Does anyone have any tips for how to compute the kernel of a map between
polynomial algebras, or for checking whether the map is injective? I have
families of such maps involving algebras with many generators. I'm working
over GF(2), if that matters. In one example I defined the map phi: R -> S
where R has 12 generators, S has 19 generators, and did
sage: phi.is_injective()
After about 30 hours, Sage quit on me, perhaps running out of memory
("Killed: 9"). An example of the sort of map I'm interested in:
sage: phi
Ring morphism:
From: Multivariate Polynomial Ring in h20, h21, h30, h31, h40, h41, h50
over Finite Field of size 2
To: Multivariate Polynomial Ring in h20, h21, h30, h31, h40, h41, h50,
xi1, xi2, xi3, xi4, xi5 over Finite Field of size 2
Defn: h20 |--> h20
h21 |--> h21
h30 |--> h20*xi1^4 + h21*xi1 + h30
h31 |--> h21*xi1^8 + h31
h40 |--> h21*xi1^9 + h30*xi1^8 + h20*xi2^4 + h31*xi1
h41 |--> h31*xi1^16 + h21*xi2^8
h50 |--> h31*xi1^17 + h21*xi1*xi2^8 + h30*xi2^8 + h20*xi3^4
Any suggestions?
--
John
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