Python monomial 예제들

예제 #1

파일: searching.py 프로젝트: tom111/GraphBinomials

def axisSaturate (binomials, i, degree, Verbose=False):
    """
    TODO: Think about termination issue

    Compute the axis saturation with respect to variable index i, terminating
    at a given search degree.

    Algorithm:
    
    For each degree:

      consider all pairs of monomials both divisible by the variable in index
      i and check whether they can be connected, while the divided monomials
      can't be connected.
    """
    result = [b for b in binomials]
    # This is again assumed to be a constant over all binomials, but not
    # checked.
    length = binomials[0].length
    d = 1;
    while d < degree:
        if Verbose: print ("Now searching for degree " + str (d) + " moves.")
        # List monomials of degree d, divisible by i.
        mi = monomial(length, exponents = [1 if j==i else 0 for j in range (length)])
        divisibleMonomials = listDivisibleMonomials (d+1, mi, length)
        # Filter the isolated Monomials:
        if Verbose: print ("Filtering isolated monomials")
        divisibleMonomials = [m for m in divisibleMonomials if not isIsolated (m, result)]
        if Verbose: print ("Done")
        if Verbose:
            n = len (divisibleMonomials)
            numpairs = n*(n-1)/2
            print ("There are " + str (numpairs) + " pairs to investigate.")
        # Get an iterator of the pairs
        pairs = combinations(divisibleMonomials, 2)
        counter = 0;
        for p in pairs:
            counter = counter + 1
            if Verbose and counter%100 == 0:
                print (str(counter) + " pairs done.")
            # Check if they are in the same connected component via the current result
            if inSameComponent (p[0], p[1], result):
                # Check if the divided monomials were already connected
                if not inSameComponent(p[0].divide(mi), p[1].divide(mi), result):
                    # Found a new element
                    newbinomial = p[0].divide(p[1])
                    print ("Found element of the saturation: ")
                    print newbinomial
                    result.append (newbinomial)
        d=d+1
    return result

예제 #2

파일: witnessSearch.py 프로젝트: tom111/GraphBinomials

 def findWitness(self, stoppingDegree=False):
     """ Stopping degree is the last degree of potential witnesses that will be checked"""
     d = 1;
     variables=[createVar(i,self.nvars) for i in range(self.nvars)]
     while (stoppingDegree == False or (d <= stoppingDegree)):
         todo = combinations_with_replacement(variables, d)
         for t in todo:
             m=monomial(self.nvars)
             for tt in t: m = m.multiply(tt)
             if self.verbose:
                 print "Now testing:"
                 print m
             mp = self.markovElement.positivePart().multiply(m)
             mn = self.markovElement.negativePart().multiply(m)
             if inSameComponent(mp, mn, self.moves, Verbose=self.verbose):
                 if self.verbose: print "Witness found!"
                 return m
         d = d+1
     print "No witness found"
     raise NoWitnessFound

예제 #3

파일: K23.py 프로젝트: tom111/GraphBinomials

""" Analyzing the CI ideal of K23 """

from searching import *
from monomial import *
from witnessSearch import *

nvars=32

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0,0,0,0,0,1,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]],[[0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]],[[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0]],[[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,0,0,0,0,0,0,0]],[[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,0,0,0]],[[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,0],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1]]]

K23Binomials=[monomial(nvars, b[0]).divide(monomial(nvars, b[1])) for b in K23Edges]

higherMarkovMoves=[monomial (nvars, h) for h in [
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,-1,-1,1,0,0,0,0,-1,1,1,-1,0,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,-1,0,0,-1,1,-1,1,0,0,1,-1,0,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,-1,-1,0,1,0,0,-1,0,1,1,0,-1,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,-1,0,-1,0,1,-1,0,1,0,1,0,-1,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,-1,0,0,-1,1,0,0,0,0,-1,1,0,0,1,-1],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,-1,0,0,0,0,-1,1,-1,1,0,0,0,0,1,-1],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,-1,0,-1,0,1,0,0,-1,0,1,0,1,0,-1],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,-1,0,0,-1,0,1,-1,0,1,0,0,1,0,-1],
[0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,-1,0,-1,0,0,0,1,0,0,1,0,-1,0,-1,0,1,0],
[0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,-1,0,0,-1,0,0,0,1,0,1,-1,0,0,-1,1,0,0],
[0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,-1,1,-1,0,0,-1,1,0,0,0,0,-1,0,0,0,1,0],
[0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,-1,1,0,-1,0,-1,0,1,0,0,-1,0,0,0,1,0,0],
[0,0,0,0,0,0,0,0,0,0,1,-1,-1,1,0,0,0,0,0,0,0,0,0,0,0,0,-1,1,1,-1,0,0],
[0,0,0,0,0,0,0,0,0,0,1,-1,0,0,-1,1,-1,0,0,0,1,0,0,0,0,1,0,0,0,-1,0,0],
[0,0,0,0,0,0,0,0,0,0,1,-1,0,0,-1,1,-1,1,0,0,1,-1,0,0,0,0,0,0,0,0,0,0],
[0,0,0,0,0,0,0,0,0,0,1,-1,0,0,-1,1,0,0,0,0,0,0,0,0,-1,1,0,0,1,-1,0,0],
[0,0,0,0,0,0,0,0,0,0,1,-1,0,0,-1,1,0,1,0,0,0,-1,0,0,-1,0,0,0,1,0,0,0],
[0,0,0,0,0,0,0,0,0,0,1,0,0,0,-1,0,-1,0,0,0,1,0,0,0,0,1,0,-1,0,-1,0,1],

예제 #4

파일: K22.py 프로젝트: tom111/GraphBinomials

from monomial import *
from witnessSearch import *

nvars=16

K22Edges=[
[[0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0]],
[[0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0]],
[[0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0]],
[[0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1]],
[[0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]],
[[0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0]],
[[0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0]],
[[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1]]]

K22Binomials=[monomial(nvars, b[0]).divide(monomial(nvars, b[1])) for b in K22Edges]

# result = axisSaturate(K22Binomials, 0, 5, Verbose=True)

higherMarkovEdges=[[0,0,0,0,1,-1,-1,1,-1,1,1,-1,0,0,0,0],
[0,0,1,-1,-1,1,0,0,0,0,-1,1,1,-1,0,0],
[0,1,-1,0,0,-1,1,0,0,-1,1,0,0,1,-1,0],
[0,1,0,-1,0,-1,0,1,-1,0,1,0,1,0,-1,0],
[1,-1,-1,1,0,0,0,0,0,0,0,0,-1,1,1,-1],
[1,-1,0,0,0,0,-1,1,-1,1,0,0,0,0,1,-1],
[1,0,-1,0,-1,0,1,0,0,-1,0,1,0,1,0,-1],
[1,0,0,-1,-1,0,0,1,-1,0,0,1,1,0,0,-1]]

for h in [monomial(nvars, hh) for hh in higherMarkovEdges]:
    wF = WitnessSearch(nvars, K22Binomials, h, Verbose=False)
    print ("Witness for " + str(h) + "  :  " + str(wF.findWitness()))

예제 #5

파일: witnessSearch.py 프로젝트: tom111/GraphBinomials

def createVar (i,n):
    l = [0 for j in range(n)]
    l[i]=1
    return monomial(n, l)