Maple Questions and Posts

These are Posts and Questions associated with the product, Maple

I am using Maple 12 in Win 64. I have some difficulties in evaluating expressions in Maple. For example simply writing cos(x) then differentiating it w.r.t x. After writing cos(x) in 2D Math mode, I do right click for selecting diff but it does not work. The pointer turns in to busy mode and nothing comes to select. Also, I tried this operation in the tutorial file teaching differentiation, however problem persists.

Hello,

I'm looking to export the results of calculated variables to cells in a excel sheet.

For that purpose, I have used this code

with(ExcelTools);
Fichier:="Z:\2_Boulot\tabledeparametrage.xls";
Feuille:="Feuil1";
Export(xA1_Fus, Fichier, Feuille, "B3");

The error message is the following :

ExcelTools:-Export called with arguments: Array(1..1, 1..1, {(1, 1) = .3182057489}), Z:2_Boulot tabledeparametrage.xls, Feuil1, B3
#(ExcelTools:-Export,6): streamcall(INTERFACE_EXCEL_EXPORT(R,_params[2 .. -1]))
Error, (in ExcelTools:-Export) file I/O error La syntaxe du nom de fichier, de répertoire ou de volume est incorrecte
locals defined as: d = d, R1 = R1

Do you have idea why I didn't manage to export a result to a cell in excel ?

I think that it is probably because I don't define well the adress of my file. How do you define a the adress of a file which is contained in a folder on a harddrive in Maple?

Thanks a lot for your help.

This is an application of vector position to better understand the vector speed and acceleration is a well defined vector space. Fully developed with embedded components for proper use.

 

    Vector_Posición.mw                   (in spanish)

 

L. Araujo C.

Physics Pure

Computer Science

Let's say I have 2 functions, the first being y=sin^2(x) and the second one is y=e^(-x)cos(x). When I try to solve on Maple, it only gives me one intersecting point, while I would like to see ALL intersections between the 2 functions. How would I go about doing this?

Good day, can any one help in writing maple programme for the finite difference (FD) formulae define to solve this coupled non-linear  ODEs. See it here FDM_programme.mw Thank you

NOTE: please disregard the earlier link.

Hi. It is be good to be with you after 4 years.

I want to ask about Curvefitting for Data. If I have a numerical data and i want to find a function in x and y for these data.

After I've set my infolevel and used the ProjectionPlot command, is there any way to force Maple to display the information using exact values, instead of decimal approximations? See the attached file for the additional information.


with(Student[LinearAlgebra]):

infolevel[Student[LinearAlgebra]] := 1:

ProjectionPlot(`<,>`(-2, 3, 2), `<,>`(7, -3, -4))

 

``


Download projection_plot.mw

Obsolete

See my Camera Profiler application instead.

 

This application creates DNG matrices by optimizing Delta E from a raw photo of x-rites color checker. The color temperature for the photograph is also estimated.  Inputs are raw data from RawDigger and generic camera color response from DXO Mark.

Initialization

   

NULL

NULL

NULL

NULL

NULL

XYZoptical to RGB to XYZdata

 

 

Sr,g,b is the relative spectral transmittance of the filter array not selectivity for XY or Z of a given color.

Pulling Sr,g,b out of the integral assumes they are scalars. For example Sr attenuates X, Y and Z by the same amount.

Raw Balance is not White Point Adaptation.

The transmission loss of Red and Blue pixels relative to green is compensated by D=inverse(S). The relation to incident chromaticity, xy is unchanged as S.D=1.

(See Bruce Lindbloom; "Spectrum to XYZ" and "RGB/XYZ Matrices" also, Marcel Patek; "Transformation of RGB Primaries")

 

 

X = (Int(I*xbar*S, lambda))/N:

Y = (Int(I*ybar*S, lambda))/N:

Z = (Int(I*zbar*S, lambda))/N:

N = Int(I*ybar, lambda):

• 

XYZ to RGB

(Vector(3, {(1) = R_Tbb, (2) = G_Tbb, (3) = B_Tbb})) = (Matrix(3, 3, {(1, 1) = XR*Sr, (1, 2) = YR*Sr, (1, 3) = ZR*Sr, (2, 1) = XG*Sg, (2, 2) = YG*Sg, (2, 3) = ZG*Sg, (3, 1) = XB*Sb, (3, 2) = YB*Sb, (3, 3) = ZB*Sb})).(Vector(3, {(1) = X_Tbb, (2) = Y_Tbb, (3) = Z_Tbb}))

