-- see src/algebra/numeigen.spad.pamphlet for documentation

(88) -> a:=matrix [[1.7,2.8,-3.5],[4.7,-2.3,4.9],[9.7,-5.2,6.3]]

         +1.7   2.8   - 3.5+
         |                 |
   (88)  |4.7  - 2.3   4.9 |
         |                 |
         +9.7  - 5.2   6.3 +
                                                                                            Type: Matrix Float
(89) -> )what op genvectors

Operations whose names satisfy the above pattern(s):

complexEigenvectors        eigenvectors               generalizedEigenvectors    innerEigenvectors
radicalEigenvectors        realEigenvectors

      To get more information about an operation such as generalizedEigenvectors , issue the command
      )display op generalizedEigenvectors
(89) -> complexEigenvectors(a::MATRIX FRAC INT,1.e-20)

   (89)
   [
     [outval= 1.6023593474 484895959 + 5.2929925254 201773538 %i, outmult= 1,
                +- 0.1761475358 4004346541 + 0.3604260666 8596495651 %i+
                |                                                      |
      outvect= [| 0.5748095297 8905553647 - 0.3455499381 8583024532 %i |]]
                |                                                      |
                +                         1.0                          +
     ,

     [outval= 1.6023593474 484895959 - 5.2929925254 201773538 %i, outmult= 1,
                +- 0.1761475358 4004346541 - 0.3604260666 8596495651 %i+
                |                                                      |
      outvect= [| 0.5748095297 8905553647 + 0.3455499381 8583024532 %i |]]
                |                                                      |
                +                         1.0                          +
     ,
                                                        +0.3277715241 0582423428+
                                                        |                       |
    [outval= 2.4952813051 03020808,outmult= 1,outvect= [|1.3430966305 237450509 |]]]
                                                        |                       |
                                                        +          1.0          +
                  Type: List Record(outval: Complex Float,outmult: Integer,outvect: List Matrix Complex Float)
(90) -> realEigenvectors(a::MATRIX FRAC INT,1.e-20)

                                                              +0.3277715241 0582423428+
                                                              |                       |
   (90)  [[outval= 2.4952813051 03020808,outmult= 1,outvect= [|1.3430966305 237450509 |]]]
                                                              |                       |
                                                              +          1.0          +
                                  Type: List Record(outval: Float,outmult: Integer,outvect: List Matrix Float)

(91) -> )what op genvalues

Operations whose names satisfy the above pattern(s):

complexEigenvalues    eigenvalues           radicalEigenvalues    realEigenvalues

      To get more information about an operation such as complexEigenvalues , issue the command )display
      op complexEigenvalues

(91) -> complexEigenvalues(a::MATRIX FRAC INT,1.e-20)

   (91)
   [2.4952813051 03020808, 1.6023593474 484895959 - 5.2929925254 201773538 %i,
    1.6023593474 484895959 + 5.2929925254 201773538 %i]
                                                                                      Type: List Complex Float
(92) -> realEigenvalues(a::MATRIX FRAC INT,1.e-20)

   (92)  [2.4952813051 03020808]
                                                                                              Type: List Float



--------------------------------------------------------------------------------------------------------------



(81) -> pol:= 2.7*x^3+7.0*x^2+9

              3        2
   (81)  2.7 x  + 7.0 x  + 9.0
                                                                                        Type: Polynomial Float
(82) -> qpol := pol::POLY FRAC INT::FRAC POLY INT

            3      2
         27x  + 70x  + 90
   (82)  ----------------
                10
                                                                             Type: Fraction Polynomial Integer
(83) -> realRoots(qpol,1.e-20)

   (83)  [- 2.9703850232 552105051]
                                                                                              Type: List Float
(84) -> complexRoots(qpol,1.e-20)

   (84)
   [- 2.9703850232 552105051, 0.1888962153 3130895627 - 1.0423565598 071182905 %i,
    0.1888962153 3130895627 + 1.0423565598 071182905 %i]
                                                                                      Type: List Complex Float
-- computationally expensive algorithm
(85) -> complexZeros(pol,1.e-15)$ComplexRootFindingPackage(FLOAT,UP(x, COMPLEX FLOAT))

   (85)
   [0.1888962153 3130895627 - 1.0423565598 071182905 %i, 0.1888962153 3130895627 + 1.0423565598 071182905 %i,
    - 2.9703850232 552105051]
                                                                                      Type: List Complex Float