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 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^31)/(x1);
(x^31)/(x1)
[1] red((x^31)/(x1));
x^2+x+1
[2] red((x^3+y^3+z^33*x*y*z)/(x+y+z));
x^2+(yz)*x+y^2z*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
.
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