NULL

(Vector(3, {(1) = R_Tbb, (2) = G_Tbb, (3) = B_Tbb})) = (Matrix(3, 3, {(1, 1) = Sr, (1, 2) = 0, (1, 3) = 0, (2, 1) = 0, (2, 2) = Sg, (2, 3) = 0, (3, 1) = 0, (3, 2) = 0, (3, 3) = Sb})).(Matrix(3, 3, {(1, 1) = XR, (1, 2) = YR, (1, 3) = ZR, (2, 1) = XG, (2, 2) = YG, (2, 3) = ZG, (3, 1) = XB, (3, 2) = YB, (3, 3) = ZB})).(Vector(3, {(1) = X_Tbb, (2) = Y_Tbb, (3) = Z_Tbb}))

 

Camera_Neutral = (Matrix(3, 3, {(1, 1) = Sr, (1, 2) = 0, (1, 3) = 0, (2, 1) = 0, (2, 2) = Sg, (2, 3) = 0, (3, 1) = 0, (3, 2) = 0, (3, 3) = Sb})).(Matrix(3, 3, {(1, 1) = XR, (1, 2) = YR, (1, 3) = ZR, (2, 1) = XG, (2, 2) = YG, (2, 3) = ZG, (3, 1) = XB, (3, 2) = YB, (3, 3) = ZB})).(Vector(3, {(1) = X_wht, (2) = Y_wht, (3) = Z_wht}))

NULL

NULL

NULL

• 

RGB to XYZ (The extra step of adaptation to D50 is included below)

 

(Vector(3, {(1) = X_D50, (2) = Y_D50, (3) = Z_D50})) = (Matrix(3, 3, {(1, 1) = XTbbtoXD50, (1, 2) = YTbbtoXD50, (1, 3) = ZTbbtoXD50, (2, 1) = XTbbtoYD50, (2, 2) = YTbbtoYD50, (2, 3) = ZTbbtoYD50, (3, 1) = XTbbtoZD50, (3, 2) = YTbbtoZD50, (3, 3) = ZTbbtoZD50})).(Matrix(3, 3, {(1, 1) = RX*Dr, (1, 2) = GX*Dg, (1, 3) = BX*Db, (2, 1) = RY*Dr, (2, 2) = GY*Dg, (2, 3) = BY*Db, (3, 1) = RZ*Dr, (3, 2) = GZ*Dg, (3, 3) = BZ*Db})).(Vector(3, {(1) = R_Tbb, (2) = G_Tbb, (3) = B_Tbb})) NULL

NULL

(Vector(3, {(1) = X_D50, (2) = Y_D50, (3) = Z_D50})) = (Matrix(3, 3, {(1, 1) = XTbbtoXD50, (1, 2) = YTbbtoXD50, (1, 3) = ZTbbtoXD50, (2, 1) = XTbbtoYD50, (2, 2) = YTbbtoYD50, (2, 3) = ZTbbtoYD50, (3, 1) = XTbbtoZD50, (3, 2) = YTbbtoZD50, (3, 3) = ZTbbtoZD50})).(Matrix(3, 3, {(1, 1) = RX, (1, 2) = GX, (1, 3) = BX, (2, 1) = RY, (2, 2) = GY, (2, 3) = BY, (3, 1) = RZ, (3, 2) = GZ, (3, 3) = BZ})).(Matrix(3, 3, {(1, 1) = Dr, (1, 2) = 0, (1, 3) = 0, (2, 1) = 0, (2, 2) = Dg, (2, 3) = 0, (3, 1) = 0, (3, 2) = 0, (3, 3) = Db})).(Vector(3, {(1) = R_Tbb, (2) = G_Tbb, (3) = B_Tbb}))

NULL

(Vector(3, {(1) = X_D50, (2) = Y_D50, (3) = Z_D50})) = (Matrix(3, 3, {(1, 1) = RX_D50, (1, 2) = GX_D50, (1, 3) = BX_D50, (2, 1) = RY_D50, (2, 2) = GY_D50, (2, 3) = BY_D50, (3, 1) = RZ_D50, (3, 2) = GZ_D50, (3, 3) = BZ_D50})).(Matrix(3, 3, {(1, 1) = Dr, (1, 2) = 0, (1, 3) = 0, (2, 1) = 0, (2, 2) = Dg, (2, 3) = 0, (3, 1) = 0, (3, 2) = 0, (3, 3) = Db})).(Vector(3, {(1) = R_Tbb, (2) = G_Tbb, (3) = B_Tbb}))

