On Fri, Oct 18, 2019 at 12:38 PM Frédéric Chapoton <fchapot...@gmail.com> wrote: > > The bug over the cyclotomic field is caused by > > > sage: K = CyclotomicField(8) > sage: K(-1/16) > 0 > True > This is not a bug, as the ordering of K has nothing to do with the ordering on the real elements of K.
Note that sage: K(-1/16).sign() -1 sage: K(-1/16).sign()>0 False works as it should. I have a pile of homeworks on my desk and no time to look in the code now, but if indeed it can be fixed by using `sign()` in appropriate places, it should be done. I have opened https://trac.sagemath.org/ticket/28635 > > > Le vendredi 18 octobre 2019 13:24:51 UTC+2, Frédéric Chapoton a écrit : >> >> This works (in sage 8.9) when using >> >> K.<z>=QuadraticField(2) >> >> >> >> Le vendredi 18 octobre 2019 02:12:02 UTC+2, Ignat Soroko a écrit : >>> >>> I am computing the signature of a quadratic form having entries 0, 1, -1/2, >>> -sqrt(2)/2. I noticed that the result of signature_vector() is different if >>> we treat the number sqrt(2) as a cyclotomic or as a real number. Please >>> look at the example: >>> >>> sage: K.<z>=CyclotomicField(8) >>> sage: a=z-z^3 # a is a square root of 2 >>> sage: a-sqrt(2) >>> 0 >>> sage: >>> Q=QuadraticForm(K,8,[1/2,-a/2,0,0,0,0,0,0,1/2,-a/2,0,0,0,0,0,1/2,-1/2,0,0, >>> ....: 0,0,1/2,-1/2,0,0,0,1/2,-1/2,0,0,1/2,-a/2,0,1/2,-a/2,1/2]) >>> sage: Q.signature_vector() >>> (8, 0, 0) >>> >>> this cannot be true since there exists an isotropic vector: >>> >>> sage: v=vector([1,a,1,0,0,0,0,0]) >>> sage: v*Q.matrix()*v >>> 0 >>> >>> Let's try it over reals: >>> >>> sage: a=sqrt(2) >>> sage: >>> Q=QuadraticForm(RR,8,[1/2,-a/2,0,0,0,0,0,0,1/2,-a/2,0,0,0,0,0,1/2,-1/2,0,0 >>> ....: ,0,0,1/2,-1/2,0,0,0,1/2,-1/2,0,0,1/2,-a/2,0,1/2,-a/2,1/2]) >>> sage: Q.signature_vector() >>> (6, 2, 0) >>> >>> however, the isotropic vector above is not isotropic anymore: >>> >>> sage: v=vector([1,a,1,0,0,0,0,0]) >>> sage: v*Q.matrix()*v >>> sqrt(2)*(1.00000000000000*sqrt(2) - 1.41421356237310) - >>> 1.41421356237310*sqrt(2) + 2.00000000000000 >>> >>> I also tried to define >>> >>> sage: a=sqrt(AA(2)) >>> sage: >>> Q=QuadraticForm(AA,8,[1/2,-a/2,0,0,0,0,0,0,1/2,-a/2,0,0,0,0,0,1/2,-1/2,0,0 >>> ....: ,0,0,1/2,-1/2,0,0,0,1/2,-1/2,0,0,1/2,-a/2,0,1/2,-a/2,1/2]) >>> >>> but Q.signature_vector() gives a runtime error with many lines of code >>> ending in: >>> >>> RuntimeError: maximum recursion depth exceeded >>> >>> >>> Questions: >>> 1) is Q.signature_vector() over cyclotomic field is interpreted in some >>> other way than for reals, thus making the result (8,0,0) somehow correct? >>> >>> 2) Which setting would guarantee both the correct result for >>> signature_vector() using the exact arithmetic and at the same time show >>> that v is actually an isotropic vector? >>> >>> Thank you! >>> >>> >>> > -- > You received this message because you are subscribed to the Google Groups > "sage-devel" group. > To unsubscribe from this group and stop receiving emails from it, send an > email to sage-devel+unsubscr...@googlegroups.com. > To view this discussion on the web visit > https://groups.google.com/d/msgid/sage-devel/710cf4ab-c782-4ad0-a195-fcd47ed1abc5%40googlegroups.com. -- You received this message because you are subscribed to the Google Groups "sage-devel" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-devel+unsubscr...@googlegroups.com. To view this discussion on the web visit https://groups.google.com/d/msgid/sage-devel/CAAWYfq1qFMGymUuHLmswvLUoKAe%3DN8G30gfV8hO7byNik3y97Q%40mail.gmail.com.
