
eq_10 := H*t+V*(c+d+t+s+h)*f/(a+b+c+d+e+f+g+h+s+t+u+v)-(U+B+C+S+S)*s;
eq_11 := T*t+W*(b+d)*x/(a+b+c+d+e+f+g+h+s+t+u+v)-(B+H+Y)*u;
eq_12 := U*s-(B+S)*v+H*u-Y*H*v/(H+S);
with(linalg);
J := Jacobian([eq_1, eq_2, eq_3, eq_4, eq_5, eq_6, eq_7, eq_8, eq_9, eq_10, eq_11, eq_12], [a, b, c, d, e, f, g, h, s, t, u, v]);

I am getting the message: 

 Vector(4, {(1) = ` 12 x 12 `*Matrix, (2) = `Data Type: `*anything, (3) = `Storage: `*rectangular, (4) = `Order: `*Fortran_order})

Thanks!!

Hello,

       I am new to this forum. I have typed the follwing code in Maple17:

restart; eq1 := A-B*a-V*a*q/z-W*(b+d)*a/z = 0; eq2 := W*(b+d)*a/z-V*b*q/z-(F*G+B+D)*b = 0; eq3 := V*a*q/z-W*c(b+d)/z-(B+C+E)*c = 0; eq4 := V*b*q/z+W*(b+d)*c/z-(B+C+D+F)*d = 0; eq5 := G*F*b-V*q*e/z-(B+H)*e = 0; eq6 := H*e-V*q*f/z-(B+S)*f = 0; eq7 := S*f-V*q*g/z-B*g = 0; eq8 := V*q*g/z+S*s-(B+C+E)*h = 0; eq9 := F*d+V*q*e/z-(B+C+H+T)*t = 0; eq10 := H*t+V*q*f/z-(U+B+C+2*S)*s = 0; eq11 := T*t+W*(b+d)*x/z-(B+H+Y)*u = 0; eq12 := U*s-(B+S)*v+H*u-Y*H*v/(H+S) = 0; eq13 := g-c-d-t-s-h = 0; eq14 := z-a-b-c-d-e-f-g-h-s-t-u-v = 0; soln := solve({eq1, eq10, eq11, eq12, eq13, eq14, eq2, eq3, eq4, eq5, eq6, eq7, eq8, eq9}, {a, b, c, d, e, f, g, h, q, s, t, u, v, z});

This is to symbolically solve a nonlinear system of (14) equations. But when I press Enter, it just returns the message "Ready". Shouldn't it say "Evaluating"?

I don't see anything syntactically wrong with my code...

Hello there!

There seems to be an issue with indexed variables and the instruction "DGsetup" of the differential geometry package when used with Maple 17. An error is returned to the effect that DGsetup is expecting independent variables to be unassigned names. This phenomenon does not occur with Maple 16!

Here is what I get:

> restart;
> with(DifferentialGeometry); with(Tools); with(Tensor); with(LinearAlgebra);

Executing the following command, I get an error with Maple 17 which does not occur with Maple 16!

> DGsetup([seq(x[i], i = 1 .. 4)], M, verbose);
Error, (in DifferentialGeometry:-DGsetup) expected 1st independent variable to be an unassigned name, received: x[1]

Is there any fix for this problem?

Kind regards
Freddy Baudine

solve Differential equation "a-y=y' bc" use maple 17

the result is y(x)=a+_C1e^-(1/bc)

but the correct result  isn't y(x)=a-_C1e^-(1/bc) ?

Thank you in advance for your help

hi.i encountered this erroe  [Error, (in dsolve/numeric/bvp/convertsys) unable to convert to an explicit first-order system] with solving set of differential equation.please help me.thanks a lot  

