1 | initial version |

Yes it is the rank over the polynomial ring. Houw could it be the rank over the rationals ? Note that `x`

and `y`

do not belong to the rational field, but the rank depends on the rational values you associate (the zero vector has rank 0, the other have rank one):

```
sage: J.substitute({x:0,y:0}).rank()
0
sage: J.substitute({x:0,y:1}).rank()
1
```

2 | No.2 Revision |

Yes it is the rank over the polynomial ring. Houw could it be the rank over the rationals ? Note that `x`

and `y`

do not belong to the rational field, but the rank depends on the rational values you associate to them (the zero vector has rank 0, the other have rank one):

```
sage: J.substitute({x:0,y:0}).rank()
0
sage: J.substitute({x:0,y:1}).rank()
1
```

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