Dear All,

Let $r=x_{1}^{4} + 2 \, x_{1}^{3} x_{2} + 4 \, x_{1}^{2} x_{2}^{2} + 2 \,
x_{1}
x_{2}^{3} + x_{2}^{4} + 2 \, x_{1}^{3} x_{3} + 2 \, x_{2}^{3} x_{3} + 4
\, x_{1}^{2} x_{3}^{2} + 4 \, x_{2}^{2} x_{3}^{2} + 2 \, x_{1} x_{3}^{3}
+ 2 \, x_{2} x_{3}^{3} + x_{3}^{4}$.

1. How to return the list of exponents of the monomials in $r$ in Sage?

The result I want is $[(4,0,0), (3,1,0), \ldots]$.

2. How to list of terms in Sage?

The result I want is $[x_{1}^{4}, 2 \, x_{1}^{3} x_{2}, \ldots]$.

For Question 1, I used

R.<x1,x2,x3> = PolynomialRing(QQbar, 3)

r.exponents()

This works. But when I tried to use op for Question 2. It is said that

AttributeError: 'MPolynomial_polydict' object has no attribute 'op'

How could I solve both Questions 1 and 2 in Sage? Thank you very much.

Best regards,
Jianrong.

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