GNU-Darwin Web

### `red`

red(rat)
:: Reduced form of rat by canceling common divisors.
return
rational expression
rat
rational expression
• Asir automatically performs cancellation of common divisors of rational numb ers. But, without an explicit command, it does not cancel common polynomial divisors of rational expressions. (Reduction of rational expressions to a common denominator will be always done.) Use command red() to perform this cancellation.
• Cancel the common divisors of the numerator and the denominator of a rational expression rat by computing their GCD.
• The denominator polynomial of the result is an integral polynomial which has no common divisors in its coefficients, while the numerator may have rational coefficients.
• Since GCD computation is a very hard operation, it is desirable to detect and remove by any means common divisors as far as possible. Furthermore, a call to this function after swelling of the denominator and the numerator shall usually take a very long time. Therefore, often, to some extent, reduction of common divisors is inevitable for operations of rational expressions.
```[0] (x^3-1)/(x-1);
(x^3-1)/(x-1)
[1] red((x^3-1)/(x-1));
x^2+x+1
[2] red((x^3+y^3+z^3-3*x*y*z)/(x+y+z));
x^2+(-y-z)*x+y^2-z*y+z^2
[3] red((3*x*y)/(12*x^2+21*y^3*x));
(y)/(4*x+7*y^3)
[4] red((3/4*x^2+5/6*x)/(2*y*x+4/3*x));
(9/8*x+5/4)/(3*y+2)
```
References
section `nm`, `dn`, section `gcd`, `gcdz`, section `ptozp`.