## Can Maple find a determinant corresponding to a sy...

For exaqmple, the quadratic equation w^2 + uw + v = 0 corresponds to the deter minant

| -u  1  1  |

| v    0  1  |  = 0

|w^2 w w-1|

Is there any way to find a determinant corresponding to an equation, as above?

This is an issue in the preparation of a nomograph for the initial equation.

It is generally solved by trial and error.

## Why is Determinant often incorrect for matrices wi...

When I use the Determinant function on a matrix with (single variable) polynomial entries with real coefficients I often get an incorrect answer. I know the answers are incorrect because they have a higher degree or a lower lowest degree than is possible given the matrix elements.

However, when I replace the coefficients in the polynomials with rational numbers or I put in the option method=minor, I get the correct answer.

The problem seems to be roundoff error. However, the important error is not simply small changes in the resulting polynomial. The important error is the presence of entirely incorrect powers of the variable and not with very small coefficients.

How does this happen and why does the help page for Determinant( ) not warn of this behavior? In particuiar, why does the help page not say that using Gaussian elimination (i.e., the default) will often give incorrect answers in such cases, but using method=minor will work? Is this behavior known? I cannot find any reference to it on the internet.

## need to procedure for calculating......

hi....how i can extract Coefficients  (i.e. {f1[2],f2[2],f2[3],f3[2],.....f3[6]}) from every algebric equations and create matrix A ,in form AX=0, (X are f1[2],f2[2],f2[3],f3[2],.....f3[6] ) then the determinant of the matrix of coefficients (A) set to zero for obtaining unknown parameter omega.?

Note that  if m=3 then 6 equations is appeare and if m=4 then 9 equations is appeare.thus i need a procedure that works for every arbitary value of ''m''.

in attached file below m=4 thus we have 9 equations, i.e. 3 for eq1[k_] and 3 for eq2[k_] and so on...

also we should use boundary conditions for some amount of fi[j] (i=1,2,3 and j=2,3,...,7)

be extacting above Coefficients for example from first equation ,

''**:= (1/128)*f1[2]*omega^2-(1/4)*f2[2]-(1/2)*f2[3]+(1/4)*f2[4]+(1/4)*f3[2]-(1/2)*f3[3]+(1/4)*f3[4]+140*f1[2]-80*f1[3]+20*f1[4]'''

must compute

coeff(**, f1[2]); coeff(**, f2[2]) and so on...

fdm-maple.mw

############################Define some parameters

############################Define some equation

######################################  APPLY BOUNDARY CONDITIONS

 (1)

## Impose rank deficiency of a matrix...

Hello everybody,

I would like to ask: How many ways to impose the rank deficiency of a matrix J?

1. First is the determinant(J) = 0

2. Multiply with a non-zero vector V: so that we have J*V = 0;

3. ...to be listed......

something about the minors of the matrix?

I hope to have as many methods as possible!

## Generate invertible 4x4 matrices over F_2 ...

Hi, here is the code I used to try to generate all invertible 4x4 matrices over the finite field F_2 = {0.1}. However, when I look at the elements of GROUP (see below) all the elements are 4x4 matrices with a 2 in each entry. I don't know why this is?

Also, I need help converting all of the invertible 4x4 matrices in the following way: I want the 4x4 matrices to each be written as a string of length 16 with no spaces, commas or brackets. So for example the matrix

a b c d

e f g h

i j k l

m n o p

becomes abcdefghijklmnop

restart:
with(LinearAlgebra):
PRIME := 2;
2

# the group of invertible 4 x 4 matrices over the field F_p

GROUP := []:
M := Matrix([[a,b,c,d],[x,f,g,h],[y,j,k,l],[m,n,o,p]]):
for a from 0 to PRIME-1 do
for b from 0 to PRIME-1 do
for c from 0 to PRIME-1 do
for d from 0 to PRIME-1 do
for x from 0 to PRIME-1 do
for f from 0 to PRIME-1 do
for g from 0 to PRIME-1 do
for h from 0 to PRIME-1 do
for y from 0 to PRIME-1 do
for j from 0 to PRIME-1 do
for k from 0 to PRIME-1 do
for l from 0 to PRIME-1 do
for m from 0 to PRIME-1 do
for n from 0 to PRIME-1 do
for o from 0 to PRIME-1 do
for p from 0 to PRIME-1 do
if Determinant(M) mod PRIME <> 0 then
GROUP := [ op(GROUP), M ]
fi
od od od od od od od od od od od od od od od od:

nops(GROUP);
20160

GROUP;

## Determinant of coefficient matrix...

I want to set the determinant of the coefficient matrix equal to zero and then solving for the roots. But I could not achieve it via Maple. Can you help me please?

