Unanswered Questions

This page lists MaplePrimes questions that have not yet received an answer

g3 := tanh(x+1);
a:=eval(diff(g3,x$n)/n!, x=0) assuming n>=0:
tanhx := sum(a*x^n, n=0..infinity):
tanhx2 := subs(x^n=subs(_C1=0, subs(t=n!, g2))*x^n, tanhx):
diff(tanhx2, x) - tanhx2;
 

would like to find a operator to make it equalt to itself , a new differential operator for new transcendental function tanhx2

I wonder - would it be possible to automate the following way of adding a legend to plots? If so - how?

plot([f(x), g(x), 7], legend = ['f(x)' = f(x), 'g(x)' = g(x), y = 7]);


In my opinion such a legend makes the plot much more readable - but most students (and others) will usually be too lazy to type this out, hence the wish for it be to automated.

Any help will be much appreciated.

In Maple 17, the following expression needs to be integrated with respect to q3, p3 and q. Here, mu is a real, positive scalar. 

a := 1/(sqrt(mu^2+(px-p3x-q3x)^2)*sqrt(mu^2+(-p3x+qx-q3x)^2)*sqrt(mu^2+q3x^2)*(sqrt(mu^2+(-p3x+qx-q3x)^2)+sqrt(mu^2+q3x^2)))

However, the integration will not work with the "int" command (e.g. wrt q3). The indefinite integration will work if the integral is evaluated using the steps: highlight expression -> right click -> Integrate -> wrt q3 command.

The output of the integral (using the above method) is very long, it's impossible to manipulate the answer (on my i5, 8GB machine running Maple 17) because it is very tough to copy such a long output. Also, there is no way to specify that mu is a positive scalar. 

Is there a better way to perform the integration, e.g. between 0 and lambda, -1 through 1, or -infinity to +infinity?  

 

Assume I had a 2D line

how to put and draw this line into a new geometric world defined by patch?

I have gotten an expression:

eq21 := collect(eq20, [exp(-sqrt(s)*x/sqrt(Dp)), exp(sqrt(s)*(-lh+x)/sqrt(Dp)), exp((-2*lh+x)*sqrt(s)/sqrt(Dp)), exp((lh-x)*sqrt(s+thetac)/sqrt(Dc))], simplify);

q(x, s) = exp(-sqrt(s)*x/sqrt(Dp))*_F1(s)+sqrt(Dp)*(-Dp*sqrt(s+thetac)*alpha1*pinf*s^2-2*Dp*sqrt(s+thetac)*alpha1*pinf*s*thetac-Dp*sqrt(s+thetac)*alpha1*pinf*thetac^2+A2*Dp*sqrt(s+thetac)*alpha1*s+A2*Dp*sqrt(s+thetac)*alpha1*thetac+Dc*sqrt(s+thetac)*alpha1*pinf*s^2+Dc*sqrt(s+thetac)*alpha1*pinf*s*thetac+A1*Dc*alpha1*s^2+A1*Dc*alpha1*s*thetac+A1*sqrt(Dc)*sqrt(s+thetac)*s^2+A1*sqrt(Dc)*sqrt(s+thetac)*s*thetac-A2*Dc*sqrt(s+thetac)*alpha1*s)*exp(sqrt(s)*(-lh+x)/sqrt(Dp))/((s+thetac)^(3/2)*(-sqrt(Dp)*alpha1+sqrt(s))*s*(Dc*s-Dp*s-Dp*thetac))+(sqrt(Dp)*alpha1+sqrt(s))*_F1(s)*exp((-2*lh+x)*sqrt(s)/sqrt(Dp))/(-sqrt(Dp)*alpha1+sqrt(s))+Dc*A1*exp((lh-x)*sqrt(s+thetac)/sqrt(Dc))/((Dc*s-Dp*s-Dp*thetac)*sqrt(s+thetac))-(-pinf*s-pinf*thetac+A2)/((s+thetac)*s)

I need to further simplify the coefficient of

exp(sqrt(s)*(-lh+x)/sqrt(Dp))

Would you like to give some tips?

Thanks.

