CASA Function: msolveSP
Compute a basis for the module of syzygies.
- S := msolveSP(F, b, X)
- S := msolveSP(F, b, X, torder1)
- S := msolveSP(F, b, X, torder1, torder2)
- F : list(list(polynom(rational)))
- A list of polynomial tuples.
- b : list(polynom(rational))
- A polynomial tuple. (The right-hand-side of the linear system.)
- X : list(name)
- A list of indeterminates.
- torder1 : name
- A power-product-tuple ordering. Either term (for term first) or index (for index first - default).
- torder2 : name
- A power-product ordering. Either plex (for pure lexicographic) or tdeg (for total degree - default).
- S : [list(polynom(rational)), list(list(polynom(rational)))]
- A particular solution and a basis for the module of syzygies of the linear system F * x = b.
- The command msolveSP(F, b, X, torder1, torder2) computes a basis for the module of syzygies. This procedure is based on Thm.16 and Thm.11 in . The procedure returns a list with two elements: the first element is a particular solution, the second one is a basis for the module of syzygies (represented as a list).
- The polynomial tuples in F are represented as lists of polynomials.
- The variable F is interpreted as a matrix, e.g. F := [[f11,f21],[f12,f22],[f13,f23]] is a matrix with two rows and three columns.
- If X has the form [x1, x2, ..., xn], then using the pure lexicographic ordering this is interpreted as x1 > x2 > ... > xn. Within the total degree ordering, ties are broken by inverse lexicographic order.
> F := [[x^3-y,-x+y],[x*y-1,x^3-1],[-x+y^2,y-1]]: