With Maplets, it is possible to create popup windows to tell or ask the user something, but only when it is appropriate. That is, it is not there all the time. A particular usage would be to give the user a facilitating question when they have incorrect entries.

Is that possible in some way with Möbius apps also? Or does one have to always keep a blank TextArea available, just a blank space if invisible perhaps but using up space in the presentation nonetheless, to give the student the information?

AOA. I want to plot the graph of the following function 

A new generalized complex representation of Euler gamma function in terms of Dirac delta function, which is

GAMMA(s) = 2*Pi*(sum((-1)^n*Dirac(s+n)/factorial(n), n = 0 .. infinity))

where*s = sigma+i*tau

for differenet values of parameters

Hi everyone,

I was trying to write a Maple sheet to calculate some perturbation theory expension as close to the "book notation" as possible. Lets for example consider a linearly perturbed harmonic oscillator with H = hω(n+1/2) and V = λ(a^†+a), this is one of the classical examples as it can be solved analytically by completing the square. In the Kato formulation (as used in the appended Maple worksheet), as well as in Rayleigh-Schrödinger perturbation theory one uses the projector onto the complement of the unperturbed state. I would like to do this by defining a projector in Maple. I've read the examples concerning projectors in Maple but it seems I have to use a rather ugly workaround by treating the states "below" the unperturbed state and the ones "above" separately. While this is a little annoying in one dimension it becomes a major nuisance in higher dimensions.

My question would be: How do I define the projector onto the complement of some state?

Cheers, Sören

Download kato_perturbation_theory.mw

i googled nullspace from ReducedRowEchelonForm

but when calculate it, ReducedRowEchelonForm do not contain the eigenvector in nullspace

how to calculate nullspace by hand?

i find that in maple 12 and maple 15 null space are different , however the common thing is that they are different from eigenvector by one of column multiply -1

is multiplication to one of column is due to rank=2 < 3, 3-2 = 1, so that random choose a column to multiply -1?

then i use elementary transformation, still can not get a rref which is like eigenvector, where is wrong?

sys1:=NewInput3-Matrix([[FirstEigenValue, 0, 0], [0, FirstEigenValue, 0], [0, 0, FirstEigenValue]]); sys1 := Matrix([[sys1[1,1], sys1[1,2], sys1[1,3]], [sys1[2,1]-sys1[2,1]/sys1[1,1]*sys1[1,1], sys1[2,2]-sys1[2,1]/sys1[1,1]*sys1[1,2], sys1[2,3]-sys1[2,1]/sys1[1,1]*sys1[1,3]], [sys1[3,1], sys1[3,2], sys1[3,3]]]);

sys1 := Matrix([[sys1[1,1], sys1[1,2], sys1[1,3]], [sys1[2,1], sys1[2,2], sys1[2,3]], [sys1[3,1]-sys1[3,1]/sys1[1,1]*sys1[1,1], sys1[3,2]-sys1[3,1]/sys1[1,1]*sys1[1,2], sys1[3,3]-sys1[3,1]/sys1[1,1]*sys1[1,3]]]);

sys1 := Matrix([[sys1[1,1]/sys1[1,1], sys1[1,2]/sys1[1,1], sys1[1,3]/sys1[1,1]], [sys1[2,1], sys1[2,2], sys1[2,3]], [sys1[3,1], sys1[3,2], sys1[3,3]]]);

sys1 := Matrix([[sys1[1,1], sys1[1,2], sys1[1,3]], [sys1[2,1], sys1[2,2], sys1[2,3]], [sys1[3,1]-sys1[3,2]/sys1[2,2]*sys1[2,1], sys1[3,2]-sys1[3,2]/sys1[2,2]*sys1[2,2], sys1[3,3]-sys1[3,2]/sys1[2,2]*sys1[2,3]]]);

sys1 := Matrix([[sys1[1,1], sys1[1,2], sys1[1,3]], [sys1[2,1]/sys1[2,2], sys1[2,2]/sys1[2,2], sys1[2,3]/sys1[2,2]], [sys1[3,1], sys1[3,2], sys1[3,3]]]);

http://rosettacode.org/wiki/Reduced_row_echelon_form#C.23

change c# code from integer to double, it return only an identity matrix. same as maple, how eigenvector come from rref?

when compare maple with sympy in python27,

sympy even do not have solution in nullspace!!!

