1 | initial version |

This is defined behaviour of the general inverse, as far as I understand from the code. For example,

```
sage: parent(~1)
Rational Field
```

The definition of `Matrix_generic_dense.__invert__()`

explicitly states

```
Return this inverse of this matrix, as a matrix over the fraction field.
```

I'm not an algebraist so no comment on that but, with symbolics you would stay in the ring, so symbolics seems to be good for something, contrary to many a belief.

```
sage: mat = matrix([[x^2]])
sage: mati = mat.inverse(); mati
[x^(-2)]
sage: mati[0,0].parent()
Symbolic Ring
```

2 | No.2 Revision |

This is defined behaviour of the general inverse, as far as I understand from the code. For example,

```
sage: parent(~1)
Rational Field
```

The definition of `Matrix_generic_dense.__invert__()`

explicitly states

```
Return this inverse of this matrix, as a matrix over the fraction field.
sage: R.fraction_field()
Fraction Field of Univariate Polynomial Ring in t over Integer Ring
```

I'm not an algebraist so no comment on that but, with symbolics you would stay in the ring, so symbolics seems to be good for something, contrary to many a belief.

```
sage: mat = matrix([[x^2]])
sage: mati = mat.inverse(); mati
[x^(-2)]
sage: mati[0,0].parent()
Symbolic Ring
```

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