def normalize_square_matrices(matrices): """ Find a common space for all matrices. OUTPUT: A list of matrices, all elements of the same matrix space. EXAMPLES:: sage: from sage.groups.matrix_gps.finitely_generated import normalize_square_matrices sage: m1 = [[1,2],[3,4]] sage: m2 = [2, 3, 4, 5] sage: m3 = matrix(QQ, [[1/2,1/3],[1/4,1/5]]) sage: m4 = MatrixGroup(m3).gen(0) sage: normalize_square_matrices([m1, m2, m3, m4]) [ [1 2] [2 3] [1/2 1/3] [1/2 1/3] [3 4], [4 5], [1/4 1/5], [1/4 1/5] ] """ deg = [] gens = [] for m in matrices: if is_MatrixGroupElement(m): deg.append(m.parent().degree()) gens.append(m.matrix()) continue if is_Matrix(m): if not m.is_square(): raise TypeError('matrix must be square') deg.append(m.ncols()) gens.append(m) continue try: m = list(m) except TypeError: gens.append(m) continue if isinstance(m[0], (list, tuple)): m = map(list, m) degree = ZZ(len(m)) else: degree, rem = ZZ(len(m)).sqrtrem() if rem != 0: raise ValueError( 'list of plain numbers must have square integer length') deg.append(degree) gens.append(matrix(degree, degree, m)) deg = set(deg) if len(set(deg)) != 1: raise ValueError('not all matrices have the same size') gens = Sequence(gens, immutable=True) MS = gens.universe() if not is_MatrixSpace(MS): raise TypeError('all generators must be matrices') if MS.nrows() != MS.ncols(): raise ValueError('matrices must be square') return gens
def normalize_square_matrices(matrices): """ Find a common space for all matrices. OUTPUT: A list of matrices, all elements of the same matrix space. EXAMPLES:: sage: from sage.groups.matrix_gps.finitely_generated import normalize_square_matrices sage: m1 = [[1,2],[3,4]] sage: m2 = [2, 3, 4, 5] sage: m3 = matrix(QQ, [[1/2,1/3],[1/4,1/5]]) sage: m4 = MatrixGroup(m3).gen(0) sage: normalize_square_matrices([m1, m2, m3, m4]) [ [1 2] [2 3] [1/2 1/3] [1/2 1/3] [3 4], [4 5], [1/4 1/5], [1/4 1/5] ] """ deg = [] gens = [] for m in matrices: if is_MatrixGroupElement(m): deg.append(m.parent().degree()) gens.append(m.matrix()) continue if is_Matrix(m): if not m.is_square(): raise TypeError('matrix must be square') deg.append(m.ncols()) gens.append(m) continue try: m = list(m) except TypeError: gens.append(m) continue if isinstance(m[0], (list, tuple)): m = map(list, m) degree = ZZ(len(m)) else: degree, rem = ZZ(len(m)).sqrtrem() if rem!=0: raise ValueError('list of plain numbers must have square integer length') deg.append(degree) gens.append(matrix(degree, degree, m)) deg = set(deg) if len(set(deg)) != 1: raise ValueError('not all matrices have the same size') gens = Sequence(gens, immutable=True) MS = gens.universe() if not is_MatrixSpace(MS): raise TypeError('all generators must be matrices') if MS.nrows() != MS.ncols(): raise ValueError('matrices must be square') return gens
def __init__(self, gensG, category = None): v = Sequence(gensG, immutable=True) M = v.universe() if not is_MatrixSpace(M): raise TypeError, "universe of sequence (=%s) of generators must be a matrix space"%M if M.nrows() != M.ncols(): raise ValueError, "matrices must be square." for x in v: if not x.is_invertible(): raise ValueError, "each generator must be an invertible matrix but one is not:\n%s"%x self._gensG = v MatrixGroup_gap.__init__(self, M.nrows(), M.base_ring(), category = category)
def __init__(self, gensG, category=None): v = Sequence(gensG, immutable=True) M = v.universe() if not is_MatrixSpace(M): raise TypeError, "universe of sequence (=%s) of generators must be a matrix space" % M if M.nrows() != M.ncols(): raise ValueError, "matrices must be square." for x in v: if not x.is_invertible(): raise ValueError, "each generator must be an invertible matrix but one is not:\n%s" % x self._gensG = v MatrixGroup_gap.__init__(self, M.nrows(), M.base_ring(), category=category)