1 | initial version |

Let me manually make the substitution $|x+iy|^2 = x^2 + y^2$ (it seems not easy to do in SageMath):

```
ineqn = (x+2)^2 + y^2 > x^2 + (y-2)^2 + 1
```

Then you can plot immediately:

```
sage: region_plot(ineqn, (-10,10), (-10,10))
```

You can also solve algebraically, using a slight workaround:

```
sage: ineqn.operator()((ineqn.lhs() - ineqn.rhs()).full_simplify(), 0)
4*x + 4*y - 1 > 0
```

Indeed, replacing `ineqn`

by `4*y + 4*x - 1 > 0`

produces the same picture.

You can also use the interface to QEPCAD to make a "cylindrical algebraic decomposition":

```
sage: qepcad((x+2)^2+y^2>x^2+(y-2)^2+1)
4 y + 4 x - 1 > 0
```

The output is a string, in QEPCAD syntax, which you can translate into SageMath by hand.

2 | No.2 Revision |

Let me manually make the substitution $|x+iy|^2 = x^2 + y^2$ (it seems not easy to do in SageMath):

```
var('x,y')
ineqn = (x+2)^2 + y^2 > x^2 + (y-2)^2 + 1
```

Then you can plot immediately:

```
sage: region_plot(ineqn, (-10,10), (-10,10))
```

You can also solve algebraically, using a slight workaround:

```
sage: ineqn.operator()((ineqn.lhs() - ineqn.rhs()).full_simplify(), 0)
4*x + 4*y - 1 > 0
```

Indeed, replacing `ineqn`

by `4*x + 4*y `

produces the same picture.~~+ 4*x ~~- 1 > 0

You can also use the interface to QEPCAD to make a "cylindrical algebraic decomposition":

`sage: `~~qepcad((x+2)^2+y^2>x^2+(y-2)^2+1)
~~qepcad(ineqn)
4 y + 4 x - 1 > 0

The output is a string, in QEPCAD syntax, which you can translate into SageMath by hand.

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