Solving conics over Q(t1,..., tk).

نویسنده

  • Mark van Hoeij
چکیده

Let K = Q(t1, . . . , tk) and a, b, c ∈ K. We give a simple algorithm to find, if it exists, X, Y, Z in K, not all zero, for which aX+bY +cZ = 0.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Efficient solution of rational conics

We present efficient algorithms for solving Legendre equations over Q (equivalently, for finding rational points on rational conics) and parametrizing all solutions. Unlike existing algorithms, no integer factorization is required, provided that the prime factors of the discriminant are known.

متن کامل

Efficient Solution of Rational

We present eecient algorithms for solving Legendre equations over Q (equivalently, for nding rational points on rational conics) and parametriz-ing all solutions. Unlike existing algorithms, no integer factorization is required , provided that the prime factors of the discriminant are known.

متن کامل

Categorical semantics and composition of tree transducers

ion from Y yields T∆+AI(QX) (r̂)X ←−−−− AI ( Q(ΣX)). Now we need the coproduct of monads: With T∆ = |∆ | and Lemma 6.2.4.1 we can write the rule as |∆ + ( AI(QX) )? | (r̂)X ←−−−− AI ( Q(ΣX)). Abstracting from X gives using from X gives us | | · (∆ + ) · ( ) · AI · Q r̂ ←−− AI · Q · Σ. We have the adjunctions Q a U and AI a ΛI as in Subsection 6.4.3 and ( ) ? a | | from Corollary 4.4.4.6. Now we us...

متن کامل

EXISTENCE RESULTS FOR NONLINEAR IMPULSIVE qk-INTEGRAL BOUNDARY VALUE PROBLEMS

u(T ) = ∑m i=0 ∫ ti+1 ti g(s, u(s)) dqis, where Dqk are qk-derivatives (k = 0, 1, 2, . . . ,m), f, g ∈ C(J ×R, R), Ik ∈ C(R,R), J = [0, T ](T > 0), 0 = t0 < t1 < · · · < tk < · · · < tm < tm+1 = T , J ′ = J\{t1, t2, . . . , tm}, and ∆u(tk) = u(t + k ) − u(t − k ), u(t + k ) and u(t − k ) denote the right and the left limits of u(t) at t = tk (k = 1, 2, . . . ,m) respectively. The study of q-dif...

متن کامل

CONICS, (q + 1)-ARCS, PENCIL CONCEPT OF TIME AND PSYCHOPATHOLOGY

– It is demonstrated that in the (projective plane over) Galois fields GF(q) with q = 2n and n ≥ 3 (n being a positive integer) we can define, in addition to the temporal dimensions generated by pencils of conics, also time coordinates represented by aggregates of (q+1)-arcs that are not conics. The case is illustrated by a (self-dual) pencil of conics endowed with two singular conics of which ...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2008