Bill Allombert on Sun, 19 Jul 2026 18:46:22 +0200


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experimental galoisinit support for non-WSS groups


Dear PARI developers,

I have commited a new version of galoisinit that fixes most of the limitation
of the previous version without introducing too many slowdowns.

Some remaining limitations:

1) G.gen and G.orders only filled for WSS groups because otherwise they are not
well-defined with the current specification otherwise. This could be addressed by
changing the specification but this would indirectly breaks backward compatibility.
For non WSS group G.gen=[] and G.orders=Vecsmall([])

2) galoissubgroups and galoisfixedfields only work for groups with at most one
perfect subgroup (not counting the subgroup with one element as perfect).

3) galoisidentify is limited to order <=143, 128 excluded

So for example:

? galoisgetname(60,5)
%1 = "A5"
? P=galoisgetpol(60,5)[1];
? G=galoisinit(P);
? G.gen
%9 = []
? G.orders
%10 = Vecsmall([])
? galoisidentify(G)
%11 = [60,5]
? galoischartable(G)
%12 = [[1,3,3,4,5;1,-1,-1,0,1;1,0,0,1,-1;1,-y^3-y^2,y^3+y^2+1,-1,0;1,y^3+y^2+1,-y^3-y^2,-1,0],5]
? #galoissubgroups(G)
%15 = 59

Cheers,
Bill