## finding transformation equation between two metric...

Given two metric equations, How can I find the transformation equation between these two metrices using maplesoft software?

## Angle of a triangle in geom3d[FindAngle] ...

Why in geom3d[FindAngle] we cannot get the value of the angle of a triangle greater than Pi / 2?
For example, I build a chord of a circle of unit radius along the sides of the triangle and calculate the center angle that corresponds to the given angle of the triangle. But it's not very convenient.
TR_ANGLE.mw

## dsolve taking forever to solve?...

Is there any way to simplify this code?  even with small number at discretization this take forever to solve  :(

restart;

with(plots);

numero := 5;

viscosidade := Vector[row](10, [0.000024, 0.00001113, 0.89*10^(-5), 0.00001779, 0.017299, 0.00001028, 0.927*10^(-5), 0.818*10^(-5), 0.749*10^(-5), 0.7*10^(-5)]);

H := Vector[row](8, [-0.1414243148*10^8, -0.1677843875*10^8, -0.2177577229*10^8, -0.3078557121*10^8, -0.4007777822*10^8, -0.4007777822*10^8, -0.5832487417*10^8, 0.84247483*10^7]);

a := [524, 879, 1271, 1099, 1779, -163, 241, -258, 1200, 1200];

b := [1.3383, 4.1117, 0.8467, -0.47, 0.0333, 6.78, 5.6683, 7.5933, 3, 3];
c := [-0.0008, 0.00015, -0.00145, 0.00105, 0.0008, -0.00475, -0.002, -0.00455, 0, 0];
d := [0.166667*10^(-6), -0.666667*10^(-6), 0.833333*10^(-6), -0.5*10^(-6), -0.333333*10^(-6), 0.15*10^(-5), 0.166667*10^(-6), 0.116667*10^(-5), -0.888178*10^(-15), -0.888178*10^(-15)];

Massas := Vector[row](10, [44.01, 16.04, 2.02, 28.01, 18.01, 28.05, 30.07, 44.1, 58.12, 84]);

nu := Matrix(11, 8, [[-1, -2, -2, -3, -4, -4, -6.05, -1], [-3, -4, -5, -7, -9, -9, -12.23, 1], [1, 2, 2, 3, 4, 4, 6.05, -1], [1, 0, 0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 0, 0, 1]]);

A := Vector[row](8, [65.56165, 0.045, 0.001144, 0.119*10^(-5), 0.184*10^(-9), 0.659*10^(-8), 0.198*10^(-7), 0.0000378]);
E := Vector[row](8, [83523.900, 65017, 49782, 34885.500, 27728.900, 25730.100, 23564.300, 58826.300]);
m := Vector[row](8, [0.60950, 0.37330, -0.02830, 0.43540, 0.03530, -0.25150, 0.81870, -0.36200]);
n := Vector[row](8, [-0.46790, -0.26130, 0.19130, 0.08760, 1.11630, 0.00920, 0.03420, 1.26390]);

Conc[CO] := 40.65;
Conc[H2] := 78.91;
Conc[N2] := 119.5;

Cpcte := [1.064, 14.51, 1.954, 2.889, 2.227, 2.596, 2.583, 2.619, 2.619, 2.619, 0.856, 1.056];
viscosidade := Vector[row](12, [0.0000252, 0.0000252, 0.0000252, 0.0000163, 0.0000154, 0.0000154, 0.0000154, 0.0000154, 0.0000154, 0.000023, 0.000023, 0.0000251]);
massas := Vector[row](12, [0.02801, 0.00202, 0.01801, 0.01604, 0.02805, 0.03007, 0.0441, 0.05812, 0.05812, 0.084, 0.04401, 0.02801]);

#Constantes
Rcte := 8.314;
varepsilon[B] := 0.4;
beta := 0.255;
phi := 4/3;
delta[wall] := 0.004;
lambda[wall] := 60;
h[water] := 1000;
Temp[water] := 498;
rho[B] := 380;
dt := 0.0157;
dp := 0.00015;

