CASA Function: mnormalf
Compute the normal form of a tuple of polynomials modulo a module.
Calling Sequence:
- nf := mnormalf(f, G, X)
- nf := mnormalf(f, G, X, torder1)
- nf := mnormalf(f, G, X, torder1, torder2)
Parameters:
- f : list(polynom(rational))
-
- G : list(list(polynom(rational)))
- A list of polynomial tuples. Must be a Groebner basis.
- 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).
Result:
- nf : list(polynom(rational))
- The normal form of f with respect to the Groebner basis G.
Description:
- The command mnormalf(f, G, X, torder1, torder2) computes the normal form of the tuple of polynomials f modulo the module generated by G with respect to the indeterminates X and the given orderings.
- Note that G must be a Groebner basis. Therefore, usually first a Groebner basis for a set of polynomial tuples is computed (with mgbasis) and afterwards mnormalf is called.
- 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.
Examples:
> F:=[[x-1,x*y-1],[x*y-1,y],[y,x-1]]:
> G1:=mgbasis(F,[x,y]):
> mnormalf([x^3*y^2+x^3+1,y^3+x+1],G1,[x,y]);
> G2:=mgbasis(F,[x,y],term):
> mnormalf([x^3*y^2+x^3+1,y^3+x+1],G2,[x,y],term);
See Also:
[CASA]
[mgbasis]
[mgbasisx]
[mnormalf]
[msolveGB]
[msolveSP]