## I Have a problem in Do loop...

Dears, greeting for all

I have a problem, I try to explain it by a figure

This formula does not work.

I need to substitute n=0 to give G_n+1 as a function of the parameter s, then find the limit.

.where G_n is a function in s.

this is the result

## how to express eigenvector or eigenvalues in terms...

how to express eigenvector or eigenvalues in terms of fibonacci or lucas or golden ratio?

fibonacci ratio has many

f(n)/f(n-1) , all eigenvector can not divided by any one of them

## Wrong values for Eigenvalues, depending on Digits ...

Hello!

I want to calculate Eigenvalues. Depending on values for digits and which datatype I choose Maple sometimes returns zero as Eigenvalues. Maybe there is a problem with the used routines: CLAPACK sw_dgeevx_, CLAPACK sw_zgeevx_.

 >

Problems LinearAlgebra:-Eigenvalues, Digits, ':-datatype' = ':-sfloat', ':-datatype' = ':-complex'( ':-sfloat' )

 > restart;
 > interface( ':-displayprecision' = 5 ):
 > infolevel['LinearAlgebra'] := 5; myPlatform := kernelopts( ':-platform' ); myVersion := kernelopts( ':-version' );
 (1.1)

Example 1

 > A1 := Matrix( 5, 5, [[0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], [0, 0, 0, 0, 1], [-10201/1000, 30199/10000, -5049/250, 97/50, -48/5]] );
 (1.1.1)
 > LinearAlgebra:-Eigenvalues( A1 );
 CharacteristicPolynomial: working on determinant of minor 2 CharacteristicPolynomial: working on determinant of minor 3 CharacteristicPolynomial: working on determinant of minor 4 CharacteristicPolynomial: working on determinant of minor 5
 (1.1.2)
 > A11 := Matrix( op( 1, A1 ),( i,j ) -> evalf( A1[i,j] ), ':-datatype' = ':-sfloat' );
 (1.1.3)
 > Digits := 89; LinearAlgebra:-Eigenvalues( A11 );
 Eigenvalues: calling external function Eigenvalues: initializing the output object Eigenvalues: using software external library Eigenvalues: CLAPACK sw_dgeevx_
 (1.1.4)
 > Digits := 90; LinearAlgebra:-Eigenvalues( A11 );
 Eigenvalues: calling external function Eigenvalues: initializing the output object Eigenvalues: using software external library Eigenvalues: CLAPACK sw_dgeevx_
 (1.1.5)
 > A12 := Matrix( op( 1, A1 ),( i,j ) -> evalf( A1[i,j] ), ':-datatype' = ':-complex'( ':-sfloat' ) );
 (1.1.6)
 > Digits := 100; LinearAlgebra:-Eigenvalues( A12 );
 Eigenvalues: calling external function Eigenvalues: initializing the output object Eigenvalues: using software external library Eigenvalues: CLAPACK sw_zgeevx_
 (1.1.7)
 > Digits := 250; LinearAlgebra:-Eigenvalues( A12 );
 Eigenvalues: calling external function Eigenvalues: initializing the output object Eigenvalues: using software external library Eigenvalues: CLAPACK sw_zgeevx_
 (1.1.8)
 >
 >

Example 2

 > A2 := Matrix(3, 3, [[0, 1, 0], [0, 0, 1], [3375, -675, 45]]);
 (1.2.1)
 > LinearAlgebra:-Eigenvalues( A2 );
 IntegerCharacteristicPolynomial: Computing characteristic polynomial for a 3 x 3 matrix IntegerCharacteristicPolynomial: Using prime 33554393 IntegerCharacteristicPolynomial: Using prime 33554383 IntegerCharacteristicPolynomial: Used total of  2  prime(s)
 (1.2.2)
 > A21 := Matrix( op( 1, A2 ),( i,j ) -> evalf( A2[i,j] ), ':-datatype' = ':-sfloat' );
 (1.2.3)
 > Digits := 77; LinearAlgebra:-Eigenvalues( A21 );
 Eigenvalues: calling external function Eigenvalues: initializing the output object Eigenvalues: using software external library Eigenvalues: CLAPACK sw_dgeevx_
 (1.2.4)
 > Digits := 78; LinearAlgebra:-Eigenvalues( A21 );
 Eigenvalues: calling external function Eigenvalues: initializing the output object Eigenvalues: using software external library Eigenvalues: CLAPACK sw_dgeevx_
 (1.2.5)
 > A22 := Matrix( op( 1, A2 ),( i,j ) -> evalf( A2[i,j] ), ':-datatype' = ':-complex'( ':-sfloat' ) );
 (1.2.6)
 > Digits := 58; LinearAlgebra:-Eigenvalues( A22 );
 Eigenvalues: calling external function Eigenvalues: initializing the output object Eigenvalues: using software external library Eigenvalues: CLAPACK sw_zgeevx_
 (1.2.7)
 > Digits := 59; LinearAlgebra:-Eigenvalues( A22 );
 Eigenvalues: calling external function Eigenvalues: initializing the output object Eigenvalues: using software external library Eigenvalues: CLAPACK sw_zgeevx_
 (1.2.8)
 >
 >