from sympy import *
InputMatrix3 = Matrix([[31.25,30.8,30.5],[30.8,30.5,0],[30.5,0,0]])
NewInput3 := InputMatrix3.T*InputMatrix3
NewInput3.nullspace()

InputMatrix3 := Matrix([[31.25,30.8,30.5],[30.8,30.5,0],[30.5,0,0]]);
NewInput3 := MatrixMatrixMultiply(Transpose(InputMatrix3), InputMatrix3);
Old_Asso_eigenvector := Eigenvectors(NewInput3);
FirstEigenValue := solve(Determinant(NewInput3-Matrix([[lambda1, 0, 0], [0, lambda1, 0], [0, 0, lambda1]])), lambda1)[3]; # find back eigenvalue from eigenvector
SecondEigenValue := solve(Determinant(NewInput3-Matrix([[lambda1, 0, 0], [0, lambda1, 0], [0, 0, lambda1]])), lambda1)[2]; # find back eigenvalue from eigenvector
ThirdEigenValue := solve(Determinant(NewInput3-Matrix([[lambda1, 0, 0], [0, lambda1, 0], [0, 0, lambda1]])), lambda1)[1]; # find back eigenvalue from eigenvector
sys1:=NewInput3-Matrix([[FirstEigenValue, 0, 0], [0, FirstEigenValue, 0], [0, 0, FirstEigenValue]]);
sys2:=NewInput3-Matrix([[SecondEigenValue, 0, 0], [0, SecondEigenValue, 0], [0, 0, SecondEigenValue]]);
sys3:=NewInput3-Matrix([[ThirdEigenValue, 0, 0], [0, ThirdEigenValue, 0], [0, 0, ThirdEigenValue]]);
sys1b:=MatrixMatrixMultiply(NewInput3-Matrix([[FirstEigenValue, 0, 0], [0, FirstEigenValue, 0], [0, 0, FirstEigenValue]]),Matrix([[x],[y],[z]]));
sys2b:=MatrixMatrixMultiply(NewInput3-Matrix([[SecondEigenValue, 0, 0], [0, SecondEigenValue, 0], [0, 0, SecondEigenValue]]),Matrix([[x],[y],[z]]));
sys3b:=MatrixMatrixMultiply(NewInput3-Matrix([[ThirdEigenValue, 0, 0], [0, ThirdEigenValue, 0], [0, 0, ThirdEigenValue]]),Matrix([[x],[y],[z]]));

sys1:=NewInput3-Matrix([[FirstEigenValue, 0, 0], [0, FirstEigenValue, 0], [0, 0, FirstEigenValue]]);
sys2:=NewInput3-Matrix([[SecondEigenValue, 0, 0], [0, SecondEigenValue, 0], [0, 0, SecondEigenValue]]);
sys3:=NewInput3-Matrix([[ThirdEigenValue, 0, 0], [0, ThirdEigenValue, 0], [0, 0, ThirdEigenValue]]);
ReducedRowEchelonForm(sys1);
NullSpace(sys1);
NullSpace(sys2);
NullSpace(sys3);

The following code will not produce a plot. My previous attempts with different equations have worked fine. What am I missing? Thanks for any help.

restart;
with(DEtools);

sys := diff(x(t), t) = 10*x(t)-3*x(t)^2-x(t)*y(t), diff(y(t), t) = 14*y(t)-3*y(t)^2-x(t)*y(t);

with(plots);
fcns := {x(t), y(t)}; p := dsolve({sys, x(0) = 10, y(0) = 15}, fcns, type = numeric, method = classical);

odeplot(p, [[t, x(t)], [t, y(t)]], 0 .. 14);

Hi everyone,

I'm running Maple 18 and MapleSim 6.4 on my macbook pro 13 " with retina display and the GUI is blurred like there is no smoothing or the antialiasing is not working properly. I tried to find something helpfull in the setting but with no luck.

Is there something I can do to fix this?

