1 | initial version |

The code you provide is not valid, so I don't think this is what you have... The example below show the definition of a polynomial ring, a random polynomial from this ring, and then the polynomial with all coefficients replaced by $1$. The idea is to get the list of monomials, and then simply sum this list.

```
sage: R.<x1, x2, x3> = QQ[] # polynomial ring over QQ
sage: g = R.random_element(10) # random polynopmial of degree 10
sage: g
3*x1^4*x2^5*x3 - 4*x1^7*x2*x3 + 8*x1*x2^7*x3 + 1/3*x1^4*x3^5 - 5*x1^6*x3
sage: g.monomials() # the monomials of g
[x1^4*x2^5*x3, x1^7*x2*x3, x1*x2^7*x3, x1^4*x3^5, x1^6*x3]
sage: sum(g.monomials()) # their sum
x1^4*x2^5*x3 + x1^7*x2*x3 + x1*x2^7*x3 + x1^4*x3^5 + x1^6*x3
```

2 | No.2 Revision |

The code you provide is not valid, so I don't think this is what you have... The example below show the definition of a polynomial ring, a random polynomial from this ring, and then the polynomial with all coefficients replaced by $1$. The idea is to get the list of monomials, and then simply sum this list.

```
sage: R.<x1, x2, x3> = QQ[] # polynomial ring over QQ
sage: g = R.random_element(10) # random
```~~polynopmial ~~polynomial of degree 10
sage: g
3*x1^4*x2^5*x3 - 4*x1^7*x2*x3 + 8*x1*x2^7*x3 + 1/3*x1^4*x3^5 - 5*x1^6*x3
sage: g.monomials() # the monomials of g
[x1^4*x2^5*x3, x1^7*x2*x3, x1*x2^7*x3, x1^4*x3^5, x1^6*x3]
sage: sum(g.monomials()) # their sum
x1^4*x2^5*x3 + x1^7*x2*x3 + x1*x2^7*x3 + x1^4*x3^5 + x1^6*x3

Note that the use of `sum(...)`

is equivalent to the following:

```
sage: g0 = R.zero() # the polynomial equal to zero
sage: for m in g.monomials():
....: g0 += m
```

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