#Equações Auxiliares
for k to 11 do
Y[k](t, z) := Rcte*C[k](t, z)*T(t, z)/1000000;
end do;

Cp[mix] := (t, z) -> 1000*Cpcte[12];
mu[mix] := (t, z) -> viscosidade[12];
M[mix] := (t, z) -> massas[12];

h[int] := (t, z) -> rho[mix](t, z)*0.458/varepsilon[B]/((Cp[mix](t, z)*mu[mix](t, z))^4.074*(dp/mu[mix](t, z))^4.407);
Reynolds := (t, z) -> dp*rho[mix](t, z)/mu[mix](t, z);
f := (t, z) -> 172/Reynolds(t, z) + 4.36/Reynolds(t, z)^0.12;
U := (t, z) -> 1/(1/h[water] + delta[wall]/lambda[wall] + 1/h[int](t, z));
P[CO] := (t, z) -> 1000000*Y[1](t, z);
P[H2] := (t, z) -> 1000000*Y[2](t, z);
for j to 8 do
R[j](t, z) := A[j]*exp(-E[j]/(Rcte*T(t, z)))*P[CO](t, z)^m[j]*P[H2](t, z)^n[j];
end do;

#EDP's

for k to 11 do
edp[k] := diff(C[k](t, z), t) = -v(t, z)*diff(C[k](t, z), z) + rho[B]*beta*add(nu[k][j]*R[j](t, z), j = 1 .. 8);
end do;
edp[12] := diff(T(t, z), t) = -v(t, z)*diff(T(t, z), z) + rho[B]*beta*add(add(-H[j]*nu[i][j]*R[j](t, z), i = 1 .. 10), j = 1 .. 8)/(rho[mix](t, z)*Cp[mix](t, z)) - 4*U(t, z)*(T(t, z) - Temp[water])/(dt*rho[mix](t, z)*Cp[mix](t, z));
edp[13] := diff(v(t, z), z) = -v(t, z)*diff(rho[mix](t, z), z)/rho[mix](t, z);
edp[14] := diff(rho[mix](t, z), z) = M[mix](t, z)/Rcte*(-1000000*diff(T(t, z), z)/T(t, z)^2);
edp[15] := diff(PT(t, z), z) = -f(t, z)*v(t, z)^2*rho[mix](t, z)/dp;

#Discretização do Modelo
hh := 0.11/numero;
for k to 11 do
dis[k] := diff(C[k](t, z), z) = (x[k, i](t) - x[k, i - 1](t))/hh;
end do;
dis[12] := diff(T(t, z), z) = (x[12, i](t) - x[12, i - 1](t))/hh;
dis[13] := diff(rho[mix](t, z), z) = (x[13, i](t) - x[13, i - 1](t))/hh;
dis[14] := diff(v(t, z), z) = (x[14, i](t) - x[14, i - 1](t))/hh;
dis[15] := diff(PT(t, z), z) = (x[15, i](t) - x[15, i - 1](t))/hh;
for k from 16 to 26 do
dis[k] := C[k - 15](t, z) = x[k - 15, i](t);
end do;
dis[27] := T(t, z) = x[12, i](t);
dis[28] := rho[mix](t, z) = x[13, i](t);
dis[29] := v(t, z) = x[14, i](t);
dis[30] := PT(t, z) = x[15, i](t);
listadis := seq(dis[k], k = 1 .. 30);
for k to 15 do
end do;

#Resolução

ci[1, i] := x[1, i](0) = Conc[CO];
ci[2, i] := x[2, i](0) = Conc[H2];
for k from 3 to 11 do
ci[k, i] := x[k, i](0) = 0;
end do;
ci[12, i] := x[12, i](0) = 503;
ci[13, i] := x[13, i](0) = 0.005165;
ci[15, i] := x[15, i](0) = 1000000;
cis := seq(seq(eval(ci[k, i], i = j), k = 1 .. 15), j = 1 .. numero);
unassign(i);
eqs := seq(seq(eval(equacao[k], i = j), k = 1 .. 15), j = 2 .. numero);
final[1] := x[1, 1](t) = Conc[CO];
final[2] := x[2, 1](t) = Conc[H2];
for k from 3 to 11 do
final[k] := x[k, 1](t) = 0;
end do;
final[12] := x[12, 1](t) = 503;
final[13] := x[13, 1](t) = 0.005165;
final[15] := x[15, 1](t) = 1000000;
seqfinal := seq(final[k], k = 1 .. 15), eqs;
sol := dsolve({cis, seqfinal}, numeric, stiff = true, range = 0 .. 180);
odeplot(sol, [t, x[12, 4](t)], t = 0 .. 180);

