1 | initial version |

As explained in the documentation, `qepcad`

is supposed to deal with polynomials, so it is likely it is not able to handle the square root (nor the fraction). The following works:

```
sage: qepcad(qf.implies(qf.and_(f>0, f<=1, z>=0, z^2*(1+4*f/5)>=1), ((z + f)^2 - f^2 - 1)^2 + (z - 1 + 2*f)^2 - 4*f^2>0))
TRUE
```

The main concern is that it does not raises an error when there is a square root in the formula (probably a lack of sanity checking). I will have a deeper look to the source code and tell if i found something intersting.

2 | No.2 Revision |

As explained in the documentation, `qepcad`

is supposed to deal with polynomials, so it is likely it is not able to handle the square root (nor the fraction). The following works:

```
sage: qepcad(qf.implies(qf.and_(f>0, f<=1, z>=0, z^2*(1+4*f/5)>=1), ((z + f)^2 - f^2 - 1)^2 + (z - 1 + 2*f)^2 - 4*f^2>0))
TRUE
```

The main concern is that it does not raises an error when there is a square root in the formula (probably a lack of sanity checking). I will have a deeper look to the source code and tell if i found something ~~intersting.~~interesting. Thanks for reporting anyway.

3 | No.3 Revision |

As explained in the documentation, `qepcad`

is supposed to deal with polynomials, so it is likely it is not able to handle the square root (nor the fraction). ~~The following works:~~So, a correct way to formulate your statement using qepcad would be the following:

```
sage: qepcad(qf.implies(qf.and_(f>0, f<=1, z>=0, z^2*(1+4*f/5)>=1), ((z + f)^2 - f^2 - 1)^2 + (z - 1 + 2*f)^2 - 4*f^2>0))
TRUE
```

The main concern is that it does not raises an error when there is a square root in the formula (probably a lack of sanity ~~checking). ~~checking and/or error handling). I will have a deeper look to the source code and tell if ~~i found something interesting. ~~it couls be improved. Thanks for reporting anyway.

4 | No.4 Revision |

As explained in the documentation, `qepcad`

is supposed to deal with polynomials, so it is likely it is not able to handle the square root (nor the fraction). So, a correct way to formulate your statement using qepcad would be the following:

```
sage: qepcad(qf.implies(qf.and_(f>0, f<=1, z>=0, z^2*(1+4*f/5)>=1), ((z + f)^2 - f^2 - 1)^2 + (z - 1 + 2*f)^2 - 4*f^2>0))
TRUE
```

The main concern is that it does not raises an error when there is a square root in the formula (probably a lack of sanity checking and/or error handling). I will have a deeper look to the source code and tell if it ~~couls ~~could be improved. Thanks for reporting anyway.

5 | No.5 Revision |

As explained in the documentation, `qepcad`

is supposed to deal with polynomials, so it is likely it is not able to handle the square root (nor the fraction). So, a correct way to formulate your statement using qepcad would be the ~~following:~~following (note the additional `z>=0`

because of the square):

```
sage: qepcad(qf.implies(qf.and_(f>0, f<=1, z>=0, z^2*(1+4*f/5)>=1), ((z + f)^2 - f^2 - 1)^2 + (z - 1 + 2*f)^2 - 4*f^2>0))
TRUE
```

The main concern is that it does not raises an error when there is a square root in the formula (probably a lack of sanity checking and/or error handling). I will have a deeper look to the source code and tell if it could be improved. Thanks for reporting anyway.

6 | No.6 Revision |

As explained in the documentation, `qepcad`

is supposed to deal with polynomials, so it is likely it is not able to handle the square root (nor the fraction). So, a correct way to formulate your statement using qepcad would be the following (note the additional `z>=0`

because of the square):

```
sage: qepcad(qf.implies(qf.and_(f>0, f<=1, z>=0, z^2*(1+4*f/5)>=1), ((z + f)^2 - f^2 - 1)^2 + (z - 1 + 2*f)^2 - 4*f^2>0))
TRUE
```

The main concern is that it does not raises an error when there is a square root in the formula (probably a lack of sanity checking and/or error handling). I will have a deeper look to the source code and tell if it could be improved. Thanks for reporting anyway.

**EDIT**

`qepcad`

seem indeed not able to deal with the sqrt, but Sage interace does not handle the error, here is a qepcad session:

```
Enter a variable list:
(f,z)
Enter the number of free variables:
0
Enter a prenex formula:
(A f) (A z) [[f > 0 /\ f <= 1 /\ z >= 1/sqrt(4/5 f + 1)] ==> ((f + z)^2 - f^2 - 1)^2 + (2 f + z - 1)^2 - 4 f^2 > 0]
Error RPFACTREAD: Digit was expected.
(A f) (A z) [[f > 0 /\ f <= 1 /\ z >= 1/s
```

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