We normally learned this for real in primary school which is remember in the name of ค.ร.น. . For polynomial mathematic, Maple provides one function called ‘lcm’. To see how it work see the following example.
In Maple you can say
f1:= 2*x^2-y*x-y^2: f2:= 2*x^2+3*y*x+y^2: factor(f1); factor(f2);
to get the answer.
Find the LCM
You can see that the second part is just f2 and you can see now why f3 is the LCM.
In OrePolynomial case the thing is more difficult, since
In this case and . The Maple code is shown below.
with(OreTools): SS:=SetOreRing(t,'defferential'): f1:= [OrePoly(b),OrePoly(a)]: f2:= [OrePoly(d),OrePoly(c)]: beta := LCM['left'](f1,f2,SS); beta2:= Quotient['right'](beta,f1,SS); alpha1:= Quotient['right'](beta,f2,SS); [Multiply(alpha1,f2,SS),Multiply(beta2,f1,SS)];