## How to get this Maple V R4 worksheet in Maple 2020...

Got a lot of worksheets who are not complete anymore once opened in maple 2020

It can be only opened with a old version of Maple
Can it be imported in Maple 2020?

example

Dynmod03.mws

## How to verify Fourier transform property?...

Is there a way to verify the following Fourier transform property: F[f(x) exp(x)](k) = F[f(x)](k − b)? This is what I tried:

 >
 >
 >
 (1)
 >
 (2)
 >
 (3)
 >
 (4)
 >

## How to change definition of Fourier transform?...

Is there a way to specify options or something to change the definition of fourier and invfourier to have a 1/sqrt(2Pi) factor instead? I don't want to manually multiply the result by 1/sqrt(2Pi) every time in case I forget to do it and it leads to a mistake in the future.

## How to specify the number of points to show on a c...

Dear all,

Please I want only 8 points to show on this curve, how do I specify it?

plot(ln(1+sin(Pi*x)), x = 0 .. 1, legend = numerical, style = point, symbol = box, color = blue, symbolsize = 15, numpoints = 8);

Thank you all and kind regards.

Please do keep safe amidst this global pandemic.

## How to compute a sequence based on the digit sum o...

I would appreciate to know how to compute the following in Maple:

Sequence of distinct primes (starting term is 2) such that each subsequent term is the smallest prime not yet seen whose leading digits and the sum of the digits of the previous term are the same. It starts: 2,23,5,53,83,11,29..

it should be interesting to see which primes with first digit 3 appear (given that 3 is not a term). I would also like to be able to change the first term (eg to 3).

Best regards

David.

## The right notation for a ode ? ...

Found in old studymaterial about Loka-volterra ode

`dsolve({D(N)(t)=r*N(t)-k*N(t)^2,N(0)=N[0]},N(t));`

Seems to me not logical notation to use a D operator  : D(N)(t)  for this ode : makes it unneeded complicated this notation..or do i miss something?

## How do I remove this error ''Error, (in dsolve/nu...

Please can you help me in resolving this error?

Here is the codeOptimal_control_model_of_DF_and_LP_2.mw

## Solve linear equations with non negative variable...

Hi all, I have a linear equations 31 variables, I want to solve for m[i] >=0. Someone can help me, thank you very much.

