def get_transformation_function(segments, fixed_endpoint=None, fixed_basepoint=None, use_dict=True):
  if fixed_endpoint:
    coordinate_labels = []
  else:
    coordinate_labels = ['x','y','z']
  if fixed_basepoint:
    inverse_coordinate_labels = []
  else:
    inverse_coordinate_labels = ['base_x','base_y','base_z']
  trans_mat, inv_trans_mat, var_names = get_sympy_reduction(segments, fixed_endpoint, fixed_basepoint, coordinate_labels, inverse_coordinate_labels)

  # Bake into a lambda func
  base_func = lambdify(flatten((coordinate_labels, var_names)), trans_mat)
  base_inv_func = lambdify(flatten((inverse_coordinate_labels, var_names)), inv_trans_mat)

  if use_dict:
    if fixed_endpoint:
      func = lambda var_dict: base_func(*flatten([var_dict[var_name] for var_name in var_names])).A
    else:
      func = lambda coords, var_dict: base_func(*flatten((coords, [var_dict[var_name] for var_name in var_names]))).A
    if fixed_basepoint:
      inv_func = lambda var_dict: base_inv_func(*flatten([var_dict[var_name] for var_name in var_names])).A
    else:
      inv_func = lambda coords, var_dict: base_inv_func(*flatten((coords, [var_dict[var_name] for var_name in var_names]))).A
  else:
    if fixed_endpoint:
      func = lambda var_vals: base_func(*flatten(var_vals)).A
    else:
      func = lambda coords, var_vals: base_func(*flatten((coords, var_vals))).A
    if fixed_basepoint:
      inv_func = lambda var_vals: base_inv_func(*flatten(var_vals)).A
    else:
      inv_func = lambda coords, var_vals: base_inv_func(*flatten((coords, var_vals))).A

  return func, inv_func

def eval_expr(expr,variables,container,name):
        vals={}
        for k in container:
                vals[k.name]=k.x
                vals["S"+k.name]=k.Sx
        #x = expr.evalf(subs=vals)
        f=lambdify(tuple(vals.keys()),expr,"numpy")
        x = f(**vals)
        #little workaround
        leer=sy.Symbol("leer")
        f=0*leer

        for k in variables:
                f=f+ (sy.diff(expr,k))**2*sy.Symbol("S"+k.__str__())**2
        f=sy.sqrt(f)
        #print "Formel:"
        #print ur"\begin*{equation}"
        #print sy.latex(expr)
        #print ur"\end{equation}"
        #print "Fehler"
        #print ur"\begin*{equation}"
	#sy.pprint(f)
        #print ur"\end{equation}"
        gf = lambdify(tuple(vals.keys()),f,"numpy")
        Sx = gf(**vals)
        return (Groesse(name,x.dimensionality.string,x.magnitude,Sx.magnitude),expr,f)

    def _eval_evalf(self, prec):
        """Evaluate this complex root to the given precision. """
        with workprec(prec):
            g = self.poly.gen
            if not g.is_Symbol:
                d = Dummy('x')
                func = lambdify(d, self.expr.subs(g, d))
            else:
                func = lambdify(g, self.expr)

            interval = self._get_interval()
            if not self.is_real:
                # For complex intervals, we need to keep refining until the
                # imaginary interval is disjunct with other roots, that is,
                # until both ends get refined.
                ay = interval.ay
                by = interval.by
                while interval.ay == ay or interval.by == by:
                    interval = interval.refine()

            while True:
                if self.is_real:
                    x0 = mpf(str(interval.center))
                else:
                    x0 = mpc(*map(str, interval.center))
                try:
                    root = findroot(func, x0, verify=False)
                    # If the (real or complex) root is not in the 'interval',
                    # then keep refining the interval. This happens if findroot
                    # accidentally finds a different root outside of this
                    # interval because our initial estimate 'x0' was not close
                    # enough.
                    if self.is_real:
                        a = mpf(str(interval.a))
                        b = mpf(str(interval.b))
                        if a == b:
                            root = a
                            break
                        if not (a < root < b):
                            raise ValueError("Root not in the interval.")
                    else:
                        ax = mpf(str(interval.ax))
                        bx = mpf(str(interval.bx))
                        ay = mpf(str(interval.ay))
                        by = mpf(str(interval.by))
                        if ax == bx and ay == by:
                            root = ax + S.ImaginaryUnit*by
                            break
                        if not (ax < root.real < bx and ay < root.imag < by):
                            raise ValueError("Root not in the interval.")
                except ValueError:
                    interval = interval.refine()
                    continue
                else:
                    break

        return Float._new(root.real._mpf_, prec) + I*Float._new(root.imag._mpf_, prec)