 

how to calculate potential energy in terms of gauss curvature?

how to find back a patch in maple from Pi+GaussCurvature*Area(triangle) = Pi

restart:
with(LinearAlgebra):
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 proc;

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 proc:

GK := proc(X)
local E,F,G,l,m,n,S,T;
S := EFG(X);
T := lmn(X);
E := S[1];
F := S[2];
G := S[3];
l := T[1];
m := T[2];
n := T[3];
simplify((l*n-m^2)/(E*G-F^2),sqrt,trig,symbolic);
end proc:

sph := <f(u,v)|g(u,v)|h(u,v)>;
cur := GK(sph);
X := sph;
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);
AreaTriangle := int(int(Z[1]^2+Z[2]^2+Z[3]^2,v=-Pi/2..Pi/2),u=0..2*Pi);
dsolve(Pi+cur*AreaTriangle = Pi, [f(u,v),g(u,v),h(u,v)]);
 

I have a package of routines meant to help Danish highschool students use Maple. I would like to use MapleCloud to distribute this but have run into a major stumbling block:

While Maple is perfectly happy to use non-latin letters such as the Scandinavian letters æ, ø and å it seems that MapleCloud can't handle that. Specifically, strings containing such letters is displayed in garbled form (the non-latin letters are shows as squares), and symbolic names containing such characters seems not to be recognized. The latter problem in particular makes MapleCloud quite useless to me.

I have attached a simple workbook demonstrating the problems to this message.

 i need a help on how to find the local truncation error of a hybird block method of three order IVP. here is the one of the discrete methods i need to find the local truncation error. please any solution should put here thanks 


Hi. I would like to learn to use your package. The example  document for it not running (for me). Included a screen shot and my test document. Basicially It would like to import .mpl procedures and use them as the exports of a module/package. I have no experience with code editors and this is the first time I have tried to use the code edit region. Also whathat does the (**) mean/do?

Edit: I redid the documet.


 

restart

``

with(CodeBuilder)

[Build, Directory, Export, File, Import, Mint, Read, Regions, Version]

(1)

"Directory("interface('worksheetdir')")"

"C:\Users\Ronan\AppData\Local\Temp\Rtestm"

(2)

Regions()

["Rtestm.mpl", "NewTest.mpl", "NewTest_ModuleApply.mpl"]

(3)

libname

"C:\Program Files\Maple 2017\lib", "C:\Users\Ronan\maple\toolbox\CodeBuilder\lib", "C:\Users\Ronan\maple\toolbox\personal\lib"

(4)
Rtestm := module ()

_m2199891725024

["C:\Users\Ronan\AppData\Local\Temp\Rtestm\Rtestm.mpl", "C:\Users\Ronan\AppData\Local\Temp\Rtestm\NewTest.mpl", "C:\Users\Ronan\AppData\Local\Temp\Rtestm\NewTest_ModuleApply.mpl"]

``

NewTest:=module()

"This is a NEW TEST"

_m2199890918688

``

``

ModuleApply:=proc()

proc () print("This is a NEW TEST") end proc

``

"" CodeBuilder:-Build"('mint','maplet', 'infolevel'=2,  'prefix' = "#!",  'main' = "Rtestm.mpl");"

mint, maplet, infolevel = 2, prefix = "#!", main = "Rtestm.mpl"

(5)

Rtestm:-Rtest()

"this is a test"

(6)

""Rtestm:-NewTest"()"

``

``

currentdir()

"C:\Users\Ronan\Documents\MAPLE\Rational_Trinonometry"

(7)

restart

Read*"C:\\Users\\Ronan\\AppData\\Local\\Temp\\Rtestm\\Rtestm.mpl"

Read*"C:\Users\Ronan\AppData\Local\Temp\Rtestm\Rtestm.mpl"

(8)

Rtestm:-Rtest()

Error, Rtest is not a command in the Rtestm package

 

Rtestm:-NewTest()

Error, NewTest is not a command in the Rtestm package

 

``


 

Download 1-CodeBuilder_Pkg_test.mw

@Joe Riel 

mathcontainerUses_Doubt.mw
 

restart; d[1] := [2.36, 26.90], [2.75, 30.0], [3.14, 31.9], [3.53, 32.8], [3.93, 33.4], [4.32, 32.8], [4.71, 31.9]

