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


> 
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) 