L := {m[4]+4*m[7]+m[10]+m[13]+m[16]+m[19]+m[22] = 2*sqrt(2)+7, m[15]+3*m[18]+11*m[21]+m[6]+9*m[12]+2*m[3]-2*sqrt(2)*m[18]+6*sqrt(2)*m[21]-4*sqrt(2)*m[12]+m[24] = 2*sqrt(2)+61, -4*sqrt(2)*m[14]+6*m[14]+m[17]+11*m[20]+m[2]+4*m[5]+18*m[8]+6*sqrt(2)*m[20]-8*sqrt(2)*m[8]+m[23] = 2*sqrt(2)+34, m[27]-2*sqrt(2)*m[19]+4*sqrt(2)*m[7]+2*sqrt(2)*m[13]-2*m[16]+m[17]-6*m[19]-4*m[4]+m[5]+m[20]-16*m[7]+4*m[8]+m[11]-4*m[13]+m[14] = 6*sqrt(2)-6, m[28]+2*sqrt(2)*m[19]-4*sqrt(2)*m[10]-2*sqrt(2)*m[16]+m[15]+2*m[16]+m[18]+2*m[4]+m[6]+6*m[19]+m[21]+4*m[9]+2*m[10]+m[12]-2*m[13] = 6*sqrt(2)+21, m[25]+6*sqrt(2)*m[19]-2*sqrt(2)*m[20]-8*sqrt(2)*m[7]+4*sqrt(2)*m[8]-4*sqrt(2)*m[13]+2*sqrt(2)*m[14]+6*m[13]-4*m[14]+m[16]-2*m[17]+m[1]+4*m[4]+11*m[19]-6*m[20]-4*m[5]+18*m[7]-16*m[8] = 6*sqrt(2)-33, m[26]+6*sqrt(2)*m[19]+2*sqrt(2)*m[21]-4*sqrt(2)*m[10]-4*sqrt(2)*m[12]-2*sqrt(2)*m[16]-2*sqrt(2)*m[18]+m[13]-2*m[15]+3*m[16]+2*m[18]+2*m[1]+11*m[19]+6*m[21]+m[4]+2*m[6]+9*m[10]+2*m[12] = 6*sqrt(2)-33, m[29]+2*sqrt(2)*m[18]+6*sqrt(2)*m[20]-12*sqrt(2)*m[21]-2*sqrt(2)*m[3]-4*sqrt(2)*m[11]-2*sqrt(2)*m[15]-2*sqrt(2)*m[17]+m[14]+4*m[15]+3*m[17]-2*m[18]+2*m[2]+11*m[20]-22*m[21]+m[5]-4*m[6]+9*m[11] = 6*sqrt(2)-6, m[30]-12*sqrt(2)*m[20]+6*sqrt(2)*m[21]-2*sqrt(2)*m[2]-8*sqrt(2)*m[9]-2*sqrt(2)*m[14]-4*sqrt(2)*m[15]+2*sqrt(2)*m[17]+4*m[14]+6*m[15]-2*m[17]+m[18]+m[3]-22*m[20]+11*m[21]-4*m[5]+4*m[6]+18*m[9] = 6*sqrt(2)+21, -4*m[4]+2*m[5]+2*m[17]-2*m[18]-22*m[19]+6*m[20]-6*m[21]-2*m[16]-4*m[15]+m[31]-4*m[6]-16*m[9]+2*m[11]+4*m[13]-2*m[14]-2*sqrt(2)*m[1]+4*sqrt(2)*m[9]-2*sqrt(2)*m[17]-4*sqrt(2)*m[11]+2*sqrt(2)*m[15]+2*sqrt(2)*m[16]-12*sqrt(2)*m[19]-2*sqrt(2)*m[13]+2*sqrt(2)*m[20]-2*sqrt(2)*m[21] = 12*sqrt(2)-120}

## DataFrames -sorting by primary then secondary colu...

In reference to the nice application: https://www.mapleprimes.com/posts/209845-Dataframes--Looking-For-A-New-Flashlight by @Christopher2222 ,  my question is:

is there a simple way to sort primarily by one column, but if two elements possess identical values, then using a second column to determine the order? For example, what if we wanted to sort the flashlight dataframe primarily by "B-type" but use a subsort by "Minutes".

I wrote a function which used recursion. It worked fine for small dataframes, but was painfully slow with a multi-thousand element spreadsheet.

## Problem with pdsolve and piecewise functions...

Hello,

I have a nonhomogeneous heat conduction problem, where the thermal conductivity, the density, and the specific heat of the
material are piecewise functions.

The thermal conductivity derivative has a discontinuity that causes a problem in the pdsolve command (see the first test).

To avoid this problem, I did a second test where the product rule was calculated directly.

Is there a better way to deal with this problem?

thank you

problem.mw

## Import an indexed matrix from a .csv ...

Dear Maple community,

I am trying to import from a .csv (or .xls) a matrix, whose symbolic elements have subscripts of a type "a[1, 2, 3, 4]" (i.e., datatype=indexed). However, when I enter "ImportMatrix(csvFile, datatype = indexed)", I receive an error message "Error, (in ImportMatrix) unable to store '0' when datatype=indexed". I would highly appreciate your help with importing an indexed matrix. Thank you.