[2.36, 26.90], [2.75, 30.0], [3.14, 31.9], [3.53, 32.8], [3.93, 33.4], [4.32, 32.8], [4.71, 31.9]

(1)

NULL

d[2] := [2.36, 32.40], [2.75, 34.90], [3.14, 36.90], [3.53, 38.00], [3.93, 38.40], [4.32, 37.8], [4.71, 36.5]

[2.36, 32.40], [2.75, 34.90], [3.14, 36.90], [3.53, 38.00], [3.93, 38.40], [4.32, 37.8], [4.71, 36.5]

(2)

d[3] := [2.36, 27.9], [2.75, 28.3], [3.14, 30.0], [3.53, 30.9], [3.93, 31.3], [4.32, 30.8], [4.71, 29.7]

[2.36, 27.9], [2.75, 28.3], [3.14, 30.0], [3.53, 30.9], [3.93, 31.3], [4.32, 30.8], [4.71, 29.7]

(3)

y := a*x^2+b*x+c; for i to 3 do d[i] := [d[i]]; c[i] := CurveFitting[LeastSquares](d[i], x, curve = y) end do

HFloat(8.047886108501745)+HFloat(11.793324911833839)*x-HFloat(1.5172878997894277)*x^2

(4)

 

curve1 := [c[1], c[2]]; k[1] := [1, 2]; curve1p := [d[1], d[2]]; l[1] := "plot 1"

"plot 1"

(5)

curve2 := [c[2], c[3]]; k[2] := [2, 3]; curve2p := [d[2], d[3]]; l[2] := "plot 2"

"plot 2"

(6)

curve3 := [c[1], c[3]]; k[3] := [1, 3]; curve3p := [d[1], d[3]]; l[3] := "plot 3"

"plot 3"

(7)
Table 1

 

xlabel := "Brake Power"; ylabel := "Efficiency"

"Efficiency"

(8)

p1 := plot(curve1, x = 2.0 .. 5.0, labels = [xlabel, ylabel], labeldirections = ["horizontal", "vertical"], color = [black], linestyle = [1, 2], thickness = [3, 1], title = Title, caption = "Fig. 1 cool  Example 1", legend = ["curve1", "curve2"]); p2 := plot(curve1p, style = point, color = [black], symbol = [soliddiamond, box], symbolsize = 10); plots:-display(p1, p2)

 

p1 := plot(curve2, x = 2.0 .. 5.0, labels = [xlabel, ylabel], labeldirections = ["horizontal", "vertical"], color = [black], linestyle = [1, 2], thickness = [3, 1], title = Title, caption = "Fig. 1 cool  Example 1", legend = ["curve1", "curve2"]); p2 := plot(curve2p, style = point, color = [black], symbol = [box, point], symbolsize = 10); plots:-display(p1, p2)

 

p1 := plot(curve3, x = 2.0 .. 5.0, labels = [xlabel, ylabel], labeldirections = ["horizontal", "vertical"], color = [black], linestyle = [1, 2], thickness = [3, 1], title = Title, caption = "Fig. 1 cool  Example 1", legend = ["curve1", "curve2"]); p2 := plot(curve3p, style = point, color = [black], symbol = [soliddiamond, point], symbolsize = 10); plots:-display(p1, p2)

 

 

"for j from 1 to 3 do  print( Report on l[j]); for i in k[j] do x1(i):=solve((&DifferentialD;)/(&DifferentialD; x)c[i]);  y1(i):=eval( c[i], [x = x1(i)]):  print( Maximum brake thermal efficiency of,y1(i) "%"occurs at brake power value of , x1(i)kW);  end do;  end do;"

Maximum*brake*thermal*efficiency*of, HFloat(30.964188366461613)*"%"*occurs*at*brake*power*value*of, 3.886317459*kW

(9)

NULL


 

Download mathcontainerUses_Doubt.mw

Can any one state the uses of mathcontainer?

1. It can store only one algebraic expression at a time?

2. Can it handle list of algebraic expressions?

3. Can it store list data points (x,y) for a list of curves?

4. Can there be any use for click to edit this component?

More than a simple Yes or No a simple example for each yes answer would be very helpful.