dsys3 := {`1`*h1(theta)+`1`*(diff(h1(theta), theta, theta))+`1`*(diff(h2(theta), theta))+`1`*(diff(h2(theta), theta, theta, theta))+`1`*h3(theta)+`1`*(diff(h3(theta), theta, theta))+`1`*(diff(h1(theta), theta, theta, theta, theta)) = 0, `1`*h2(theta)+`1`*(diff(h2(theta), theta, theta, theta, theta))+`1`*(diff(h2(theta), theta, theta))+`1`*(diff(h1(theta), theta))+`1`*(diff(h1(theta), theta, theta, theta))+`1`*(diff(h3(theta), theta))+`1`*(diff(h3(theta), theta, theta, theta)) = 0, h3(theta)^5*(`1`+ln(h3(theta))^2*`1`+2*ln(h3(theta))*`1`)+(diff(h3(theta), theta, theta))*h3(theta)^4*(`1`+ln(h3(theta))^2*`1`+2*ln(h3(theta))*`1`)+(diff(h3(theta), theta, theta, theta, theta))*h3(theta)^4*(`1`+ln(h3(theta))^2*`1`+2*ln(h3(theta))*`1`)+h1(theta)*h3(theta)^4*(`1`+ln(h3(theta))^2*`1`+2*ln(h3(theta))*`1`)+(diff(h1(theta), theta, theta))*h3(theta)^4*(`1`+ln(h3(theta))^2*`1`+2*ln(h3(theta))*`1`)+(diff(h2(theta), theta))*h3(theta)^4*(`1`+ln(h3(theta))^2*`1`+2*ln(h3(theta))*`1`)+(diff(h2(theta), theta, theta, theta))*h3(theta)^4*(`1`+ln(h3(theta))^2*`1`+2*ln(h3(theta))*`1`)+h3(theta)^4*(`1`+ln(h3(theta))^2*`1`+2*ln(h3(theta))*`1`)+h3(theta)^4*(diff(h2(theta), theta, theta, theta, theta, theta, theta))*(`1`+ln(h3(theta))^2*`1`+2*ln(h3(theta))*`1`)-beta*h3(theta)^3*`1`-chi*ln(h3(theta))^2*`1`/kappa-chi*`1`/kappa-2*chi*ln(h3(theta))*`1`/kappa = 0, h1(0) = 0, h1(1) = 0, h2(0) = 0, h2(1) = 0, h3(0) = 1, h3(1) = 1, ((D@@1)(h1))(0) = 0, ((D@@1)(h1))(1) = 0, ((D@@1)(h2))(0) = 0, ((D@@1)(h2))(1) = 0, ((D@@1)(h3))(0) = 0, ((D@@1)(h3))(1) = 0, ((D@@2)(h3))(0) = 0, ((D@@2)(h3))(1) = 0}; dsol5 := dsolve(dsys3, 'maxmesh' = 600, numeric, output = listprocedure);
%;
Error, (in dsolve/numeric/bvp/convertsys) unable to convert to an explicit first-order system

What´s the error here??????

Download laplace.mw

Code was computed on two different PC:
1) Win 8.1, Maple 17.02 x64
2) Win 8.1, Maple 18.01 x64

In brief:

n:=3: 
Grid:-Seq('f(i)', i = 1 .. n): 

works well in Maple 17.02 but gives an error in Maple 18.01. Why?

However,

(j -> Grid:-Seq('f(i)', i = 1 .. j))(n):

works well for both Maple versions.

according to examples from Maple help page
http://www.maplesoft.com/support/help/Maple/view.aspx?path=Grid%2fSeq
we have to pass exactly 'f(i)' (not just f(i)) into Grid:-Seq(...). Why?

Why doesn't Digits:=30: work properly for Grid:-Seq(...)?

For details see attached file. Output was produced in Maple 17.02. In Maple 18.01 the output will differ.

Download Grid[Seq].mw

I want to solve the equation sqrt(x) + sqrt(1 - x^2) = sqrt(2 - 3*x - 4*x^2) in RealDomain. I tried

RealDomain:-solve(sqrt(x) + sqrt(1 - x^2) = sqrt(2 - 3*x - 4*x^2),x);

And I got one solution. But, at here 

At here http://mathematica.stackexchange.com/questions/51316/how-can-i-get-the-exact-real-solution-of-this-equation 

they said the given equation has two real solutions. How must I understand?

I am not able to simplify my equation, any help would be appreciated ! I want the  term to be eliminated

Download 1.mw

Hi Mapleprimers,

I was wondering if there way a way to use restart(); and clear Maple's memory, but protect the memory in a certain variable?  I would like to return the memory to the operating system, but keep a symholic function in memory.

Alternatively, is there a way to save a symbolic function to a file, then reload it at a seperate time?

Hi MaplePrime-ers,

I'm using Maple17 in Matlab 2012b to evaluate a symbolic function over a grid of values.  The number of values is generally ~500k, and therefore I have a loop that dumps the solutions into MATLAB where the values are parsed and stored more efficiently.

I put this proceess in an optimization routine, and I keep getting crashes.  The crashes are NOT repeatable.  They generally happen after 4-10 times the routine has been called.  

This is one of the stack dumps.  Anybody have any ideas?  I talked to MATLAB support, but they weren't very useful (they started pointing fingers).

------------------------------------------------------------------------
Segmentation violation detected at Wed Jun 4 17:38:11 2014
------------------------------------------------------------------------

Configuration:
Crash Decoding : Disabled
Current Visual : 0x24 (class 4, depth 24)
Default Encoding: UTF-8
GNU C Library : 2.15 stable
MATLAB Root : /opt/Matlab/R2012b
MATLAB Version : 8.0.0.783 (R2012b)
Operating System: Linux 3.2.0-37-generic #58-Ubuntu SMP Thu Jan 24 15:28:10 UTC 2013 x86_64
Processor ID : x86 Family 6 Model 23 Stepping 6, GenuineIntel
Virtual Machine : Java 1.6.0_17-b04 with Sun Microsystems Inc. Java HotSpot(TM) 64-Bit Server VM mixed mode
Window System : The XFree86 Project, Inc (40300000), display wildnode0:15.0

