コード例 #1
0
ファイル: expandParallel.py プロジェクト: nbliss/puiseux
def initialTerms(poly, positivesOnly=False):
    """
    Return a list of (*gamma,c)* pairs giving the
    first terms of each Puiseux solution of :py:data:`poly`.
    """
    #hull = lowerHull(poly.support())
    hull = ploty(poly.support(), 'hi')
    if len(hull) == 1:
        return []
    slopes = []
    for i in xrange(len(hull) - 1):
        slopes.append(slp(hull[i], hull[i + 1]))
    slope_vertices = {
    }  # dictionary with slope:[list of vertices on that edge]
    for slope in slopes:
        slope_vertices[slope] = []
    slope_vertices[slopes[0]].append(hull[0][0])
    oldSlope = slopes[0]
    for i in xrange(1, len(hull)):
        slope_vertices[oldSlope].append(hull[i][0])
        if (i < len(hull) - 1) and slopes[i] != oldSlope:
            oldSlope = slopes[i]
            slope_vertices[oldSlope].append(hull[i][0])
    slope_roots = {}
    for slope in slope_vertices.keys():
        if positivesOnly and slope >= 0: continue
        deg = max(slope_vertices[slope])
        toAdd = []
        for i in xrange(deg + 1):
            toAdd.append(0)
        slope_roots[slope] = toAdd
        for i in slope_vertices[slope]:
            slope_roots[slope][i] = poly.internal[i].LC()
        slope_roots[slope].reverse()
    for key in slope_roots.keys():
        while slope_roots[key][-1] == 0:  #don't care about coeffs that are 0
            slope_roots[key].pop()
        toAdd = []
        for x in np.roots(slope_roots[key]):
            toAdd.append(complex(x))
        slope_roots[key] = toAdd
    toReturn = []
    for slope in slope_roots.keys():
        for coeff in slope_roots[slope]:
            toReturn.append((-slope, coeff))
    ############################
    # Removing duplicates
    toReturn2 = []
    for item in toReturn:
        if item not in toReturn2:
            toReturn2.append(item)
    ############################
    return toReturn2
コード例 #2
0
ファイル: expandParallel.py プロジェクト: nbliss/puiseux
def initialTerms(poly,positivesOnly=False):
    """
    Return a list of (*gamma,c)* pairs giving the
    first terms of each Puiseux solution of :py:data:`poly`.
    """
    #hull = lowerHull(poly.support())
    hull = ploty(poly.support(),'hi')
    if len(hull)==1:
        return []
    slopes = []
    for i in xrange(len(hull)-1):
        slopes.append(slp(hull[i],hull[i+1])) 
    slope_vertices = {} # dictionary with slope:[list of vertices on that edge]
    for slope in slopes:
        slope_vertices[slope] = []
    slope_vertices[slopes[0]].append(hull[0][0])
    oldSlope = slopes[0]
    for i in xrange(1,len(hull)):
        slope_vertices[oldSlope].append(hull[i][0])
        if (i<len(hull)-1) and slopes[i]!=oldSlope:
            oldSlope = slopes[i]
            slope_vertices[oldSlope].append(hull[i][0])
    slope_roots = {}
    for slope in slope_vertices.keys():
        if positivesOnly and slope>=0: continue
        deg = max(slope_vertices[slope])
        toAdd = []
        for i in xrange(deg+1):
            toAdd.append(0)
        slope_roots[slope] = toAdd
        for i in slope_vertices[slope]:
            slope_roots[slope][i] = poly.internal[i].LC()
        slope_roots[slope].reverse()
    for key in slope_roots.keys():
        while slope_roots[key][-1]==0: #don't care about coeffs that are 0
            slope_roots[key].pop()
        toAdd = []
        for x in np.roots(slope_roots[key]):
            toAdd.append(complex(x))
        slope_roots[key] = toAdd
    toReturn = []
    for slope in slope_roots.keys():
        for coeff in slope_roots[slope]:
            toReturn.append((-slope,coeff))
    ############################
    # Removing duplicates
    toReturn2 = []
    for item in toReturn:
        if item not in toReturn2:
            toReturn2.append(item)
    ############################
    return toReturn2
コード例 #3
0
ファイル: puiseuxExpansion.py プロジェクト: nbliss/puiseux
def initialTerms(poly,positivesOnly=False):
    """
    Return a list of (gamma,c) pairs giving the
    first terms of each Puiseux solution of poly.
