Trying

pp := x^4-2729960418308000*x^3-395258439243352250000*x^2-55499520947716391500000000*x-345363656226658026765625000000
xxx := radicalRoots(pp,'x)$RadicalSolvePackage(INT)
x4 := xxx.4
)set mess bot on

in a fresh session gives

%%% (14) -> imag(x4)

 Function Selection for imag
      Arguments: EXPR(INT)

 [1]  signature:   EXPR(INT) -> EXPR(INT)
implemented: slot (Expression (Integer))(Expression (Integer)) from TRIGMNIP(INT,EXPR(INT))
 [2]  signature:   EXPR(COMPLEX(INT)) -> EXPR(INT)
implemented: slot (Expression (Integer))(Expression (Complex (Integer))) from CTRIGMNP(INT,EXPR(COMPLEX(INT)))


   (14)  0
Type: Expression(Integer)

Interestingly, in the session where I originaly started with, I now get ... (see below). Isn't that weird?

Unfortunately, I cannot reproduce what actually caused that different behaviour for the same thing.

Oh... the modifying behaviour comes from

%%% (20) -> digits 1000

After that, I also get a non-zero expression for

  imag(x4)

Very weird.

Ralf

%%% (476) -> imag(x4)

 Function Selection for imag
      Arguments: EXPR(INT)

 [1]  signature:   EXPR(INT) -> EXPR(INT)
implemented: slot (Expression (Integer))(Expression (Integer)) from TRIGMNIP(INT,EXPR(INT))
 [2]  signature:   EXPR(COMPLEX(INT)) -> EXPR(INT)
implemented: slot (Expression (Integer))(Expression (Complex (Integer))) from CTRIGMNP(INT,EXPR(COMPLEX(INT)))


   (476)
     ROOT
                  9
               *
                    ROOT

17298950126166306420162339540714414395414132884375_
                             0000000000000
                          *
                              +-+
                             \|3
                         +

4115957937119953121577632743454820763125572620312500_
                           00000000000
                      /
                             +-+
                         27 \|3
                   ,
                       3
                 ^
                    2
              +
                -
                     33537077489620857808043115000000
                  *
                     ROOT

1729895012616630642016233954071441439541413288437_
                              50000000000000
                           *
                               +-+
                              \|3
                          +

411595793711995312157763274345482076312557262031250_
                            000000000000
                       /
                              +-+
                          27 \|3
                    ,
                        3
              +
                - 298305252478017928101288965487125000000000
           *
              ROOT
                       9
                    *
                         ROOT

172989501261663064201623395407144143954141328_
                                  843750000000000000
                               *
                                   +-+
                                  \|3
                              +

41159579371199531215776327434548207631255726203_
                                1250000000000000
                           /
                                  +-+
                              27 \|3
                        ,
                            3
                      ^
                         2
                   +
                       16768538744810428904021557500000
                    *
                       ROOT

17298950126166306420162339540714414395414132884_
                                3750000000000000
                             *
                                 +-+
                                \|3
                            +

4115957937119953121577632743454820763125572620312_
                              50000000000000
                         /
                                +-+
                            27 \|3
                      ,
                          3
                   +
                     - 298305252478017928101288965487125000000000
                /
                     9
                  *
                     ROOT

1729895012616630642016233954071441439541413288437_
                              50000000000000
                           *
                               +-+
                              \|3
                          +

411595793711995312157763274345482076312557262031250_
                            000000000000
                       /
                              +-+
                          27 \|3
                    ,
                        3
          +
              45777447049433703438392223807463148736000000000
           *
              ROOT

17298950126166306420162339540714414395414132884375000000_
                       0000000
                    *
                        +-+
                       \|3
                   +

4115957937119953121577632743454820763125572620312500000000_
                     00000
                /
                       +-+
                   27 \|3
             ,
                 3
       /
            ROOT

1729895012616630642016233954071441439541413288437500000000_
                     00000
                  *
                      +-+
                     \|3
                 +

411595793711995312157763274345482076312557262031250000000000000
              /
                     +-+
                 27 \|3
           ,
               3
         *
            ROOT
                     9
                  *
                       ROOT

17298950126166306420162339540714414395414132884_
                                3750000000000000
                             *
                                 +-+
                                \|3
                            +

4115957937119953121577632743454820763125572620312_
                              50000000000000
                         /
                                +-+
                            27 \|3
                      ,
                          3
                    ^
                       2
                 +
                     16768538744810428904021557500000
                  *
                     ROOT

1729895012616630642016233954071441439541413288437_
                              50000000000000
                           *
                               +-+
                              \|3
                          +

411595793711995312157763274345482076312557262031250_
                            000000000000
                       /
                              +-+
                          27 \|3
                    ,
                        3
                 +
                   - 298305252478017928101288965487125000000000
              /
                   9
                *
                   ROOT

172989501261663064201623395407144143954141328843750_
                            000000000000
                         *
                             +-+
                            \|3
                        +

41159579371199531215776327434548207631255726203125000_
                          0000000000
                     /
                            +-+
                        27 \|3
                  ,
                      3
  /
     6
Type: Expression(Integer)

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