wrong computation of genus / error when calling genus

[Martin Albrecht <malb@…]

Martin Albrecht <malb@…>:

Hi,

the following output is wrong in 3-1-1-0 and was correct in the previous version:

ring r = 7,(x,y),dp; LIB("normal.lib"); ideal i = x10 + x3 + y2; genus(i);

32 should be 0

[seelisch]

Here's another bug related to genus:

ring r = 5,(x,y,z),dp;

ideal i = -x3 + y2*z - 2*x*z2 + y*z2; LIB("normal.lib"); genus(i);

? ideal defines not a curve ? leaving normal.lib::genus

[seelisch]

concerning "Here's another bug related to genus" Gert-Martin Greuel wrote:

"this is not a bug, since Singular computes only the genus for ideals defining a curve (also said in the help for genus) Your ideal defines a surface and therefore the genus cannot be computed (in fact it is not even well defined)."

[seelisch]

Hi Santiago, in the last SINGULAR meeting (24 March) we decided to redirect this ticket to you. I hope you can do something about the issue. Wolfram and Gert-Martin both asked what the term "genus" in this example should actually mean. Maybe that's the starting point.

Hans suspects that we get a different result with SINGULAR 3-1-1 (than with 3-1-0) because of the changes in normal.lib, especially for positive char.

Regards, Frank

[hannes]

fixed with 224b2e921d6c7b67544a659057dc7a1821e104b5 (master) dc2e7d521c529b1881baa1cbaeb461c0e7d3c88c (spielwiese)

[kroeker@…]

It is very likely that a corresponding regression test is missing

(I looked for genus calls in ALL test examples)

[hannes]

stop reporting rubbish.see Tst/Manual?/genus.tsta for the test you did not find.

[kroeker@…]

stop reporting rubbish.see Tst/Manual??/genus.tsta for the test you did not find.

In the second ticket post an issue with the "not a curve"-check is described(see ticket history). Now if that check will be screwed up by future changes, this will be not be detected by current regression tests.

Simulating broken curve check in genus():

--- normal.orig.lib	2014-03-31 12:05:04.339213110 +0200
+++ normal.lib	2014-03-31 12:05:32.924846209 +0200
@@ -2191,6 +2191,7 @@ EXAMPLE: example genus; shows an example
      I=std(I);
      if(dim(I)!=1)
      {
+       ERROR("This is not a curve");
        if(((homog(I))&&(dim(I)!=2))||(!homog(I)))
        {
          ERROR("This is not a curve");

The Tst/Manual/genus.tst will still pass:

>LIB("normal.lib");
> ring r=0,(x,y),dp;
> ideal i=y^9 - x^2*(x - 1)^9;
> genus(i);
0
> ring r7=7,(x,y),dp;
> ideal i=y^9 - x^2*(x - 1)^9;
> genus(i);
0

but the example by Frank Seelisch (see ticket history) will detect the bug:

LIB("normal.lib");
ring r = 5,(x,y,z),dp;
ideal i = -x3 + y2*z - 2*x*z2 + y*z2;
genus(i);

output:

> ring r = 5,(x,y,z),dp;
> ideal i = -x3 + y2*z - 2*x*z2 + y*z2;
> genus(i);
   ? This is not a curve
   ? leaving normal.lib::genus

My report was not rubbish.

[hannes]

this may or may not be a bug (just not looking into it), but it definitely has nothing to do with ticket 212: genus of curves in prime characteristic returns a wrong value. (see ​http://www.singular.uni-kl.de:8002, first point)