** Using WeBWorK **

I want to use .roots() function in Sage to compute complex roots. However, webwork cannot recognize complex roots but only real roots. And in Sage Cell Server, if I want to compute the complex roots, it will time out but if I just want to compute real roots, it works fine. Is computing complex roots a different function? Thanks a lot for your help!

DOCUMENT(); 

loadMacros(

"PGstandard.pl",

"MathObjects.pl",

"AnswerFormatHelp.pl",

"PGcourse.pl",

"PGunion.pl",

);

TEXT(beginproblem());

Context("Complex");

Context()->constants->add( I=>{value => i} );

$SageCode1=<<END;

I = ComplexDoubleElement(0,1)

var('x')

#f1= (x+2)*(x+4)*(x+5)*(x+6)# this works, everything works well

f1= (x+2)*(x+4)*(x+5)*(x+6) + 36*(x*x-2*x+2)# this does not work, no thing will show in the answer

Root = f1.roots()

if abs(Root[0][0]) > 4: 

   Pe_real = real(Root[0][0])

   Pe_imag= imag(Root[0][0])

elif abs(Root[1][0]) >4:  

   Pe_real = real(Root[1][0])

   Pe_imag= imag(Root[1][0])

elif abs(Root[2][0]) >4:  

   Pe_real = real(Root[2][0])

   Pe_imag= imag(Root[2][0])

else :  

   Pe_real = real(Root[3][0])

   Pe_imag= imag(Root[3][0])

WEBWORK['poles1']= Pe_real + Pe_imag*I

WEBWORK['poles2']= Pe_real - Pe_imag*I

END

$result= AskSage($SageCode1,{

       accepted_tos=>true, 

});

$result->{webwork}->{poles1}=~s/e/E/g;

$result->{webwork}->{poles2}=~s/e/E/g;

$poles1= Compute($result->{webwork}->{poles1});

$poles2= Compute($result->{webwork}->{poles2});

$poles = List($poles1,$poles2);

Context()->texStrings;

BEGIN_TEXT

\( poles = \) \{ ans_rule(20)\} (Enter answer as comma separated list)

END_TEXT

Context()->normalStrings;

$showPartialCorrectAnswers = 1;

ANS( $poles -> cmp(ordered=>0));     # list of two elements

ENDDOCUMENT();