Python sympy.var方法代碼示例

# 需要導入模塊: import sympy [as 別名]
# 或者: from sympy import var [as 別名]
def optm(quboh,numM):
	try:
		import sympy
	except ImportError:
		raise ImportError("optm() requires sympy. Please install before call this function.") 
	optm_E = sympy.expand(quboh) 
	symbol_list = ["q"+str(i) for i in range(numM)] 
	sympy.var(' '.join(symbol_list),positive=True) 

	symbol_list_proto = list(optm_E.free_symbols) 
	for i in range(len(symbol_list_proto)): 
		optm_E = optm_E.subs(symbol_list_proto[i]*symbol_list_proto[i],symbol_list_proto[i]) 

	optm_M = np.zeros((numM,numM)) 

	for i in range(numM): 
		for j in range(i+1,numM): 
			optm_M[i][j] = optm_E.coeff(symbol_list[i]+"*"+symbol_list[j]) 

		temp1 = sympy.poly(optm_E.coeff(symbol_list[i])) 
		optm_M[i][i] = sympy.poly(optm_E.coeff(symbol_list[i])).coeff_monomial(1) 

	return optm_M 

# 需要導入模塊: import sympy [as 別名]
# 或者: from sympy import var [as 別名]
def R3():
    var('x y z')
    f = x+y+z
    t1 = clock()
    a = [bool(f==f) for _ in range(10)]
    t2 = clock()
    return t2 - t1 

# 需要導入模塊: import sympy [as 別名]
# 或者: from sympy import var [as 別名]
def compose(value, sample_args, context=None):
  """E.g., "Let f(x)=2x+1, let g(x)=3x+10. What is f(g(x))?"."""
  del value  # unused
  if context is None:
    context = composition.Context()

  entropy, sample_args = sample_args.peel()
  entropy_f, entropy_g = entropy * np.random.dirichlet([1, 1])

  coeffs_f = polynomials.sample_coefficients([random.randint(1, 2)], entropy_f)
  coeffs_g = polynomials.sample_coefficients([random.randint(1, 2)], entropy_g)

  entity_f, entity_g = context.sample(
      sample_args,
      [composition.Polynomial(coeffs_f), composition.Polynomial(coeffs_g)])

  variable = sympy.var(context.pop())

  poly_f = polynomials.coefficients_to_polynomial(coeffs_f, variable)
  poly_g = polynomials.coefficients_to_polynomial(coeffs_g, variable)

  poly_f_g = poly_f.sympy().subs(variable, poly_g.sympy()).expand()

  expression = composition.FunctionHandle(entity_f, entity_g).apply(variable)

  template = random.choice(_TEMPLATES)
  return example.Problem(
      question=example.question(context, template, composed=expression),
      answer=poly_f_g) 

# 需要導入模塊: import sympy [as 別名]
# 或者: from sympy import var [as 別名]
def R2():
    def hermite(n,y):
          if n == 1: return 2*y
          if n == 0: return 1
          return (2*y*hermite(n-1,y) - 2*(n-1)*hermite(n-2,y)).expand()
    t1 = clock()
    hermite(15, var('y'))
    t2 = clock()
    return t2 - t1 

# 需要導入模塊: import sympy [as 別名]
# 或者: from sympy import var [as 別名]
def R5():
    def blowup(L,n):
        for i in range(n):
            L.append( (L[i] + L[i+1]) * L[i+2] )
    def uniq(x):
        v = list(set(x))
        return v
    var('x y z')
    L = [x,y,z]
    blowup(L,8)
    t1 = clock()
    L = uniq(L)
    t2 = clock()
    return t2 - t1 

# 需要導入模塊: import sympy [as 別名]
# 或者: from sympy import var [as 別名]
def S1():
    var("x y z")
    e = (x+y+z+1)**7
    f = e*(e+1)
    t1 = clock()
    f = f.expand()
    t2 = clock()
    return t2 - t1 

# 需要導入模塊: import sympy [as 別名]
# 或者: from sympy import var [as 別名]
def S2():
    var("x y z")
    e = (x**sin(x) + y**cos(y) + z**(x + y))**100
    t1 = clock()
    f = e.expand()
    t2 = clock()
    return t2 - t1 

