1 | initial version |

This is really a long comment to calc314's answer.

`simplify`

just sends things to Maxima and back. Apparently we don't send the information about the domain to Maxima (nor is it immediately obvious to me if that would be easy).

```
Maxima 5.26.0 http://maxima.sourceforge.net
using Lisp ECL 12.12.1
Distributed under the GNU Public License. See the file COPYING.
Dedicated to the memory of William Schelter.
The function bug_report() provides bug reporting information.
(%i1) -a^2+a*conjugate(a);
(%o1) 0
(%i2) declare(a,complex);
(%o2) done
(%i3) -a^2+a*conjugate(a);
2
(%o3) a conjugate(a) - a
```

Now this is a little odd, because we *explicitly* initialize Maxima with `'domain : complex'`

. But apparently that only fixes some of these type of things.

```
Maxima 5.26.0 http://maxima.sourceforge.net
using Lisp ECL 12.12.1
Distributed under the GNU Public License. See the file COPYING.
Dedicated to the memory of William Schelter.
The function bug_report() provides bug reporting information.
(%i1) domain:complex;
(%o1) complex
(%i2) -a^2+a*conjugate(a);
(%o2) 0
```

Anyway, Trac 6862 is essentially this issue, I think.

2 | No.2 Revision |

This is really a long comment to calc314's answer.

This has nothing to do with asking for complex domain specially, because we automatically do that.

```
sage: var('a')
a
sage: b=a*a.conjugate()-a*a
sage: b
-a^2 + a*conjugate(a)
sage: simplify(b)
0
```

`simplify`

just sends things to Maxima and back. Apparently we don't send the information about the domain to Maxima (nor is it immediately obvious to me if that would be easy).

```
Maxima 5.26.0 http://maxima.sourceforge.net
using Lisp ECL 12.12.1
Distributed under the GNU Public License. See the file COPYING.
Dedicated to the memory of William Schelter.
The function bug_report() provides bug reporting information.
(%i1) -a^2+a*conjugate(a);
(%o1) 0
(%i2) declare(a,complex);
(%o2) done
(%i3) -a^2+a*conjugate(a);
2
(%o3) a conjugate(a) - a
```

Now this is a little odd, because we *explicitly* initialize Maxima with `'domain : complex'`

. But apparently that only fixes some of these type of things.

```
Maxima 5.26.0 http://maxima.sourceforge.net
using Lisp ECL 12.12.1
Distributed under the GNU Public License. See the file COPYING.
Dedicated to the memory of William Schelter.
The function bug_report() provides bug reporting information.
(%i1) domain:complex;
(%o1) complex
(%i2) -a^2+a*conjugate(a);
(%o2) 0
```

Anyway, Trac 6862 is essentially this issue, I think.

3 | No.3 Revision |

This is really a long comment to calc314's answer.

This has nothing to do with asking for complex domain specially, because we automatically do that.

```
sage: var('a')
a
sage: b=a*a.conjugate()-a*a
sage: b
-a^2 + a*conjugate(a)
sage: simplify(b)
0
```

`simplify`

just sends things to Maxima and back. Apparently we don't send the information about the domain to Maxima (nor is it immediately obvious to me if that would be easy).

```
Maxima 5.26.0 http://maxima.sourceforge.net
using Lisp ECL 12.12.1
Distributed under the GNU Public License. See the file COPYING.
Dedicated to the memory of William Schelter.
The function bug_report() provides bug reporting information.
(%i1) -a^2+a*conjugate(a);
(%o1) 0
(%i2) declare(a,complex);
(%o2) done
(%i3) -a^2+a*conjugate(a);
2
(%o3) a conjugate(a) - a
```

Now this is a little odd, because we *explicitly* initialize Maxima with `'domain : complex'`

. But apparently that only fixes some of these type of things.

```
Maxima 5.26.0 http://maxima.sourceforge.net
using Lisp ECL 12.12.1
Distributed under the GNU Public License. See the file COPYING.
Dedicated to the memory of William Schelter.
The function bug_report() provides bug reporting information.
(%i1) domain:complex;
(%o1) complex
(%i2) -a^2+a*conjugate(a);
(%o2) 0
```

Edit: according to the Maxima manual, the *only* thing this does is

```
Option variable: domain
Default value: real
When domain is set to complex, sqrt (x^2) will remain sqrt (x^2) instead of returning abs(x).
```

Sigh.

Anyway, Trac 6862 is essentially this ~~issue, I think.~~

Copyright Sage, 2010. Some rights reserved under creative commons license. Content on this site is licensed under a Creative Commons Attribution Share Alike 3.0 license.