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D.15.1.14 regularBasis
Procedure from library arnold.lib (see arnold_lib).
- Usage:
- regularBasis(F,a); F Poly, a int
- Return:
- a list that contains a regular basis of F.value with respect to the piecewiseweight defined by the Newton polygon of F.value. If a=1, the only the elements of the
regular basis that lie above or on the Newton polygon defined by F.value is given.
Example:
| | LIB "arnold.lib";
ring R = 0,(x,y),ds;
poly f = x^9+x^2*y^4+y^2*x^4+y^8;
Poly F = makePoly(f);
regularBasis(F,0);
==> [1]:
==> x4y4
==> [2]:
==> x4y3
==> [3]:
==> x3y4
==> [4]:
==> x4y2
==> [5]:
==> x3y3
==> [6]:
==> x2y4
==> [7]:
==> x8
==> [8]:
==> y7
==> [9]:
==> x3y2
==> [10]:
==> x2y3
==> [11]:
==> x7
==> [12]:
==> y6
==> [13]:
==> x2y2
==> [14]:
==> x6
==> [15]:
==> xy3
==> [16]:
==> y5
==> [17]:
==> x3y
==> [18]:
==> x5
==> [19]:
==> x2y
==> [20]:
==> xy2
==> [21]:
==> y4
==> [22]:
==> x4
==> [23]:
==> y3
==> [24]:
==> xy
==> [25]:
==> x3
==> [26]:
==> y2
==> [27]:
==> x2
==> [28]:
==> y
==> [29]:
==> x
regularBasis(F,1);
==> [1]:
==> x4y4
==> [2]:
==> x4y3
==> [3]:
==> x3y4
==> [4]:
==> x4y2
==> [5]:
==> x3y3
==> [6]:
==> x2y4
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