Dear Feng,

	Thanks for spotting this typo. Indeed currently the following
  lines
	symbol x("x");
	ex a = pow(x+1/x,2);
	cout << a << endl;

	exmap mp1,  mp2;
	ex p = a.to_polynomial(mp1);
	cout << " = " << p << "\n   with " << mp1 << endl;
	p = a.expand().to_polynomial(mp2);
	cout << " = " << p << "\n   with " << mp2 << endl;

  produce the output with not a polynomial in the first instance:

(x^(-1)+x)^2
 = (x^(-1)+x)^2
   with {}
 = 2+symbol3^2+x^2
   with {symbol3==x^(-1)}

  If to_rational() is replaced by to_polynomial() as you suggested, then
  we do have (although slightly different) polynomial outputs in both cases:

(x+x^(-1))^2
 = (x+symbol3)^2
   with {symbol3==x^(-1)}
 = 2+x^2+symbol4^2
   with {symbol4==x^(-1)}

  I am attaching a one-line patch to fix this and copy the message to
  the developer list.

  Best wishes,
  Vladimir
-- 
Vladimir V. Kisil                 http://www.maths.leeds.ac.uk/~kisilv/
  Book:      Geometry of Mobius Maps       https://doi.org/10.1142/p835
  Soft:      Geometry of cycles         http://moebinv.sourceforge.net/
  Jupyter notebooks:        https://github.com/vvkisil?tab=repositories
>>>>> On Tue, 11 Jan 2022 07:10:40 +0000, Feng Feng <f.feng@outlook.com> said:

    FF> Dear Vladimir V. Kisil,

    FF> Thanks very much for suggestion to use expand() method on e3
    FF> first.

    FF> And I have given a look at the source code at
    FF> power::to_polynomial

    FF> https://www.ginac.de/reference/normal_8cpp_source.html#l02688


    FF>  ...

    FF> and I wonfer if there is a typo on line 2691, the
    FF> basis.to_rational can be replaced with basis.to_polynomial?

    FF> Best regards!  Feng