g := (1/8)*x*sin(13/x)+arcsin(5*x^2/(8*x^2+1))

G := unapply(g, x)

H(x) :=G(G(x))

I need to find the value of H'(pi/2). I tried this, but it didn't work;

simplify(eval(diff(H(x), x), x = (1/2)*Pi))

Will it not work for this type of question? 

Thanks :)

f(x) :=(x^(12)-x*sin(x^(11)))/(x^(34))+e^(sqrt(x+4))*ln(abs((cos(x)^(5))-6))

diff(f(x), x$2)

What would I need to type in if I would want to find f^-2(5)? I've tried this;

diff(f(5), x$2)

But it keeps giving me zero... Thanks in advance! :)

Statistics:-Histogram by default choses the vertical axis such that the area under the histogram is 1 (or something like that). In my work, I invariably need to add "frequencyscale=absolute" to get the scale I need. Is there any way to make this the default? Typing this every time gets so old... I have been looking to something analogous to plots:-setoptions but that doesn't seem to exist for Statistics.

M.D.

This is going to sounds so stupid probably, but I'm a newbie with the software and I really am clueless at the moment.

I was asked to define given information as a function, then sub -25 in for x to verify I typed the function correctly. But it's not working.. (I have a screenshot saved to my computer, but apperently I can't post it).

f(x) :=(x^(12)-x*sin(x^(11)))/(x^(34))+e^(sqrt(x+4))*ln(abs((cos^(5)x)-6))

This is my function...how do I check what value f(-25) will give me? When I calculate it (first with evalf, then without) it only showed another function as the answer, rather than the answer..sigh, I'm terrible with this software.

Dear MaplePrime's guys,

I would like that the font style of  all (new) worksheets I open are with 'style" "CMaple input" " Courier 20 "..

How could I modify the setting please? Any hint is more than welcome.

I am using Maple 16 (on a MacBook pro).

Thank for your attention,

J.-J. 

I have seen no posting on the following issue: on a high density monitor, example QHD+, where the resolution is 3200x1800, the titlebar, the palettes and the graphs are so small that they are essentially invisible. In addition, the symbols in the palettes overextend the edge of the palette. I see this with both Dell computers and Apple computers that run Maple under Windows. Is true with other computers? Is Maplesoft aware of this issue? I'm assuming it has something to do with the Java graphics library. Is there a solution?

I have an expression like this:
B0:=(phi(x))^2:
B1:=diff(phi(x),x):
B2:=diff(phi(x),x,x):
B3:=B2^2:
B4:=(phi(x))^2:
B5:=B1^2:

C0:=(psi(x))^2:
C1:=diff(psi(x),x):
C2:=:C1^2:
C3:=

D0:=(eta(x))^2:

F1:=phi(x)*psi(x):
F2:=phi(x)*eta(x):
F3:=psi(x)*eta(x):

g1:=B1*C1:
g2:=B2*phi(x):
g3:=B2*psi(x):
g4:=B2*eta(x):

T:=A0011*B0+A0022*C0+A0033*D0+A0012*F1+A0013*F2+A0023*F3+A1111*B5+A1122*C2+A1112*g1+A2011*g2+A2012*g3+A2013*g4+A2211*B5:

A0011 and A0022 and etc are constants and coefficients.

Now I want to extract some constants like A1112 or A2013 from T. Please write out an useful code for extract these coefficients!

Thanks

SmithChart.mw
 If I want to plot Smith Chart ,how do I mark a circle of arbitrary values?

then,How do I avoid the polar line to cover other  circle line?

Any body can give me some ideas or better ways to plot Smith Chart?

Thanks.

Download SmithChart.mwSmithChart.mw

Dear Maple enthusiasts,

I am unable to find a working method to solve a system of 8 equations, of which 4 are differential equations. The system contains 8 unknown variables and the goal is to find an expression for each of these variables as a function of the time t. I have attached the code of my project at the bottom of this message.

I have tried the following:

1. Using solve/dsolve to solve all 8 equations at once. This results in Maple eating up all of my memory and never finishing its calculations.
2. First using solve to solve the 4 non-differential equations so that I get 4 out of 8 variables as a function of the 4 remaining variables. This results in an expression containing RootOf() for each of the 4 veriables I'm solving for, which prevents me from using these expressions in the 4 remaining differential equations.
3. First using dsolve to solve the differential equations, which gives once again an expression for 4 variables as a function of the 4 remaining variables. I then use solve to solve the 4 remaining equations with the new found expressions. This results in an extremely long solution for each of the variables.