# 需要導入模塊: import sympy [as 別名]
# 或者: from sympy import var [as 別名]
def S3a():
    var("x y z")
    e = (x**y + y**z + z**x)**500
    e = e.expand()
    t1 = clock()
    f = e.diff(x)
    t2 = clock()
    return t2 - t1 

# 需要導入模塊: import sympy [as 別名]
# 或者: from sympy import var [as 別名]
def get_generating_function(f, T=None):
    """
    Get the generating function

    :param f: function addr
    :param T: edges matrix of the function f
    :return: the generating function
    """

    if not T:
        edges = [(a[0].addr, a[1].addr) for a in f.graph.edges()]
        N = sorted([x for x in f.block_addrs])
        T = []
        for b1 in N:
            T.append([])
            for b2 in N:
                if b1 == b2 or (b1, b2) in edges:
                    T[-1].append(1)
                else:
                    T[-1].append(0)
    else:
        N = T[0]

    T = sympy.Matrix(T)
    z = sympy.var('z')
    I = sympy.eye(len(N))

    tmp = I - z * T
    tmp.row_del(len(N) - 1)
    tmp.col_del(0)
    det_num = tmp.det()
    det_den = (I - z * T).det()
    quot = det_num / det_den
    g_z = ((-1) ** (len(N) + 1)) * quot
    return g_z 

# 需要導入模塊: import sympy [as 別名]
# 或者: from sympy import var [as 別名]
def optx(quboh): 
	try:
		import sympy
	except ImportError:
		raise ImportError("optx() requires sympy. Please install before call this function.")

	optx_E = sympy.expand(quboh)
	symbol_list = list(optx_E.free_symbols)
	sympy.var(' '.join(map(str,symbol_list)),positive=True)
	for i in range(len(symbol_list)):
		optx_E = optx_E.subs(symbol_list[i]*symbol_list[i],symbol_list[i])
	return optx_E 

# 需要導入模塊: import sympy [as 別名]
# 或者: from sympy import var [as 別名]
def add(value, sample_args, context=None):
  """E.g., "Let f(x)=2x+1, g(x)=3x+2. What is 5*f(x) - 7*g(x)?"."""
  is_question = context is None
  if context is None:
    context = composition.Context()

  entropy, sample_args = sample_args.peel()

  if value is None:
    max_degree = 3
    degree = random.randint(1, max_degree)
    entropy -= math.log10(max_degree)
    entropy_value = entropy / 2
    entropy -= entropy_value
    value = polynomials.sample_coefficients(
        degree, entropy=entropy_value, min_non_zero=random.randint(1, 3))
    value = composition.Polynomial(value)

  c1, c2, coeffs1, coeffs2 = polynomials.coefficients_linear_split(
      value.coefficients, entropy)
  coeffs1 = polynomials.trim(coeffs1)
  coeffs2 = polynomials.trim(coeffs2)

  c1, c2, fn1, fn2 = context.sample(
      sample_args,
      [c1, c2, composition.Polynomial(coeffs1), composition.Polynomial(coeffs2)]
  )

  var = sympy.var(context.pop())

  expression = (
      c1.handle * fn1.handle.apply(var) + c2.handle * fn2.handle.apply(var))

  if is_question:
    answer = polynomials.coefficients_to_polynomial(value.coefficients, var)
    answer = answer.sympy()
    template = random.choice(_TEMPLATES)
    return example.Problem(
        question=example.question(context, template, composed=expression),
        answer=answer)
  else:
    intermediate_symbol = context.pop()
    intermediate = sympy.Function(intermediate_symbol)(var)
    return composition.Entity(
        context=context,
        value=value,
        description='Let {intermediate} = {composed}.',
        handle=composition.FunctionHandle(intermediate_symbol),
        intermediate=intermediate,
        composed=expression) 

# 需要導入模塊: import sympy [as 別名]
# 或者: from sympy import var [as 別名]
def __init__(self, context, value, description='', handle=None,
               expression=None, polynomial_variables=None,
               **description_kwargs):
    """Initializes an entity.