Thanks

Carlo

got an error when try to jacobian this

with(VectorCalculus):
f1 := -2*x1-x2; f2 := -x1-4*x2; g1 := 2*x1+3*x2-6; g2 := -x1; g3 := -x2;
penalty := lambda1*max(f1-M,0) + lambda2*max(f2-M,0) + (M^2)*(max(g1,0) + max(g2,0) + max(g3,0)):
obj := eval(penalty,[lambda1=3,lambda2=0.645,M=1]);
Hf := Jacobian(Jacobian(obj, [x1, x2, x3]), [x1, x2, x3]);

Error, invalid input: VectorCalculus:-Jacobian expects its 1st argument, f,
to be of type {Vector(algebraic), list(algebraic)}, but received 3*max(0, -2*x1-x2-1)+.645*max(0, -x1-4*x2-1)+max(0, 2*x1+3*x2-6)+max(0, -x1)+max(0, -x2)

Why does MapletViewer launch the Maplet Splash Screen and then pop up a box saying it has an error launching the Maplet spash screen? As my previous question stated, it also will not run the maplet, popping up another error box as "explanation".

convert(50, base, 12);

this can change base for integer, however can not change decimal

assume i change decimal to fraction first and then apply convert base to 12 to numer and denom, and divide again to get decimal

it may get a decimal based on base 12

however, how to make this base 12 operation apply in linear algebra calculation

https://drive.google.com/file/d/0B2D69u2pweEvUDJIeGlOVjFvNWc/edit?usp=sharing
https://drive.google.com/file/d/0B2D69u2pweEvV1BiRXhULTNPcWM/edit?usp=sharing
https://drive.google.com/file/d/0B2D69u2pweEvdXNrRlNadldXS0U/edit?usp=sharing

i find that maple 15 values are the same as extreme optimization library however, the sign are different

is it maple 15 accuracy correct or extreme library correct?

https://drive.google.com/file/d/0B2D69u2pweEvT01pazBxOEk1bWc/edit?usp=sharing

i worry for my research whether based on correct accuracy.

it can run without error in maple 15, however, the eigenvector values are wrong in maple 15 different from eigenvector function's result

then i test it in maple 12, it got error when run with following input

Warning, solutions may have been lost
Error, invalid input: simplify uses a 1st argument, s, which is missing
> InputMatrix3;
                           [[30.15,29.95,29.95],[29.95,29.95,0],[29.95,0,0]]

NewInput3 := MatrixMatrixMultiply(Transpose(InputMatrix3), InputMatrix3);
FirstEigenValue := solve(Determinant(NewInput3-Matrix([[lambda1, 0, 0], [0, lambda1, 0], [0, 0, lambda1]])), lambda1)[1]; # find back eigenvalue from eigenvector
SecondEigenValue := solve(Determinant(NewInput3-Matrix([[lambda1, 0, 0], [0, lambda1, 0], [0, 0, lambda1]])), lambda1)[2]; # find back eigenvalue from eigenvector
ThirdEigenValue := solve(Determinant(NewInput3-Matrix([[lambda1, 0, 0], [0, lambda1, 0], [0, 0, lambda1]])), lambda1)[3]; # find back eigenvalue from eigenvector
v:=[ FirstEigenValue, SecondEigenValue, ThirdEigenValue];
NewMatrix3 := Matrix([[x1,x2,x3], [x4,x5,x6], [x7,x8,x9]]);
EigenvectorSol := simplify(solve({seq(seq((NewMatrix3 . NewInput3(1..-1,i))[j]=(v[i]* NewInput3(1..-1,i))[j], j=1..3), i=1..3)}, {seq(x||i, i=1..9)}));
EigenvectorT := Matrix([[rhs(EigenvectorSol[1]), rhs(EigenvectorSol[2]), rhs(EigenvectorSol[3])],[ rhs(EigenvectorSol[4]), rhs(EigenvectorSol[5]), rhs(EigenvectorSol[6])],[ rhs(EigenvectorSol[7]), rhs(EigenvectorSol[8]), rhs(EigenvectorSol[9])]]);
Old_Asso_eigenvector := Eigenvectors(MatrixMatrixMultiply(Transpose(InputMatrix3), InputMatrix3));

hi

DirectSearch answer has confused me. How to reduce the residual.
See the program.Direct.mw

Hi Maple users :)

do you know if exists a Maple package in order to perform a Panel method, for instance in the Hess-Smith version, for solving incompressible potential flow over thick 2d and 3d airfoil geometries?

Thank in advance for the help.

I have a matrix then I need to plot its columns as curves on one plot.

how to convert decimal number into given decimal number like algebra

for example, convert 191.715 , given a=12.2, b=3.5

how to find this a^2 + b^3

m := Matrix([[a1,a2,a3],[a4,a5,a6],[a7,a8,a9]]);

m2 := Determinant(m-Matrix([[1,0,0],[0,1,0],[0,0,1]]));

1. which family of polynomials do m2 belong to?

2. how to analyze m2?