    """
    hull = lowerHull(poly.support())
    slopes = [slp(hull[i],hull[i+1]) for i in xrange(len(hull)-1)]
    # dictionary with slope:[list of vertices on that edge]
    slope_vertices = {slope:[] for slope in slopes}
    slope_vertices[slopes[0]].append(hull[0][0])
    oldSlope = slopes[0]
    for i in xrange(1,len(hull)):
        slope_vertices[oldSlope].append(hull[i][0])
        if (i<len(hull)-1) and slopes[i]!=oldSlope:
            oldSlope = slopes[i]
            slope_vertices[oldSlope].append(hull[i][0])
    slope_roots = {}
    for slope in slope_vertices:
        if positivesOnly and slope>=0: continue
        deg = max(slope_vertices[slope])
        slope_roots[slope] = [0 for i in xrange(deg+1)]
        for i in slope_vertices[slope]:
            slope_roots[slope][i] = poly.internal[i].LC()
        slope_roots[slope].reverse()
    for key in slope_roots:
        while slope_roots[key][-1]==0: #don't care about coeffs that are 0
            slope_roots[key].pop()
        slope_roots[key]=[complex(x) for x in np.roots(slope_roots[key])]
    toReturn = []
    for slope in slope_roots:
        for coeff in slope_roots[slope]:
            toReturn.append((-slope,coeff))
    #########################
    # Removing duplicates
    toReturn2 = []
    for item in toReturn:
        if item not in toReturn2:
            toReturn2.append(item)
    #########################
    return toReturn2
コード例 #4
0
ファイル: puiseuxExpansion.py プロジェクト: nbliss/puiseux
def initialTerms(poly, positivesOnly=False):
    """
    Return a list of (gamma,c) pairs giving the
    first terms of each Puiseux solution of poly.
    """
    hull = lowerHull(poly.support())
    slopes = [slp(hull[i], hull[i + 1]) for i in xrange(len(hull) - 1)]
    # dictionary with slope:[list of vertices on that edge]
    slope_vertices = {slope: [] for slope in slopes}
    slope_vertices[slopes[0]].append(hull[0][0])
    oldSlope = slopes[0]
    for i in xrange(1, len(hull)):
        slope_vertices[oldSlope].append(hull[i][0])
        if (i < len(hull) - 1) and slopes[i] != oldSlope:
            oldSlope = slopes[i]
            slope_vertices[oldSlope].append(hull[i][0])
    slope_roots = {}
    for slope in slope_vertices:
        if positivesOnly and slope >= 0: continue
        deg = max(slope_vertices[slope])
        slope_roots[slope] = [0 for i in xrange(deg + 1)]
        for i in slope_vertices[slope]:
            slope_roots[slope][i] = poly.internal[i].LC()
        slope_roots[slope].reverse()
    for key in slope_roots:
        while slope_roots[key][-1] == 0:  #don't care about coeffs that are 0
            slope_roots[key].pop()
        slope_roots[key] = [complex(x) for x in np.roots(slope_roots[key])]
    toReturn = []
    for slope in slope_roots:
        for coeff in slope_roots[slope]:
            toReturn.append((-slope, coeff))
    #########################
    # Removing duplicates
    toReturn2 = []
    for item in toReturn:
        if item not in toReturn2:
            toReturn2.append(item)
    #########################
    return toReturn2