You can reach two examples in the following file.  Yeni_Microsoft_Word_Belgesi_(2).docx

Besides. how can i compute the following transcental equations via maple

sinh(beta*L)*sin(beta*L)=0

cosh(beta*L)*cos(beta*L)-1=0

cosh(beta*L)*cos(beta*L)+1=0

regards

mehmet

## How to factorize to matrix ...

from determinant's polynomial?

## Problem with procedure...

I tried to make a procedure that would find the determinant of any 3x3 matrix but I keep getting unterminated procedure what should I change??

Code:
DeterminantMat:=proc(matA::Array)
local  i::integer,  j::integer,  x::integer,  y::integer,  A::integer,  B::integer,  indice::integer,  S::integer:
A:=0:  B:=0:  S:=0: i:= 1:  j:=1:  x:=1:  y := 1:  indice:=1:

for x from 1 to 3 do
indice := 1:
for i  from 1 to  3 do
if x = i then
end do:
else if x <>i then
for j from 1 to 3 do
if y = j then  end do:
else if indice = 1 then  A := matA(i,j):  indice := 2:
else if indice = 2 then  B:=matA(i,j):  indice :=3:
else if indice = 3 then  B :=B * matA(i,j):  indice :=4:
else if indice = 4 then  A := A * matA(i,j):
if x = 2 then  S := S + (-1 * matA(x,y)) * (A-B):
else  S := S + matA(x,y) * (A-B):   end if:   end if:
end do:
end if:
end do:
end do:
end proc:

## Problem with Determinant...

hi.after calculate Determinant of matrix  and gain value omega'' ω'' by fsolve rule ,when substuting result (ω) in matrix (q) and calculate Determinant again, this value is not zero!!!! may i use LUDecomposition?determinan.mw

## Error in determinant ...

hi...amount of Determinant  is infinity?how i can remove this bad calculation ?

thanks...mode_shape2.mw

## Simplifying multivariate polynomial ...

I have a multivariate polynomial in x and y. How can I firstly collect the terms with respect to the powers of x and y and then simplifying their coefficients.

 >
 >
 >
 >
 (1)
 >
 (2)
 >

## How can i solve nonlinear equation?...

Hi all,

I need to solve det[M]=0 for omega.

M is:

M := Matrix(8, 8, {(1, 1) = BesselJ(n, tp*a), (1, 2) = 0, (1, 3) = 0, (1, 4) = 0, (1, 5) = -BesselJ(n, tg*a), (1, 6) = -BesselY(n, tg*a), (1, 7) = 0, (1, 8) = 0, (2, 1) = k*n*BesselJ(n, tp*a)/(tp^2*a), (2, 2) = I*k*n*mu0*omega*(diff(BesselJ(n, tp*a), a))/(tp^2*a), (2, 3) = 0, (2, 4) = 0, (2, 5) = -k*n*BesselJ(n, tg*a)/(tg^2*a), (2, 6) = -k*n*BesselY(n, tg*a)/(tg^2*a), (2, 7) = -I*`&mu;g`*omega*(diff(BesselJ(n, tg*a), a))/tg^2, (2, 8) = -I*`&mu;g`*omega*(diff(BesselY(n, tg*a), a))/tg^2, (3, 1) = 0, (3, 2) = BesselJ(n, tp*a), (3, 3) = 0, (3, 4) = 0, (3, 5) = 0, (3, 6) = 0, (3, 7) = -BesselJ(n, tg*a), (3, 8) = -BesselY(n, tg*a), (4, 1) = -I*omega*`&varepsilon;p`*(diff(BesselJ(n, tp*a), a))/tp^2, (4, 2) = k*n*BesselJ(n, tp*a)/(tp^2*a), (4, 3) = 0, (4, 4) = 0, (4, 5) = I*`&varepsilon;g`*omega*(diff(BesselJ(n, tg*a), a))/tg^2, (4, 6) = I*`&varepsilon;g`*omega*(diff(BesselY(n, tg*a), a))/tg^2, (4, 7) = -k*n*BesselJ(n, tg*a)/(tg^2*a), (4, 8) = -k*n*BesselY(n, tg*a)/(tg^2*a), (5, 1) = 0, (5, 2) = 0, (5, 3) = k*n*BesselY(n, t0*b)/(t0^2*b), (5, 4) = I*mu0*omega*(diff(BesselY(n, t0*b), b))/t0^2, (5, 5) = -k*n*BesselJ(n, tg*b)/(tg^2*b), (5, 6) = -k*n*BesselY(n, tg*b)/(tg^2*b), (5, 7) = -I*`&mu;g`*omega*(diff(BesselJ(n, tg*b), b))/tg^2, (5, 8) = -I*`&mu;g`*omega*(diff(BesselY(n, tg*b), b))/tg^2, (6, 1) = 0, (6, 2) = 0, (6, 3) = BesselY(n, t0*b), (6, 4) = 0, (6, 5) = -BesselJ(n, tg*b), (6, 6) = -BesselY(n, tg*b), (6, 7) = 0, (6, 8) = 0, (7, 1) = 0, (7, 2) = 0, (7, 3) = 0, (7, 4) = BesselY(n, t0*b), (7, 5) = 0, (7, 6) = 0, (7, 7) = -BesselJ(n, tg*b), (7, 8) = -BesselY(n, tg*b), (8, 1) = 0, (8, 2) = 0, (8, 3) = -I*epsilon0*omega*(diff(BesselY(n, t0*b), b))/t0^2, (8, 4) = -k*n*BesselY(n, t0*b)/(t0^2*b), (8, 5) = I*`&varepsilon;g`*omega*(diff(BesselJ(n, tg*b), b))/tg^2, (8, 6) = I*`&varepsilon;g`*omega*(diff(BesselY(n, tg*b), b))/tg^2, (8, 7) = -k*n*BesselJ(n, tg*b)/(tg^2*b), (8, 8) = -k*n*BesselY(n, tg*b)/(tg^2*b)});

and n=0,1,2.

Except of omega and k ,other parameters is canstant.

After using
with(LinearAlgebra):
detM := Determinant(M):

I used solve(detM=0,omega) and fsolve() but it dosnt work. how can i solve it?

Thanks alot.

## Calculating determinant of a matrix of Bessel Func...

Hello Everyone

I am new to Maple and I have to find the determinant of the following matrix

Here k is a constant.

## Error trying to Solve unknown variable within a de...

Hi there,

I am trying to compute the following, and I am getting this error.

> A := map(convert, M, unit_free)*Unit('m'*(1/'s'^2));
(I had to put the Unit('m'*(1/'s'^2)) because the original units were kNm/s^2 (kg), and even though I simplified it, it's still using kNm/s^2, and leaves the m/s^2 for some reason when I try to remove the units. I tried simply changing the units on the original matrix, but the units menu has disappeared from the right-click menu!!)

> B := map(convert, K, unit_free);

solve;

Error, (in assuming) when calling 'Engine:-Dispatch'. Received: 'should not happen: Rename expects the input to contain unknown functions'

Why is it giving me this error? omega is an unknown variable that I am trying to solve for. I am going a modal analysis, so maybe there is a better way to find omega?

Any help appreciated!

Raquel

## on the frequent change of determinant in each run ...

Hi,

Recently a a simple problem which i can not handle by myself, made me confused.

I have simple code of maple which is not stable at all. Everytime I run the code, the final result which is the determinant of a matrix, changes and I can not see the problem with the code. In fact i noticed that problem occures when the matrix is being build by culculating the coefficients of some constant values.  I have attached the code. Could you see what is wrong here?

Thanks by the way.