NULL

(Vector(3, {(1) = X_D50wht, (2) = Y_D50wht, (3) = Z_D50wht})) = (Matrix(3, 3, {(1, 1) = RX_D50, (1, 2) = GX_D50, (1, 3) = BX_D50, (2, 1) = RY_D50, (2, 2) = GY_D50, (2, 3) = BY_D50, (3, 1) = RZ_D50, (3, 2) = GZ_D50, (3, 3) = BZ_D50})).(Matrix(3, 3, {(1, 1) = Dr, (1, 2) = 0, (1, 3) = 0, (2, 1) = 0, (2, 2) = Dg, (2, 3) = 0, (3, 1) = 0, (3, 2) = 0, (3, 3) = Db})).Camera_Neutral

NULL

Functions

   

NULL

Input Data

   

NULL

Solve for Camera to XYZ D50 and T

   

NULL

 

 

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.

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.

(Z0)   + I Ω    

(ZL) + I Ω

(ω) rad/s

α dB/m= Np/m

(β) rad/m

Zg

(l)

(z)  l

(Vg)

(u)

output:                                                                 

                

(Γ)                                 

(Γ)

            

 (SWR)  

 

(zL):

           

 (YL): S

  tanhγℓ

  tanβℓ

 (Zin):   Ω

  (zin):

    (γ):

(Vo)(z=0): V

      (Io)(z=0): A

Vo+):      V         

(Vo-):  V 

               (Vs): V

  (Is): A

             ):

  r=     ,   x=   Yo=

``
with(plots):

 

``

 

