lcm -- the least common multiple of
polynomials
Introductionlcm(p, q...) returns the least common
multiple of the polynomials p, q, ...
Call(s)lcm(p, q...)
lcm(f, g...)
Parametersp, q... |
- | polynomials of type
DOM_POLY |
f, g... |
- | polynomial expressions |
Returnsa polynomial, a polynomial expression, or the value FAIL.
p, q, f, g
Related
Functionscontent, factor, gcd, gcdex, icontent, ifactor, igcd, igcdex, ilcm, poly
Detailslcm(p, q...) calculates the greatest
common divisor of any number of polynomials. The coefficient ring of the polynomials may either be
the integers or the rational numbers, Expr, a residue class ring IntMod(n) with a prime number
n, or a domain.
All polynomials must have the same indeterminates and the same coefficient ring.
poly for details.
FAIL is returned if an argument cannot be converted to a
polynomial.DOM_POLY or a polynomial
expression.lcm returns 1 if all arguments are
1 or -1, or if no argument is given. If at least
one of the arguments is 0, then lcm returns
0.ilcm if all
arguments are known to be integers, since it is much faster than
lcm.
Example
1The least common multiple of two polynomial expressions can be computed as follows:
>> lcm(x^3 - y^3, x^2 - y^2);
4 4 3 3
y - x + x y - x y
One may also choose polynomials as arguments:
>> p := poly(x^2 - y^2, [x, y], IntMod(17)): q := poly(x^2 - 2*x*y + y^2, [x, y], IntMod(17)): lcm(p, q)
3 2 2 3
poly(x - x y - x y + y , [x, y], IntMod(17))
>> delete f, g, p, q: