# CASA Function: mgbasis

Compute the normed reduced Groebner basis.

### Calling Sequence:

- GB := mgbasis(F, X)
- GB := mgbasis(F, X, torder1)
- GB := mgbasis(F, X, torder1, torder2)

### Parameters:

- F : list(list(polynom(rational)))
- A list of polynomial tuples.

- 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:

- GB : list(list(polynom(rational)))
- The normed reduced Groebner basis of F.

### Description:

- The command mgbasis(F, X, torder1, torder2) computes the normed reduced Groebner basis of F with respect to the indeterminates X and the given orderings. The algorithm used in mgbasis is described as Alg.13 in [2].
- The polynomial tuples in F are represented as lists of polynomials.
- 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*y-1,x+2], [y^2+x+1,y-1]]:**

`> ` **mgbasis(F, [x,y]);**

`> ` **mgbasis(F, [y,x], term, plex);**

### See Also:

[CASA]
[mgbasis]
[mgbasisx]
[mnormalf]
[msolveGB]
[msolveSP]