The code below contains the 3rd option I tried.

Any help or suggestions would be greatly appreciated. I have been scratching my head so much that I'm getting bald and whatever I search for on google or in the Maple help, I can't find a good reference to a system of differential equations together with other equations.

Download Park_-_mixed_control_model.mw

Hello all of you,

I'm new here and I have a problem.

For homework I have to write a Maple package for the usage of dual quaternions. This is not a problem.

For example two functions of the package:

MyQuaternions := module()

  export Pretty, Ugly:
  local l1:
  option package:
 
  protect('i,j,k,epsilon'):
 
Pretty := proc(q::Vector)
  description "":
  return LinearAlgebra[Transpose](q)[1..4].Vector([1,i,j,k])+epsilon*(LinearAlgebra[Transpose](q)[5..8].Vector([1,i,j,k])):
end proc:

Ugly := proc(q)
  description "":
  local a;
  a := Vector(8);
  a[1]:=remove(has,remove(has,q,epsilon),{i,j,k});
  a[2]:=coeff(remove(has,q,epsilon),i,1);
  a[3]:=coeff(remove(has,q,epsilon),j,1);
  a[4]:=coeff(remove(has,q,epsilon),k,1);
  a[5]:=remove(has,coeff(q,epsilon),{i,j,k});
  a[6]:=coeff(coeff(q,epsilon),i,1);
  a[7]:=coeff(coeff(q,epsilon),j,1);
  a[8]:=coeff(coeff(q,epsilon),k,1);
  return a:
end proc:

end module:

savelib('MyQuaternions'):

Now I can load the module in a differnet maple worksheet "main.mw" by typing "with(MyQuaternions):"

The crucial thing now is the following: i,j,k,epsilon should be protected in "main.mw". I can do this by typing "protect('i,j,k,epsilon'):" Is there a way to tell maple to protect these variables automatically when the module is loaded? Or do I always have to type in the protect command by hand?

Thank you,

Josef

For application of object recognition with 3d sensor

plot3d(subs(c=1, a*b+a*c), a=-1..1, b=-1..1);
plot3d(subs(c=1, a+a*b*c), a=-1..1, b=-1..1);

after draw above two equations, they looked having similar structure

i find a book

Differential Geometry and its application John Oprea, page 98

having some measure to determine the shape, however they seems for

2 variables and need parametric form

how to use them to determine above two equations which have 3 variables

a*b+a*c  and  a+a*b*c

though not know the 3 variables version of below code, 

i think subs(c=1, a*b+a*c), subs(a=1, a*b+a*c), subs(b=1, a*b+a*c)

3 sets of equations after substitute third variables with 1, is it still possible to determine the shape?

