Accompanying files of the preprint Lexicographic Gröbner bases of bivariate polynomials modulo a univariate one (by X. Dahan) arXiv:2010.14775

• D5.mgm Contains the functions:
  • HL (and oneIterHL that implements one iteration of lifting) corresponds to standard quadratic Hensel lifting (see page 10)
  • MusserQ corresponds to Algorithm 2
  • isolFac corresponds to Algorithm 6
  • invertNil corresponds to Algorithm 7
  • WeierForm corresponds to Algorithm 8
  • monicForm corresponds to Algorithm 9
  • LNL corresponds to Algorithm 10
  • SToGB_Aux and SToGB_D5 corresponds to Algorithms 11 and 12
  
  
• Or input your own polynomials:
• By default, the base field Q is the field of rational numbers. To change it, edit the first line of the file.
• Univariate monic and non-constant polynomial (say \(T\)) \(\in\) p1 or \(\in\) P (in x)
  (see below for the global variable p1 and for the corresponding homomorphism phip1)
• Two monic polynomials (say \(a, b\)) \(\in\) p2 or \(\in\) P (see below for the global variable p2, and for the corresponding homomorphism phip2)
• Type B := SToGB_D5( a, b, T ) if \(a,b \in\) p2 and \(T\in \) p1
  or B := SToGB_D5( phip2(a), phip2(b), phip1(T) ) if \(a, b, T \in\) P .

• Q field of coefficients. (by default, is the field of rational numbers. Edit the first line of the file to change it.)
• P Ring of bivariate polynomials in x,y over Q.
• p1 ring of univariate polynomials (in x) over Q.
• p2 Ring of univariate polynomials (in y) over p1
• phip1 Homomorphism from P to p1 (converts a univariate polynomial in P to p1 )
• phip2 Homomorphism from P to p2 (Converts a polynomial in P to a polynomial in p2 )
• phiP Homomorphism from p2 to P (converts a polynomial in p2 to a polynomial in P )