Example 3

 > A3 := Matrix(4, 4, [[0, 1, 0, 0], [0, 0, 1, 0], [0, 0, 0, 1], [-48841, 8840, -842, 40]]);
 (1.3.1)
 > LinearAlgebra:-Eigenvalues( A3 );
 IntegerCharacteristicPolynomial: Computing characteristic polynomial for a 4 x 4 matrix IntegerCharacteristicPolynomial: Using prime 33554393 IntegerCharacteristicPolynomial: Using prime 33554383 IntegerCharacteristicPolynomial: Used total of  2  prime(s)
 (1.3.2)
 > A31 := Matrix( op( 1, A3 ),( i,j ) -> evalf( A3[i,j] ), ':-datatype' = ':-sfloat' );
 (1.3.3)
 > Digits := 75; LinearAlgebra:-Eigenvalues( A31 );
 Eigenvalues: calling external function Eigenvalues: initializing the output object Eigenvalues: using software external library Eigenvalues: CLAPACK sw_dgeevx_
 (1.3.4)
 > Digits := 76; LinearAlgebra:-Eigenvalues( A31 );
 Eigenvalues: calling external function Eigenvalues: initializing the output object Eigenvalues: using software external library Eigenvalues: CLAPACK sw_dgeevx_
 (1.3.5)
 > A32 := Matrix( op( 1, A3 ),( i,j ) -> evalf( A3[i,j] ), ':-datatype' = ':-complex'( ':-sfloat' ) );
 (1.3.6)
 > Digits := 100; LinearAlgebra:-Eigenvalues( A32 );
 Eigenvalues: calling external function Eigenvalues: initializing the output object Eigenvalues: using software external library Eigenvalues: CLAPACK sw_zgeevx_
 (1.3.7)
 > Digits := 250; LinearAlgebra:-Eigenvalues( A32 );
 Eigenvalues: calling external function Eigenvalues: initializing the output object Eigenvalues: using software external library Eigenvalues: CLAPACK sw_zgeevx_
 (1.3.8)
 >
 >

Example 4

 > A4 := Matrix(8, 8, [[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], [-1050625/20736, 529925/1296, -15417673/10368, 3622249/1296, -55468465/20736, 93265/108, -1345/8, 52/3]]);
 (1.4.1)
 > LinearAlgebra:-Eigenvalues( A4 );
 CharacteristicPolynomial: working on determinant of minor 2 CharacteristicPolynomial: working on determinant of minor 3 CharacteristicPolynomial: working on determinant of minor 4 CharacteristicPolynomial: working on determinant of minor 5 CharacteristicPolynomial: working on determinant of minor 6 CharacteristicPolynomial: working on determinant of minor 7 CharacteristicPolynomial: working on determinant of minor 8
 (1.4.2)
 > A41 := Matrix( op( 1, A4 ),( i,j ) -> evalf( A4[i,j] ), ':-datatype' = ':-sfloat' );
 (1.4.3)
 > Digits := 74; LinearAlgebra:-Eigenvalues( A41 );
 Eigenvalues: calling external function Eigenvalues: initializing the output object Eigenvalues: using software external library Eigenvalues: CLAPACK sw_dgeevx_
 (1.4.4)
 > Digits := 75; LinearAlgebra:-Eigenvalues( A41 );
 Eigenvalues: calling external function Eigenvalues: initializing the output object Eigenvalues: using software external library Eigenvalues: CLAPACK sw_dgeevx_
 (1.4.5)
 > A42 := Matrix( op( 1, A4 ),( i,j ) -> evalf( A4[i,j] ), ':-datatype' = ':-complex'( ':-sfloat' ) );
 (1.4.6)
 > Digits := 100; LinearAlgebra:-Eigenvalues( A42 );
 Eigenvalues: calling external function Eigenvalues: initializing the output object Eigenvalues: using software external library Eigenvalues: CLAPACK sw_zgeevx_
 (1.4.7)
 > Digits := 250; LinearAlgebra:-Eigenvalues( A42 );
 Eigenvalues: calling external function Eigenvalues: initializing the output object Eigenvalues: using software external library Eigenvalues: CLAPACK sw_zgeevx_
 (1.4.8)
 >
 >
 >
 >
 >
 >
 >
 >
 >
 >

## FUNCTIONAL FORM OF INTERPOLATON...

How to get the functional form of interpolation in the given example below

GP.mw

## problems with ChiSquareSuitableModelTest...

Hi,

The procedure Statistics:-ChiSquareSuitableModelTest returns wrong or stupid results in some situations.
The stupid answer can easily be avoided if the user is careful enough.
The wrong answer is more serious: the standard deviation (in the second case below) is not correctly estimated.

PS: the expression "CORRECT ANSWER" is a short for "POTENTIALLY CORRECT ANSWER" given that what ChiSquareSuitableModelTest really does is not documented

 > restart:
 > with(Statistics):
 > randomize(): N := 100: S := Sample(Normal(0, 1), N):
 > infolevel[Statistics] := 1: # 0 parameter to fit from the sample S  CORRECT ANSWER ChiSquareSuitableModelTest(S, Normal(0, 1), level = 0.5e-1): print():
 Chi-Square Test for Suitable Probability Model ---------------------------------------------- Null Hypothesis: Sample was drawn from specified probability distribution Alt. Hypothesis: Sample was not drawn from specified probability distribution Bins:                    10 Degrees of freedom:      9 Distribution:            ChiSquare(9) Computed statistic:      15.8 Computed pvalue:         0.0711774 Critical value:          16.9189774487099 Result: [Accepted] This statistical test does not provide enough evidence to conclude that the null hypothesis is false
 (1)
 > # 2 parameters (mean and standard deviation) to fit from the sample S  INCORRECT ANSWER ChiSquareSuitableModelTest(S, Normal(a, b), level = 0.5e-1, fittedparameters = 2): print(): # verification m := Mean(S); s := StandardDeviation(S); t := sqrt(add((S-~m)^~2) / (N-1)); print(): error "the estimation of the StandardDeviation ChiSquareSuitableModelTest is not correct"; print():
 Chi-Square Test for Suitable Probability Model ---------------------------------------------- Null Hypothesis: Sample was drawn from specified probability distribution Alt. Hypothesis: Sample was not drawn from specified probability distribution Model specialization:    [a = -.2143e-1, b = .8489] Bins:                    10 Degrees of freedom:      7 Distribution:            ChiSquare(7) Computed statistic:      3.8 Computed pvalue:         0.802504 Critical value:          14.0671405764057 Result: [Accepted] This statistical test does not provide enough evidence to conclude that the null hypothesis is false
 (2)
 > # ONLY 1 parameter (mean OR standard deviation ?) to fit from the sample S  STUPID ANSWER # # A stupid answer: the parameter to fit not being declared, the procedure should return # an error of the type "don(t know what is the paramater tio fit" ChiSquareSuitableModelTest(S, Normal(a, b), level = 0.5e-1, fittedparameters = 1): print(): WARNING("ChiSquareSuitableModelTest should return it can't fit a single parameter"); print():
 Chi-Square Test for Suitable Probability Model ---------------------------------------------- Null Hypothesis: Sample was drawn from specified probability distribution Alt. Hypothesis: Sample was not drawn from specified probability distribution Model specialization:    [a = -.2143e-1, b = .8489] Bins:                    10 Degrees of freedom:      8 Distribution:            ChiSquare(8) Computed statistic:      3.8 Computed pvalue:         0.874702 Critical value:          15.5073130558655 Result: [Accepted] This statistical test does not provide enough evidence to conclude that the null hypothesis is false
 (3)
 > ChiSquareSuitableModelTest(S, Normal(a, 1), level = 0.5e-1, fittedparameters = 1):  #CORRECT ANSWER print(): # verification m := Mean(S); print():
 Chi-Square Test for Suitable Probability Model ---------------------------------------------- Null Hypothesis: Sample was drawn from specified probability distribution Alt. Hypothesis: Sample was not drawn from specified probability distribution Model specialization:    [a = -.2143e-1] Bins:                    10 Degrees of freedom:      8 Distribution:            ChiSquare(8) Computed statistic:      16.4 Computed pvalue:         0.0369999 Critical value:          15.5073130558655 Result: [Rejected] This statistical test provides evidence that the null hypothesis is false
 (4)
 > ChiSquareSuitableModelTest(S, Normal(0, b), level = 0.5e-1, fittedparameters = 1):  #CORRECT ANSWER print(): # verification s := sqrt((add(S^~2) - 0^2) / N); print():
 Chi-Square Test for Suitable Probability Model ---------------------------------------------- Null Hypothesis: Sample was drawn from specified probability distribution Alt. Hypothesis: Sample was not drawn from specified probability distribution Model specialization:    [b = .8492] Bins:                    10 Degrees of freedom:      8 Distribution:            ChiSquare(8) Computed statistic:      6.4 Computed pvalue:         0.60252 Critical value:          15.5073130558655 Result: [Accepted] This statistical test does not provide enough evidence to conclude that the null hypothesis is false
 (5)
 >

## Unwanted execution ...

Dear Users!