EFG := proc(X)
local Xu, Xv, E, F, G;
Xu := <diff(X[1],u), diff(X[2],u), diff(X[3],u)>;
Xv := <diff(X[1],v), diff(X[2],v), diff(X[3],v)>;
E := DotProduct(Xu,Xu,conjugate=false);
F := DotProduct(Xu,Xv,conjugate=false);
G := DotProduct(Xv,Xv,conjugate=
false);
simplify([E,F,G]);
end:
UN := proc(X)
local Xu, Xv, Z, s;
Xu := <diff(X[1],u), diff(X[2],u), diff(X[3],u)>;
Xv := <diff(X[1],v), diff(X[2],v), diff(X[3],v)>;
Z := CrossProduct(Xu,Xv);
s := VectorNorm(Z,Euclidean,conjugate=false);
simplify(<Z[1]/s|Z[2]/s|Z[3]/s>,sqrt,trig,symbolic);
end:
lmn := proc(X)
local Xu,Xv,Xuu,Xuv,Xvv,U,l,m,n;
Xu := <diff(X[1],u), diff(X[2],u), diff(X[3],u)>;
Xv := <diff(X[1],v), diff(X[2],v), diff(X[3],v)>;
Xuu := <diff(Xu[1],u), diff(Xu[2],u), diff(Xu[3],u)>;
Xuv := <diff(Xu[1],v), diff(Xu[2],v), diff(Xu[3],v)>;
Xvv := <diff(Xv[1],v), diff(Xv[2],v), diff(Xv[3],v)>;
U := UN(X);
l := DotProduct(U, Xuu, conjugate=false);
m := DotProduct(U, Xuv, conjugate=false);
n := DotProduct(U, Xvv, conjugate=false);
simplify([l,m,n],sqrt,trig,symbolic);
end:
shape := proc(X)
local Y,Z,a,b,c,d;
Y:=EFG(X);
Z:=lmn(X);
a:=simplify((Z[1]*Y[3]-Z[2]*Y[2])/(Y[1]*Y[3]-Y[2]^2));
b:=simplify((Z[2]*Y[1]-Z[1]*Y[2])/(Y[1]*Y[3]-Y[2]^2));
c:=simplify((Z[2]*Y[3]-Z[3]*Y[2])/(Y[1]*Y[3]-Y[2]^2));
d:=simplify((Z[3]*Y[1]-Z[2]*Y[2])/(Y[1]*Y[3]-Y[2]^2));
[S(x_u)=a*x_u+b*x_v,S(x_v)=c*x_u+d*x_v];
end:
shape_matrix := proc(X)
local Y,Z,a,b,c,d;
Y:=EFG(X);
Z:=lmn(X);
a:=simplify((Z[1]*Y[3]-Z[2]*Y[2])/(Y[1]*Y[3]-Y[2]^2));
b:=simplify((Z[2]*Y[1]-Z[1]*Y[2])/(Y[1]*Y[3]-Y[2]^2));
c:=simplify((Z[2]*Y[3]-Z[3]*Y[2])/(Y[1]*Y[3]-Y[2]^2));
d:=simplify((Z[3]*Y[1]-Z[2]*Y[2])/(Y[1]*Y[3]-Y[2]^2));
Matrix([[a,c],[b,d]]);
end:

how to convert between (system of polynomials or module) and rational function which is a four dimensional space

1. is module in algebraic geometry or group cohomology to classify homology group?

2. is final result like this? for example,

a dictionary  or table store

homology group 1, key=invariant = 1 hole in topological space , value = module 1, module 2 module 3 etc

homology group 2, key=invariant = 2 holes in topological space , value =module 4, module 5, module 6 etc

homology group 3, key=invariant = 3 holes in topological space , value = module 7, module 8.. etc

 ... etc

3. i find betti number can count holes, however how to know the form for

all combination?

i mean if it is module, how to change the module to get the full combination

http://www.singular.uni-kl.de/Manual/html/sing_159.htm

i find betti number's input is just ideal, but it is not module

if ideal is enough, why need module?

how to permuate module? and what do it classify and result in module?

1. is module in algebraic geometry for classification of topological space which a poset is a frame

2. which invariant is for doing this classification of topological space in algebraic geometry or group cohomology?

3. if want to do full combination before classification, which kind of polynomials be a full combination

4. is poset just like function fst and snd function for meet and join in functional programming instead of using "and" and "or" logic? how a matrix group related with topological space which a poset is a frame?

5. is there any invariant function for classification of topological space in maple?

I am working on fopurier analysis and below is what I have. The method I used worked fine when I had a piecewise continuous function, but now the bottom int function below is not calculating the integral.

restart;
with(plots);

f := 2*sin(Pi-Pi*exp(-t))

A[0] := (1/3)*(Int(f, t = 0 .. 3))

A[0] := (1/3)*(int(f, t = 0 .. 3))   I think this one is evaluating it correctly. The bold and italicized below is the answer from this calulation

A[0] := (2/3)*Si(Pi)-(2/3)*Si(exp(-3)*Pi)

a[n] := (2/3)*(Int(f*cos(2*Pi*n*t*(1/3)), t = 0 .. 3))  this prints the integral like I want it to.

a[n] := (2/3)*(int(f*cos(2*Pi*n*t*(1/3)), t = 0 .. 3))  this just reporints the integral, I want it to evaluate it. Am I doing something wrong? Even with the assume(n, integer); it still just prints the integral.

Is there any help that y'all can provide? My professor is not ver proficent in the Math softwares out there.