Compute a set of Noetherian operators for the $P$-primary component of comodule U.
i1 : R = QQ[x,y,z] o1 = R o1 : PolynomialRing |
i2 : U = image matrix{{x,y,z},{y,z,x}}
o2 = image | x y z |
| y z x |
2
o2 : R-module, submodule of R
|
i3 : P = first associatedPrimes comodule U o3 = ideal (y - z, x - z) o3 : Ideal of R |
i4 : noetherianOperators(U, P)
o4 = {| -1 |}
| 1 |
o4 : List
|
If there are no embedFded primes, running this command for all associated primes is equivalent to running a differential primary decomposition.
i5 : associatedPrimes comodule U /
(P -> {P, noetherianOperators(U,P)})
2 2
o5 = {{ideal (y - z, x - z), {| -1 |}}, {ideal (x + y + z, y + y*z + z ), {|
| 1 | |
------------------------------------------------------------------------
-z |}}}
y |
o5 : List
|
i6 : netList differentialPrimaryDecomposition U
+--------------------------------+--------+
o6 = |ideal (y - z, x - z) |{| -1 |}|
| | | 1 | |
+--------------------------------+--------+
| 2 2 | |
|ideal (x + y + z, y + y*z + z )|{| -z |}|
| | | y | |
+--------------------------------+--------+
|