``

````

``

``

help("?")

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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.

 

 

restart:

PARK - Mixed control

 

 

Input parameters

 

 

Projected interface area (m²)

A_int:=0.025^2*Pi:

 

Temperature of the process (K)

T_proc:=1873:

 

Densities (kg/m³)

Rho_m:=7000: metal

Rho_s:=2850: slag

 

Masses (kg)

W_m:=0.5: metal

W_s:=0.075: slag

 

Mass transfer coefficients (m/s)

m_Al:=3*10^(-4):

m_Si:=3*10^(-4):

m_SiO2:=3*10^(-5):

m_Al2O3:=3*10^(-5):

 

Weight percentages in bulk at t=0 (%)

Pct_Al_b0:=0.3:

Pct_Si_b0:=0:

Pct_SiO2_b0:=5:

Pct_Al2O3_b0:=50:

 

Weight percentages in bulk at equilibrium (%)

Pct_Al_beq:=0.132:

Pct_Si_beq:=0.131:

Pct_SiO2_beq:=3.13:

Pct_Al2O3_beq:=52.12:

 

Weight percentages at the interface (%)

Constants

 

 

Atomic weights (g/mol)

AW_Al:=26.9815385:

AW_Si:=28.085:

AW_O:=15.999:

AW_Mg:=24.305:

AW_Ca:=40.078:

 

Molecular weights (g/mol)

MW_SiO2:=AW_Si+2*AW_O:

MW_Al2O3:=2*AW_Al+3*AW_O:

MW_MgO:=AW_Mg+AW_O:

MW_CaO:=AW_Ca+AW_O:

 

Gas constant (m³*Pa/[K*mol])

R_cst:=8.3144621:

 

Variables

 

 

with(PDEtools):
declare((Pct_Al_b(t),Pct_Al_i(t),Pct_Si_b(t),Pct_Si_i(t),Pct_SiO2_b(t),Pct_SiO2_i(t),Pct_Al2O3_b(t),Pct_Al2O3_i(t))(t),prime=t):

Equations

 

4 rate equations

 

 

Rate_eq1:=diff(Pct_Al_b(t),t)=-A_int*Rho_m*m_Al/W_m*(Pct_Al_b(t)-Pct_Al_i(t));

 

Rate_eq2:=diff(Pct_Si_b(t),t)=-A_int*Rho_m*m_Si/W_m*(Pct_Si_b(t)-Pct_Si_i(t));

 

Rate_eq3:=diff(Pct_SiO2_b(t),t)=-A_int*Rho_s*m_SiO2/W_s*(Pct_SiO2_b(t)-Pct_SiO2_i(t));

 

Rate_eq4:=diff(Pct_Al2O3_b(t),t)=-A_int*Rho_s*m_Al2O3/W_s*(Pct_Al2O3_b(t)-Pct_Al2O3_i(t));

 

3 mass balance equations

 

 

Mass_eq1:=0=(Pct_Al_b(t)-Pct_Al_i(t))+4*AW_Al/(3*AW_Si)*(Pct_Si_b(t)-Pct_Si_i(t));

 

Mass_eq2:=0=(Pct_Al_b(t)-Pct_Al_i(t))+4*Rho_s*m_SiO2*W_m*AW_Al/(3*Rho_m*m_Al*W_s*MW_SiO2)*(Pct_SiO2_b(t)-Pct_SiO2_i(t));

 

Mass_eq3:=0=(Pct_Al_b(t)-Pct_Al_i(t))+2*Rho_s*m_Al2O3*W_m*AW_Al/(Rho_m*m_Al*W_s*MW_Al2O3)*(Pct_Al2O3_b(t)-Pct_Al2O3_i(t));

 

1 local equilibrium equation

 

 

Gibbs free energy of the reaction when all of the reactants and products are in their standard states (J/mol). Al and Si activities are in 1 wt pct standard state in liquid Fe. SiO2 and Al2O3 activities are in respect to pure solid state.

 

delta_G0:=-720680+133*T_proc:

 

Expression of mole fractions as a function of weight percentages (whereby MgO is not taken into account, but instead replaced by CaO ?)

x_Al2O3_i(t):=(Pct_Al2O3_i(t)/MW_Al2O3)/(Pct_Al2O3_i(t)/MW_Al2O3 + Pct_SiO2_i(t)/MW_SiO2 + (100-Pct_SiO2_i(t)-Pct_Al2O3_i(t))/MW_CaO);
x_SiO2_i(t):=(Pct_SiO2_i(t)/MW_SiO2)/(Pct_Al2O3_i(t)/MW_Al2O3 + Pct_SiO2_i(t)/MW_SiO2 + (100-Pct_SiO2_i(t)-Pct_Al2O3_i(t))/MW_CaO);

 

Activity coefficients

Gamma_Al_Hry:=1: because very low percentage present  during the process (~Henry's law)

Gamma_Si_Hry:=1: because very low percentage present  during the process (~Henry's law)

Gamma_Al2O3_Ra:=1: temporary value!

Gamma_SiO2_Ra:=10^(-4.85279678314968+0.457486603678622*Pct_SiO2_b(t)); very small activity coefficient?
plot(10^(-4.85279678314968+0.457486603678622*Pct_SiO2_b),Pct_SiO2_b=3..7);

 

Activities of components

a_Al_Hry:=Gamma_Al_Hry*Pct_Al_i(t);
a_Si_Hry:=Gamma_Si_Hry*Pct_Si_i(t);
a_Al2O3_Ra:=Gamma_Al2O3_Ra*x_Al2O3_i(t);
a_SiO2_Ra:=Gamma_SiO2_Ra*x_SiO2_i(t);

 

Expressions for the equilibrium constant K

K_cst:=exp(-delta_G0/(R_cst*T_proc));

Equil_eq:=0=K_cst*a_Al_Hry^4*a_SiO2_Ra^3-a_Si_Hry^3*a_Al2O3_Ra^2;

 

Output

 

 

with(ListTools):
dsys:=Rate_eq1,Rate_eq2,Rate_eq3,Rate_eq4:
dvars:={Pct_Al2O3_b(t),Pct_SiO2_b(t),Pct_Al_b(t),Pct_Si_b(t)}:
dconds:=Pct_Al2O3_b(0)=Pct_Al2O3_b0,Pct_SiO2_b(0)=Pct_SiO2_b0,Pct_Si_b(0)=Pct_Si_b0,Pct_Al_b(0)=Pct_Al_b0:
dsol:=dsolve({dsys,dconds},dvars):

Pct_Al2O3_b(t):=rhs(select(has,dsol,Pct_Al2O3_b)[1]);
Pct_Al_b(t):=rhs(select(has,dsol,Pct_Al_b)[1]);
Pct_SiO2_b(t):=rhs(select(has,dsol,Pct_SiO2_b)[1]);
Pct_Si_b(t):=rhs(select(has,dsol,Pct_Si_b)[1]);

sys:={Equil_eq,Mass_eq1,Mass_eq2,Mass_eq3}:
vars:={Pct_Al2O3_i(t),Pct_SiO2_i(t),Pct_Al_i(t),Pct_Si_i(t)}:
sol:=solve(sys,vars);

,


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

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