Usage
Loewy L
Parameter | Type | Description |
---|---|---|
L | A differential operator of order at most 3 |
Returns
Returns either L, in which case L is completely reducible, or a right Loewy decomposition where and each is a completely reducible right-factor of maximal order of .
Example
We compute the Loewy decomposition of the differential equation
as follows:
1 --> L := D^3-(x^2+1)/x*D^2-(-x^2-1+2*x^4)/x^2*D+2*x^3-4*x; 2 --> v := Loewy(L); 3 --> tex(v);
This means that the operator of (6) factors as
where the second-order factor is a completely reducible right-factor of maximal order. Note that is is reducible in this example:
4 --> w := decompose(element(v,2)); 5 --> tex(w);
which means that
is a least common left multiple of and .
See Also
decompose,factor