Fault Count: 1

Abnormal termination:
Segmentation violation

Register State (from fault):
RAX = 00007f3bcc0a80c0 RBX = 00007f3b97fe6000
RCX = 0000000000000000 RDX = 00007f3bcc0a84a0
RSP = 00007f3b8cb29d60 RBP = 0000000000000003
RSI = 5851f42d4c957f2d RDI = 00007f3bde026360

R8 = 65a1566174cc9e28 R9 = 0000000000000002
R10 = 00007f3b8cb29d90 R11 = 0000000000002e88
R12 = 0000000000000001 R13 = 00007f3b8cb29df0
R14 = 0000000000000000 R15 = 0000000000000003

RIP = 00007f3b977d0604 EFL = 0000000000010283

CS = 0033 FS = 0000 GS = 0000

Stack Trace (from fault):
[ 0] 0x00007f3c962b01de /opt/Matlab/R2012b/bin/glnxa64/libmwfl.so+00516574 _ZN2fl4diag15stacktrace_base7captureERKNS0_14thread_contextEm+000158
[ 1] 0x00007f3c962b14b2 /opt/Matlab/R2012b/bin/glnxa64/libmwfl.so+00521394
[ 2] 0x00007f3c962b2ffe /opt/Matlab/R2012b/bin/glnxa64/libmwfl.so+00528382 _ZN2fl4diag13terminate_logEPKcRKNS0_14thread_contextE+000174
[ 3] 0x00007f3c9559f093 /opt/Matlab/R2012b/bin/glnxa64/libmwmcr.so+00557203 _ZN2fl4diag13terminate_logEPKcPK8ucontext+000067
[ 4] 0x00007f3c9559bb9d /opt/Matlab/R2012b/bin/glnxa64/libmwmcr.so+00543645
[ 5] 0x00007f3c9559d835 /opt/Matlab/R2012b/bin/glnxa64/libmwmcr.so+00550965
[ 6] 0x00007f3c9559da55 /opt/Matlab/R2012b/bin/glnxa64/libmwmcr.so+00551509
[ 7] 0x00007f3c9559e0fe /opt/Matlab/R2012b/bin/glnxa64/libmwmcr.so+00553214
[ 8] 0x00007f3c9559e295 /opt/Matlab/R2012b/bin/glnxa64/libmwmcr.so+00553621
[ 9] 0x00007f3c93a86cb0 /lib/x86_64-linux-gnu/libpthread.so.0+00064688
[ 10] 0x00007f3b977d0604 /opt/maple17/bin.X86_64_LINUX/libmaple.so+01824260
[ 11] 0x00007f3b977cfc48 /opt/maple17/bin.X86_64_LINUX/libmaple.so+01821768
[ 12] 0x00007f3b977d2f88 /opt/maple17/bin.X86_64_LINUX/libmaple.so+01834888
[ 13] 0x00007f3b9763d63f /opt/maple17/bin.X86_64_LINUX/libmaple.so+00173631
[ 14] 0x00007f3c93a7ee9a /lib/x86_64-linux-gnu/libpthread.so.0+00032410
[ 15] 0x00007f3c937ab3fd /lib/x86_64-linux-gnu/libc.so.6+01000445 clone+000109

If this problem is reproducible, please submit a Service Request via:
http://www.mathworks.com/support/contact_us/

A technical support engineer might contact you with further information.

Thank you for your help.

I want to do a step by step computation for obtaining the coefficents of the sine fourier series expansion of f(x)=x over the interval [-L,L]. The steps are as follows:

1-write the fourier expansion as: Sum(A[n]*sin(n*pi*x/L),n=1..N)
2-multiply the series by: sin(m*pi*x/L)
3-integrate the series over the interval [-L,L]
3-using the orthogonality properties of the set {sin(n*pi*x/L} compute the A[n].

I can't do these steps since I have problem with the series manipulations in maple!
Can any one suggest a way from begining to the end?

Thanks. :)
Below shows what I did in Maple 17.

Hi MaplePrimers,

I've written a function that needs to be evaluated at a bunch of different points.  Evaluating it in a loop works. I'm wondering if there was a faster way to do this because I'm evaluating a list of 400k+ sets of points.  

Right now I'm using a loop with the following code.

for i from 1 to 500000 do 
     Results(i):= f(L[i][])[1];
od;

 

If I have a function f, which has 5 arguements, f(y, w, x,y,z).

I also have a list of those arguements:  L = [[1,2,3,2,3],[4,5,6,2,3],[7,8,9,2,3]]

What would be the fastest way to get a list of results?  Also, is there a way that I could preallocate memory for this list?

Ideally, I would like to get the output as as list.  ie:

Results:= [[f(1,2,3,2,3)], [f(4,5,6,2,3)], [f(7,8,9,2,3)]]