1 | initial version |

What Sage version are you using?

In Sage 7.3 (the latest public release):

```
$ sage -v
SageMath version 7.3, Release Date: 2016-08-04
$ sage -q
sage: x, y, z, lam = var('x' ,'y' ,'z', 'lam')
sage: F = x*y*z - lam * (x*y*z-9); F
x*y*z - (x*y*z - 9)*lam
sage: dFx = diff(F, x)
sage: dFy = diff(F, y)
sage: dFz = diff(F, z)
sage: dFlam = diff(F, lam)
sage: dFx, dFy, dFz, dFlam
(-lam*y*z + y*z, -lam*x*z + x*z, -lam*x*y + x*y, -x*y*z + 9)
sage: solve([dFx == 0, dFy == 0, dFz == 0, dFlam == 0], x, y, z, lam)
[[x == 9/(r1*r2), y == r1, z == r2, lam == 1]]
sage:
```

2 | No.2 Revision |

~~What Sage version are you using?~~

In This seems to work in Sage 7.3 (the latest public ~~release):~~release).

Not sure what change between Sage 7.2 and Sage 7.3 made this work.

One could try to check which ticket is responsible among those merged in Sage 7.3.

http://www.sagemath.org/changelogs/sage-7.3.txt

```
$ sage -v
SageMath version 7.3, Release Date: 2016-08-04
$ sage -q
sage: x, y, z, lam = var('x' ,'y' ,'z', 'lam')
sage: F = x*y*z - lam * (x*y*z-9); F
x*y*z - (x*y*z - 9)*lam
sage: dFx = diff(F, x)
sage: dFy = diff(F, y)
sage: dFz = diff(F, z)
sage: dFlam = diff(F, lam)
sage: dFx, dFy, dFz, dFlam
(-lam*y*z + y*z, -lam*x*z + x*z, -lam*x*y + x*y, -x*y*z + 9)
sage: solve([dFx == 0, dFy == 0, dFz == 0, dFlam == 0], x, y, z, lam)
[[x == 9/(r1*r2), y == r1, z == r2, lam == 1]]
sage:
```

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