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?

Dear Friends

I have a problem in CPU time in MAPLE.

I write the codes in maple related to the nonlinear heat conduction problem in one dimension by Collocation method, but after 30 minutes no solution has been observed!!!

My codes are for N=4!, i.e., I have 25 equations with 25 unknowns!!!

If MAPLE can not solve this simple system, How can I solve 3 dimensional pdes by N=9,

In this case, I have 1000 equations with 1000 unknowns!!!

please help me and suggest me a fast iterative solver.

I should remark that my problem is stated in this paper

http://www.sciencedirect.com/science/article/pii/S1018364713000025

If there exist any other suitable method, I will be happy to receive any support.

With kind regards,

Emran Tohidi.

> restart;
> Digits := 20; N := 4; st := time(); u := sum(sum(a[m, n]*x^m*t^n, m = 0 .. N), n = 0 .. N); u := unapply(u, x, t); ut := diff(u(x, t), `$`(t, 1)); ut := unapply(ut, x, t); ku := simplify(1+u(x, t)^2); ku := unapply(ku, x, t); ux := diff(u(x, t), `$`(x, 1)); ux := unapply(ux, x, t); K := ku(x, t)*ux(x, t); K := unapply(K, x, t); Kx := diff(K(x, t), `$`(x, 1)); Kx := unapply(Kx, x, t); f := proc (x, t) options operator, arrow; x*exp(t)*(1-2*exp(2*t)) end proc;
print(`output redirected...`); # input placeholder
> S1 := {seq(u(i/N, 0)-i/N = 0, i = 0 .. N)}; S2 := {seq(u(0, j/N) = 0, j = 1 .. N)}; S3 := {seq(u(1, j/N)+ux(1, j/N)-2*exp(j/N) = 0, j = 1 .. N)}; S4 := {seq(seq(Kx(i/N, j/N)+f(i/N, j/N)-ut(i/N, j/N) = 0, i = 1 .. N-1), j = 1 .. N)}; S := `union`(`union`(`union`(S1, S2), S3), S4); sol := DirectSearch:-SolveEquations([op(S)], tolerances = 10^(-4), evaluationlimit = 1000000);
print(`output redirected...`); # input placeholder
> assign(sol);
%;
> u(x, t);
> CPUTIME := time()-st;
plot3d(u(x, t) - x exp(t), x = 0 .. 1, t = 0 .. 1)

Hello,

I just bought and installed "The mathematical Survival Kit" but I can't figure out how does it work

Anybody can help?

Thanaks

Martina

restart;

with(combinat):

symMonomial := proc(test)

h := 0;

for i from 1 to nops(test) do

                h[i] := choose(test,i);

od;

c := copy(test);

k := 0;

for k from 1 to nops(test) do

                c[k] := 0;

                for i from 1 to nops(h[k]) do

                                ki := 1;

                                for j from 1 to nops(h[k][i]) do

                                                ki := ki*h[k][i,j];

                                od;

                                c[k] := c[k] + ki;

                od;

od;

return c;

end proc;

sympoly := proc(test, number_of_roots)

with(combinat):

h := 0;

for i from 1 to nops(test) do

                h[i] := choose(z,i);

od;

c := 0;

for k from 1 to nops(test) do

                c[k] := 0;

                for i from 1 to nops(h[k]) do

                                ki := 1;

                                for j from 1 to nops(h[k][i]) do

                                                ki := ki*h[k][i,j];

                                od;

                                c[k] := c[k] + ki;

                od;

od;

poly := x^number_of_roots;

for k from 1 to number_of_roots do

                poly := poly + c[k]*x^(number_of_roots-k);

od;

end proc;

z := [x1, x2, x3, x4, x5, x6, x7, x8, x9, x10];

sigma := symMonomial(z);

f := expand(sigma[1]*sigma[2]);

f := expand(sigma[1]*sigma[1]); # two lambda value are the same

f := expand(sigma[1]*sigma[1]*sigma[1]); # three lambda value are the same

f := expand(sigma[1]^2+2*sigma[1]*sigma[2]+sigma[2]);

f := subs(x1=3, f);

f := subs(x2=2, f);

f := subs(x3=3, f);

f := subs(x4=4, f);

f := subs(x5=5, f);

f := subs(x6=6, f);

f := subs(x7=7, f);

f := subs(x8=8, f);

f := subs(x9=9, f);

f := subs(x10=lambda, f);

evalf(solve(f, lambda));

if degree(f) = 2 then

                f := f + lambda^3;

                evalf(solve(f, lambda));

end if:

how to convert above f back to matrix form such as

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

m-Matrix([[lambda,0,0],[0,lambda,0],[0,0,lambda]]);

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

after tested m2 can not be expressed in terms of shell like polynomial,

it seems that it is from symmetric polynomial and it is from a non-homogenous polynomial which homogenize with a lambda

if solve f for new eigenvalue,

can traditional eignvector method calculate new eigenvector for these new kind of eigenvalues method?

A*x = lambda*x