Least common multiple of polynomials
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lcm(p
,q, …
) lcm(f
,g, …
)
lcm(p, q, ...)
calculates the least common
multiple 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.
Polynomial expressions are converted to polynomials. See poly
for details. FAIL
is
returned if an argument cannot be converted to a polynomial.
The return value is of the same type as the input polynomials,
i.e., either a polynomial of type 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.
Use ilcm
if
all arguments are known to be integers, since it is much faster than lcm
.
The least common multiple of two polynomial expressions can be computed as follows:
lcm(x^3  y^3, x^2  y^2);
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)
delete f, g, p, q:

polynomials of
type 

Polynomial, a polynomial expression, or the value FAIL
.
f
, g
, p
, q