I have made a code using loops. But when I exceute it I go unwanted expression please see the files and try to fix it. I shall be very thankful.

Help.mw

Special request to:

## Some details about ChiSquareSuitableModelTest ...

Hi,

I seeking for informations on the Statistics:-ChiSquareSuitableModelTest procedure:

1. Once you have choose the number of bins, what strategy does this procedure use to define the bins (equal width, equal probability, other one?).

2. It seems the procedure accepts any value for this number of bins and that its correct use then is under the sole responsability of the user. Am I right?

In the book below (but I'm sure this can also be found on the web) there is a detailed discussion concerning "good practices" in using the Chi-Square goodness of fit test: does anyone known is something comparable is used in ChiSquareSuitableModelTest ?

Statistical methods in experimental physics, W.T.Eadie, D. Drijard, F.F.James, M. Roos, B. Sadoulet
North-Holland 1971
Paragraph 11.2.3 "choosing optimal bin size"

## Copy paste at times not taking place. What is the ...

I am writing a maths books using maple now. It is fantastic to use maple for writing books in maths.

 in the polynomial  This line is not copying in full line!! Step 1: Find the sum of all the coefficients in the polynomial  This line is copying in full!!                                                  r is a factor  ; 1 is a root of the polynomial. In the next row, I copy pasted the lines above in the polynomial  This line is not copying in full line!! Step 1: Find the sum of all the coefficients in the polynomial  This line is copying in full!!                                                  r is a factor  ; 1 is a root of the polynomial. In the next row, I copy pasted the lines above

Can any one find the reason?

I enclose a part of my document where in I made a particular line with text and maths formats combined.Then I made changes in the line. Now copy paste does work only for the later half (both text and maths formats). The corrected first part is not being copied.

How do I do the corrections properly so that copy paste is not a problem at laer stages.

Ramakrishnan V

## SOLVING PDE EQUATION...

Hello Anybody can help me to write codes for PDE to solve by Galerkin finite element method or any other methods can be able to gain results? parameter omega is unknown and should be determined.

I attached a pdf file for more .

Thanks so much

 >
 >
 (1)
 > #BCs can be from following
 (2)
 >
 (3)
 >

buchanan2005.pdf

## Visualising solutions to sums of polynomials...

I'm working towards creating a way to visualise real polynomial ideals! (or at least the solutions of the polynomials in the ideals) this code creates a plot showing the solutions to all the polynomials in the ideal generated by P1 and P2 (these are specified in the code)

with(plots);
P1 := x^2+2*y^2-3;
solve(P1, y);
Plot1 := plot([%], x = -2 .. 2);

P2 := -2*x^2+2*x*y+3*y^2+x-4;
solve(%, y);
Plot2 := plot([%], x = -4 .. 2);

P2*a+P1;
solve(%, y);
seq(plot([%], x = -4 .. 2), a = 0 .. 10, .1);
display(%, Plot1, Plot2)

This is because when you multiply two polynomials their set of solution curves is just the union of the sets of curves associated with the previous polynomials.

For the next step I'd like to create a graph of the solutions associated with an ideal with three generators. To stop this from being excessively messy I'd like to do it with the RGB value of the colour of a curve is determined by  a and b where the formula for a generic polynomial that we are solving and graphing is given by:

P1+a*P2+b*P3;

where P3 is given by

P3 := x*y-3

I've tried various ways to use cury to make this work (my intuition is cury is the right function to use here)  but got no where. Any ideas how to procede?

## Which sorting of differential equations related wi...

Which sorting related with famous sequence

for example

sorting differential equation in a list

then access the list with famous sequence as index such as using https://oeis.org/

after access with sequence as index, use choose function to get combinations then most result are isomorphism differential ideals?

## Permission denied : no read access...

Last month I still can read file

by

but

now it return error

and

I saw open file at c drive has many shell folders

but still the same error

i unencrypted m file by window properties

still the same error

i save file into maple roaming directory under 12 folder , still the same error

i save into maple installation directory maple 12 , still the same error

## pdsolve 2D equations with unknown parameter...

possible to solve following equation with unknown parameter omega.

parameter constant.

I see before for one dimension ode this type equation was solved.

Now for 2d equation is possible?

can consider or I can send again.

Best

2d-2

## Cloud problem. ...

Why am I not able to use my MaplePrimes login credentials to login into MapleCloud?