I enclose a document with list of coordinates for for three curves, expression for curve fitting, three expressions derived for these plot points (coordinates), a command for optimum y for each of the three curves (maximum y and corresponding x value), 

Thanks for answering.

Ramakrishnan V

Please can someone help with maple comand to obtain Jacobian elliptic functions particularly in code editing region?

this equation is complicated

how to dsolve for this equation for function f ?

f(t,x,diff(x,t)) - f(t,x,p) - (diff(x,t)-p)*diff(f(t,x,p), p) = tan(t)
 

updated:
P := evalm(p2 + c*vector([cos(q1+q2+q3), sin(q1+q2+q3)]));
 
restart:
with(Groebner):
p1 := vector([a*cos(q1), a*sin(q1)]);
p2 := evalm(p1 + b*vector([cos(q1+q2), sin(q1+q2)]));
P := evalm(p2 + c*vector([cos(q1+q2+q3), sin(q1+q2+q3)]));
Pe := map(expand, P);
A := {cos(q1) = c1, sin(q1) =s1, cos(q2)=c2, sin(q2)=s2, cos(q3)=c3, sin(q3)=s3};
P := subs(A, op(Pe));
F1 := [x - P[1], y - P[2], s1^2+c1^2-1, s2^2+c2^2-1, s3^2+c3^2-1 ];
F2 := subs({a=1, b=1, c=1}, F1);
 
g2 := Basis(F2, plex(c3, s3, c2, s2, c1, s1));
LeadingTerm(g2[1], plex(c3, s3, c2, s2, c1, s1));
LeadingTerm(g2[2], plex(c3, s3, c2, s2, c1, s1));
LeadingTerm(g2[3], plex(c3, s3, c2, s2, c1, s1));
LeadingTerm(g2[4], plex(c3, s3, c2, s2, c1, s1));
LeadingTerm(g2[5], plex(c3, s3, c2, s2, c1, s1));
LeadingTerm(g2[6], plex(c3, s3, c2, s2, c1, s1));
LeadingTerm(g2[7], plex(c3, s3, c2, s2, c1, s1));
LeadingTerm(g2[8], plex(c3, s3, c2, s2, c1, s1));
LeadingTerm(g2[9], plex(c3, s3, c2, s2, c1, s1));
 
                                   1, c1
                               2       2    2   2
                           16 y  + 16 x , s1  s2
                                           2
                                 8 x, c1 s2
                                2      2    2  
                             2 y  + 2 x , s1  c2
                                 2 x, c1 c2
                            3            2        
                         2 x  - 2 x + 2 y  x, s2 c2
                                        2
                                   1, c2
                                   2 x, s3
                                    2, c3
originally i think
g2[1], g2[7], g2[9] have single variables c1, c2, c3 respectively
can be used to solve system
 
but without x and y, these equations can not be used
if choose leading term has x and y , but there is no single variable s1 or c1.
 
originally expect solve as follows
g2spec := subs({x=1, y=1/2}, [g2[3],g2[5],g2[6]]);
S1 := [solve([g2spec[1]])];
q1a := evalf(arccos(S1[1]));
q1b := evalf(arccos(S1[2]));
S2 := [solve(subs(s1=S1[1], g2spec[2])), solve(subs(s1=S1[2], g2spec[2])) ];
q2a := evalf(arccos(S2[1]));
q2b := evalf(arccos(S2[2]));
S3 := [solve(subs(s1=S2[1], g2spec[2])), solve(subs(s1=S2[2], g2spec[2])) ];
q2a := evalf(arccos(S3[1]));
q2b := evalf(arccos(S3[2]));
 

Not sure if this is documented explicitly to Maple users, but normally (prior to Maple 2017) interface(typesetting=extended) was all that was required to output display diff(y(x),x) as y'(x)

With Maple 2017 typesetting=extended is default and one must use with(Typesetting)  Settings(typesetprime=true) in order to output the display of diff(y(x),x) as y'(x).

Perhaps this is well documented somewhere, however I was unable to find the change. 

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