overflow hell strikes back

[kroeker@…]

A working example for a starters

LIB("primdec.lib");
ring R = 0,(x,y),dp;
short = 0;
ring G = 0,(a,b),dp;
short = 0;
ideal phi = a^3,b;
map m = R,phi;
ideal I = a^645*b;
setring R;
ideal pI = preimage(G,m,I);

setring G;
ideal mpI = m(pI);
mpI; // = a^645*b; ok
ASSUME(0, idealsEqual(mpI , I) ); //ok

and now a failing one:

LIB("primdec.lib");
ring R = 0,(x,y),dp;
short = 0;
ring G = 0,(a,b),dp;
short = 0;
ideal phi = a^3,b;
map m = R,phi;
ideal I = a^2147483645*b;
setring R;
ideal pI = preimage(G,m,I);

setring G;
ideal mpI = m(pI);
mpI; // mpI[1]=a^65535*b
ASSUME(0, idealsEqual(mpI , I) ); // fails

This is not just a single issue, this is overflow hell, you know? (unfortunately)

And it is very unlikely that I will catch them all.

[kroeker@…]

update: the failing example should really be

LIB("primdec.lib");
ring R = 0,(x,y),dp;
short = 0;
ring G = 0,(a,b),dp;
short = 0;
ideal phi = a^3,b;
map m = R,phi;
ideal I = a^131070;
setring R;
ideal pI = preimage(G,m,I);
pI;
ideal pIexpected =  x^43690;
setring G;
ideal mpIexpected = m(pIexpected);
mpIexpected;
ASSUME(0, idealsEqual(mpIexpected , I) );

ideal mpI = m(pI);
mpI;
ASSUME(0, idealsEqual(mpI , I) );

( 2147483645 is not 0 mod 3)

But screwing up that example did let me see another flaw of preimage. Can you see it, too?

[hannes]

"not a bug" is not really the right solution, but the closest one. Should be "not correctly stated problem". Solved by changing the policy from "trying the best possible" to "sticking strictly to the documentation" (which limits the maximal expontent to 32767 in this case).