    Args:
      context: Instance of `Context` keeping track of used symbols and child
          entities (that may not explicitly occur in `description_kwargs`).
      value: The value represented by this Entity.
      description: String, describing this Entity. This can contain '{self}' as
          a substring, in which case it will be substituted with a new handle
          (and `context` must be non-None).
      handle: Optional string/symbol that refers to this Entity. This must
          always be provided if '{self}' does not occur in `description`.
      expression: Optional string (or something that can be converted to a
          string, like ops.Op or sympy.expr) representing the value of this
          Entity, that can be used directly instead of using `handle`.
      polynomial_variables: If `expression` provided, then for polynomial
          entities, the variables used.
      **description_kwargs: Dict of substitutions (including entities) for use
          in `description`.

    Raises:
      ValueError: If handle specified and '{self}' in description; or neither.
    """
    self._value = value

    child_description, description_kwargs = expand_entities(
        context, **description_kwargs)

    if '{self}' in description:
      if handle is not None:
        raise ValueError('Cannot specify handle if {self} in description')
      handle = context.pop()
      description_kwargs['self'] = handle
      handle = sympy.var(handle)
    else:
      if handle is None:
        raise ValueError('Must specify handle if {self} not in description')
      if isinstance(handle, str):
        handle = sympy.var(handle)

    if (isinstance(value, Polynomial)
        and expression is not None
        and polynomial_variables is None):
      raise ValueError('Must provided polynomial_variables')

    self._child_description = child_description
    self._description = description.format(**description_kwargs)
    self._handle = handle
    self._expression = expression
    self._polynomial_variables = polynomial_variables

    # For checking that we don't use both the handle and the expression form of
    # this entity.
    self._handle_used = False
    self._expression_used = False 

# 需要導入模塊: import sympy [as 別名]
# 或者: from sympy import var [as 別名]
def get_path_n(f, T=None):
    # TODO cire paper here
    """
    Get the formula to estimate the number of path of a function, given its longest path.

    :param f: function addr
    :param T: edges matrix of the function f
    :return: formula to estimate the number of paths
    """

    g_z = get_generating_function(f, T)
    expr = g_z.as_numer_denom()[1]
    rs = sympy.roots(expr)
    D = len(set(rs.keys()))  # number of distinct roots
    d = sum(rs.values())  # number of roots

    # get taylor coefficients
    f = sympy.utilities.lambdify(list(g_z.free_symbols), g_z)
    taylor_coeffs = mpmath.taylor(f, 0, d - 1)  # get the first d terms of taylor expansion

    #
    # calculate path_n
    #

    n = sympy.var('n')
    e_path_n = 0
    e_upper_n = 0
    coeff = []

    for i in xrange(1, D + 1):
        ri, mi = rs.items()[i - 1]
        for j in xrange(mi):
            c_ij = sympy.var('c_' + str(i) + str(j))
            coeff.append(c_ij)
            e_path_n += c_ij * (n ** j) * ((1 / ri) ** n)
            if ri.is_complex:
                ri = sympy.functions.Abs(ri)
            e_upper_n += c_ij * (n ** j) * ((1 / ri) ** n)
    equations = []

    for i, c in enumerate(taylor_coeffs):
        equations.append(sympy.Eq(e_path_n.subs(n, i), c))
    coeff_sol = sympy.linsolve(equations, coeff)

    # assert unique solution
    assert type(coeff_sol) == sympy.sets.FiniteSet, "Zero or more solutions returned for path_n coefficients"
    coeff_sol = list(coeff_sol)[0]
    coeff_sol = [sympy.N(c, ROUND) for c in coeff_sol]

    for val, var in zip(coeff_sol, coeff):
        name = var.name
        e_path_n = e_path_n.subs(name, val)
        e_upper_n = e_upper_n.subs(name, val)

    return sympy.utilities.lambdify(list(e_path_n.free_symbols), e_path_n), sympy.utilities.lambdify(
        list(e_upper_n.free_symbols), e_upper_n)