6.12.8 Multiplication by the conjugate quantity: mult_conjugate
The mult_conjugate tries to remove square roots from the
bottom of an expression.
-
mult_conjugate takes one argument:
expr, an
expression. The denominator or numerator is supposed to contain a
square root.
- mult_conjugate(expr) returns the following:
-
If expr is a fraction and the denominator contains a
square root, then this expression is returned with the numerator and
denominator multiplied by the conjugate of the denominator.
- If expr is a fraction and the numerator, but not the
denominator, contains a square root (if expr is not a
fraction, it is regarded as a fraction with a denominator of 1),
then this expression is returned with the numerator and denominator multiplied by the
conjugate of the numerator.
Examples.
-
Input:
mult_conjugate((2+sqrt(2))/(2+sqrt(3)))
Output:
| ⎛
⎜
⎝ | 2+ | √ | | ⎞
⎟
⎠ | ⎛
⎜
⎝ | 2− | √ | | ⎞
⎟
⎠ |
|
|
⎛
⎜
⎝ | 2+ | √ | | ⎞
⎟
⎠ | ⎛
⎜
⎝ | 2− | √ | | ⎞
⎟
⎠ |
|
|
- Input:
mult_conjugate((2+sqrt(2))/(sqrt(2)+sqrt(3)))
Output:
| ⎛
⎜
⎝ | 2+ | √ | | ⎞
⎟
⎠ | ⎛
⎜
⎝ | − | √ | | + | √ | | ⎞
⎟
⎠ |
|
|
⎛
⎜
⎝ | √ | | + | √ | | ⎞
⎟
⎠ | ⎛
⎜
⎝ | − | √ | | + | √ | | ⎞
⎟
⎠ |
|
|
- Input:
mult_conjugate((2+sqrt(2))/2)
Output:
| ⎛
⎜
⎝ | 2+ | √ | | ⎞
⎟
⎠ | ⎛
⎜
⎝ | 2− | √ | | ⎞
⎟
⎠ |
|
|
|
|