When factoring polynomials (see Section 6.12.10), by default Xcas won’t introduce complex numbers if they aren’t already being used. For example,
simply returns
x2+2 |
but if an expression already involves complex numbers then Xcas uses them;
will return
⎛ ⎜ ⎝ | x−i | √ |
| ⎞ ⎟ ⎠ | ⎛ ⎜ ⎝ | i x− | √ |
| ⎞ ⎟ ⎠ |
Xcas can also find complex roots when complex
numbers are not present; for example, the command cfactor
(see Section 6.12.10) will factor over the complex numbers.
cFactor is a synonym for cfactor.
returns
⎛ ⎜ ⎝ | x+i | √ |
| ⎞ ⎟ ⎠ | ⎛ ⎜ ⎝ | x−i | √ |
| ⎞ ⎟ ⎠ |
If you want Xcas to use complex numbers by default, you can turn on complex mode. In complex mode,
returns
⎛ ⎜ ⎝ | x+i | √ |
| ⎞ ⎟ ⎠ | ⎛ ⎜ ⎝ | x−i | √ |
| ⎞ ⎟ ⎠ |
You can turn on complex mode from the CAS configuration screen (see Section 3.5.7). This mode is determined by the value of the variable complex_mode; if this is 1 then complex mode is on, if this is 0 then complex mode is off. This option will be stored in the configuration file (see Section 3.5.10), and so can also be set there.