## Export to file calculated parameters...

Asked by:

Hello,
I have some variables which usually have a specific value. I also have some parameters which are calculated using the previously mentioned constants. Sometimes though I want to change the value of the constants and re-calculate the parameters. Therefore I created a library with the initial values of the constants which I load inside a procedure which calculates the parameters. That way I can change the value of the constants and the initial values are not overwritten. My problem is that I want to export the calculated parameters and the value of the constants at the specific calculation. How do I do that_ I don't have an array, table or anything like that. Should I put my parameters in a table?

Thank you for your time.

## Finding complex roots in polynomial of infinite or...

Asked by:

Hi guys,

I am trying to solve for the roots in a polynomial of infinite order. The idea is simply to approximate the infinite polynomial by a high order Taylor expansion, solve for the roots in this polynomial (both real and complex roots exists) and use these roots as initial guesses for finding the authentic roots of the infinite polynomial in this specific range.

I have tried to use the evalf(RootOf(PolyInfinite=0,x,Re + Im)), however the output from RootOf seems to converge to the same 2 or 3 roots almost independent of the initial guess. Is there specific options of this RootOf function that can stabilize the solution or another/better command to use?

On the other hand i could solve this by simply minimizing a least sqaure, however i have not found any optimization solver which supports solutions in the complex domain?

I sincerely hope that you are able to help me.

Kind regards

Lasse

## Text disappearing from screen...

Asked by:

If I type in a function in 2D Math, the text disappears. for example, if I type fsolve(), until fsolve, the text appears, but after i type (, the whole text disappears. How should I solve this? Thanks.

## Help! Maple 18 wont write essential math symbols: ...

Asked by:

Just got Maple 18 on academic license. I've used Maple 15, 16 and 17 before this.

It wont write simple math symbols as + - * and :=

I have tried both document- and worksheet, reinstalling and so on...

What is the problem?

Thanks

## How can I display the relating value of each curve...

Asked by:

Consider the following two variable funtion:

f(x,y)=x^2+y^2-5

then we want to draw a contourplot:

contourplot(f,x=-10..10,y=-10..100)

My problem is that I want maple to diplay the value of the function "f" relating to each curve on the contour plot!
How can I do this?

Please see the following code.

Example.mw

## Using the position vector

Maple 18

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

## Curvefitting for Data...

Asked by:

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.

## Exact Values for ProjectionPlot...

Asked by:

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.

Download projection_plot.mw

## Create DNG Matrices Using Optimization

by: Maple 18

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

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")

 • XYZ to RGB

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

 Functions

 Input Data

 Solve for Camera to XYZ D50 and T

## Newbie Help - First Year University...

Asked by:

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.

## Solving a combined system of differential and part...

Asked by:

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

## How to protect variables in a module...

Asked by:

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

## how solve pde with plot in maple?...

Asked by:

Hello,

How can I pde with maple?please explain completely,and other question :How can I solve pde with plot in maple because some questions dont have exact answer?

## How to solve linear inequlities on a number line u...

Asked by:

Good afternoon.

I request your kind suggestion to my above cited query.

With thanks & Regards

M.Anand

Assistant Professor in Mathematics

SR International Institute of Technology,

Hyderabad, Andhra Pradesh, INDIA.

## Simplifying/solving a matrix...

Asked by:

I'm working on a complex problem in Composite Materials. I've gotten to a near-result 6x6 matrix, with several cells containing polynomial denominators. I have an equation for simplifying these, which boils the polynomials down to a single variable, but I can't seem to get it to substitute in. Can anyone help me solve this? The problem is also time-sensitive.

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