"""
For the polynomial p, finds the leading monomial for a
bunch of different weight vectors to check that they are
the Newton polygon vertices (they are, at least for this polygon)
"""
import newLT
from sympy import symbols,Poly
x,y = symbols('x,y')
symbolList = [x,y]
p = Poly(y**4+1+x**4+x**4*y**2+x**3*y**3+y+y**2+y**3+x*y+x**2*y+x*y**2+x**2*y**2+x*y**3+x**4*y)
ltFunct = lambda v:newLT.monomialOrdering(symbolList,ordering='weighted',weightVector=v).LT(p)
vertices = []
for i in xrange(40):
for j in xrange(40):
for sgn in [(1,1),(-1,1),(1,-1),(-1,-1)]:
newguy = ltFunct((sgn[0]*i/40.0,sgn[1]*j/39.0))
if newguy not in vertices:
vertices.append(newguy)
for vertex in vertices:
print vertex.as_expr()
def buchMol(points, ordering, weightVector=(1, 1, 1)):
"""
Given X = [(c11,c12,...,c1n),...,(cs1,cs2,...,csn)] affine point set
and ordering 'lex','grlex','grevlex', or 'weighted' (plus a weight vector)
computes reduced Groebner basis and Q-basis of the ring mod the ideal
"""
from sympy import symbols, Poly, div, Rational, Matrix
from newLT import monomialOrdering
dim = len(points[0])
for pt in points: # check that all pts have same dimension
assert len(pt) == dim
if dim in [1, 2, 3]:
l = ["x", "x,y", "x,y,z"]
varlist = symbols(l[dim - 1])
else:
varstring = "x0"
for i in xrange(1, dim):
varstring += ",x" + str(i)
varlist = symbols(varstring)
monClass = monomialOrdering(varlist, ordering, weightVector)
counter = 0 # keep track of number of rows of matrix & size of S
G, normalSet, S = [], [], []
L = [Poly(1, varlist, domain="QQ")]
M = Matrix(0, len(points), [])
pivots = {} # {column:row}
while L != []:
# step 2:
t = L[0]
for elmt in L:
if monClass.compare(t.as_dict().keys()[0], elmt.as_dict().keys()[0]):
t = elmt
L.remove(t)
evalVector = Matrix(1, len(points), [t.eval(pt) for pt in points])
print "hi"
print M
print evalVector
v, a = vecReduce(evalVector, M, pivots)
print v
viszero = False
if firstNonzero(v) == -1:
viszero = True
toAdd = t
for i in xrange(counter):
toAdd += Poly(-1, varlist) * Poly(a[i], varlist) * S[i]
if viszero:
G.append(toAdd)
for mon in L:
if div(t, mon)[1] == 0:
L.remove(mon)
else:
pivSpot = firstNonzero(v)
pivots[pivSpot] = M.shape[0]
M = M.col_join(v)
S.append(toAdd)
counter += 1
normalSet.append(t)
for variable in varlist:
toCheck = Poly(variable, varlist) * t
isMultiple = False
for elmt in L:
if div(elmt, toCheck)[1] == 0:
isMultiple = True
break
if isMultiple:
continue
for elmt in G:
if div(monClass.LT(elmt), toCheck)[1] == 0:
isMultiple = True
break
if isMultiple == False:
L.append(toCheck)
return G, normalSet
