Admittedly, it might be difficult to extract the imaginary part of a
radical expression. But that seems to look like a bug.
%%% (412) -> xx :=
(sqrt((((-12669586846893008563685878644359325*sqrt(3)+15974693204716576905254784724655502)*nthRoot(137198597903998437385921091448494025437519087343750000000000000*sqrt(3)+172989501261663064201623395407144143954141328843750000000000000,
3)^2+(-676159865925870354666914169665824080551250000*sqrt(3)+8217402890479177097807248979603419220411058375726750000)*nthRoot(137198597903998437385921091448494025437519087343750000000000000*sqrt(3)+172989501261663064201623395407144143954141328843750000000000000,
3)-45931279578807095346392460907109478385796132783696494926118495077505668392625000000000)*sqrt(((-5401066809391479730461765*sqrt(3)+6810039372933885991985941)*nthRoot(137198597903998437385921091448494025437519087343750000000000000*sqrt(3)+172989501261663064201623395407144143954141328843750000000000000,
3)^2+3503093079743488011787977136025306152751500000*nthRoot(137198597903998437385921091448494025437519087343750000000000000*sqrt(3)+172989501261663064201623395407144143954141328843750000000000000,
3)+19580584011451989397556080279474514673471759017621573422247980153750000000000)/138)+(75458077201551937891754164660043236993041255703201346421110021520000000*sqrt(3)-95142773619263899472829762733153800309338692262462996235137171088000000)*nthRoot(137198597903998437385921091448494025437519087343750000000000000*sqrt(3)+172989501261663064201623395407144143954141328843750000000000000,
3)^2-48941566061703353092027102734653684371144117066589419560010587508867726730881752000000000000*nthRoot(137198597903998437385921091448494025437519087343750000000000000*sqrt(3)+172989501261663064201623395407144143954141328843750000000000000,
3)+547119031158247887135235714889320242561133043433631241769109111538886308888911873326867936830640527579160000000000000000000)/32996199040131120862458002308760594)-7644000*sqrt(((-5401066809391479730461765*sqrt(3)+6810039372933885991985941)*nthRoot(137198597903998437385921091448494025437519087343750000000000000*sqrt(3)+172989501261663064201623395407144143954141328843750000000000000,
3)^2+3503093079743488011787977136025306152751500000*nthRoot(137198597903998437385921091448494025437519087343750000000000000*sqrt(3)+172989501261663064201623395407144143954141328843750000000000000,
3)+19580584011451989397556080279474514673471759017621573422247980153750000000000)/138)+91052936304600216411782349862348428000000000)/133412830008771839271564000000;
Type:
AlgebraicNumber
%%% (413) -> ee := xx::Expression(INT);
Type:
Expression(Integer)
%%% (414) -> imag(ee) $ TrigonometricManipulations(ZZ, EX(ZZ))
(414) 0
Type:
Expression(Integer)
%%% (415) -> imag ee
(415) 0
Type:
Expression(Integer)
%%% (416) -> ee::Complex(Float)
(416) - 69137.1165280576_4221 + 123509.3125610854_8141 %i
Type:
Complex(Float)
In fact, the value xx is one of radicalRoots(pp) where
pp :=
x^4-2729960418308000*x^3-395258439243352250000*x^2-55499520947716391500000000*x-345363656226658026765625000000
Interestingly, when I put xx into Mathematica, I get a much nicer
expressions.
In[15]:= p1 = Root[pp, 1] // ToRadicals
Out[15]= 250 (2729960418308 + 1930373524352 Sqrt[2] -
23569 Sqrt[2 (13416226688183641 + 9486704869150589 Sqrt[2])])
In[25]:= p3 = Root[pp, 3] // ToRadicals
Out[25]= 250 (2729960418308 - 1930373524352 Sqrt[2] -
23569 I Sqrt[2 (-13416226688183641 + 9486704869150589 Sqrt[2])])
Can I somehow "convince" FriCAS to return similarly "simple" radical
expresssions?
Thank you
Ralf
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