 def accepted(self):
     expr = parse_expr(self.fEdit.text())
     f = lambdify(x, expr)
     df = lambdify(x, expr.diff(x))
     N = 1
     delta = float(self.deltaEdit.text())
     x0 = float(self.xEdit.text())
     x1 = x0-f(x0)/df(x0)
     while not closeEnaught(x0, x1, delta):
         x0 = x1
         x1 = x0-f(x0)/df(x0)
         N += 1
     self.listWidget.addItem("x = " + str(x1) + ", N = " + str(N))

    def graphicalButtonClicked(self):
        color1 = None
        if self.f1colorBox.currentIndex() == 0:
            color1 = 'r'
        elif self.f1colorBox.currentIndex() == 1:
            color1 = 'b'
        elif self.f1colorBox.currentIndex() == 2:
            color1 = 'g'
        elif self.f1colorBox.currentIndex() == 3:
            color1 = 'y'
        elif self.f1colorBox.currentIndex() == 4:
            color1 = 'm'
        elif self.f1colorBox.currentIndex() == 5:
            color1 = 'c'

        color2 = None
        if self.f2colorBox.currentIndex() == 0:
            color2 = 'r'
        elif self.f2colorBox.currentIndex() == 1:
            color2 = 'b'
        elif self.f2colorBox.currentIndex() == 2:
            color2 = 'g'
        elif self.f2colorBox.currentIndex() == 3:
            color2 = 'y'
        elif self.f2colorBox.currentIndex() == 4:
            color2 = 'm'
        elif self.f2colorBox.currentIndex() == 5:
            color2 = 'c'

        expr1 = parse_expr(self.f1Edit.text())
        expr2 = parse_expr(self.f2Edit.text())

        f1 = lambdify(x, expr1, 'numpy')
        f2 = lambdify(x, expr2, 'numpy')

        try:
            minX = float(self.minxEdit.text())
            maxX = float(self.maxxEdit.text())
        except:
            QMessageBox.warning(self, "Warning", "Min and max values error type.")
            return

        if minX <= maxX:
            x1 = np.linspace(minX, maxX, (maxX-minX)*1000)
            self.plotW.figure.clf()
            self.plotW.plot(x1, f1(x1), color1)
            self.plotW.plot(x1, f2(x1), color2)
        else:
            QMessageBox.warning(self, "Warning", "Min value must be smaller than max value")

 def SIMethod(self):
     self.x0 = float(self.x0EditSI.text())
     self.eps = float(self.epsEditSI.text())
     self.fexpr = parse_expr(self.fEditSI.text())
     self.phiexpr = parse_expr(self.phiEditSI.text())
     self.f = lambdify(x, self.fexpr)
     self.phi = lambdify(x, self.phiexpr)
     self.x1 = 0
     self.N = 0
     while True:
         self.x1 = self.phi(self.x0)
         self.N += 1
         if closeEnaught(self.x1, self.x0, self.eps) or self.f(self.x1) == 0:
             self.listWidget.addItem("x = "+str(self.x1)+", N = "+str(self.N))
             break
         self.x0 = self.x1

def isolate(alg, eps=None, fast=False):
    """Give a rational isolating interval for an algebraic number. """
    alg = sympify(alg)

    if alg.is_Rational:
        return (alg, alg)
    elif not ask(Q.real(alg)):
        raise NotImplementedError(
            "complex algebraic numbers are not supported")

    func = lambdify((), alg, modules="mpmath", printer=IntervalPrinter())

    poly = minpoly(alg, polys=True)
    intervals = poly.intervals(sqf=True)

    dps, done = mp.dps, False

    try:
        while not done:
            alg = func()

            for a, b in intervals:
                if a <= alg.a and alg.b <= b:
                    done = True
                    break
            else:
                mp.dps *= 2
    finally:
        mp.dps = dps

    if eps is not None:
        a, b = poly.refine_root(a, b, eps=eps, fast=fast)

    return (a, b)

    def _eval_evalf(self, prec):
        """Evaluate this complex root to the given precision. """
        _prec, mp.prec = mp.prec, prec

        try:
            func = lambdify(self.poly.gen, self.expr)

            interval = self._get_interval()
            refined =  False

            while True:
                if self.is_real:
                    x0 = mpf(str(interval.center))
                else:
                    x0 = mpc(*map(str, interval.center))

                try:
                    root = findroot(func, x0)
                except ValueError:
                    interval = interval.refine()
                    refined = True
                    continue
                else:
                    if refined:
                        self._set_interval(interval)

                    break
        finally:
            mp.prec = _prec

        return Float._new(root.real._mpf_, prec) + I*Float._new(root.imag._mpf_, prec)

def d2V_func(lat, V, field_var):
    "Calculate the masses of the fields in terms of the field values:"

    field_list = lat.field_list

    from sympy import diff, Symbol, var, simplify, sympify, S, evalf
    from sympy.utilities import lambdify
    from sympy.core.sympify import SympifyError

    C_coeff = V.C_coeff
    D_coeff = V.D_coeff
    V_string = V.V

    try:
        d2V = diff(sympify(V_string),field_var,2)

    except SympifyError:
        print "Could not parse expression."

    "Replacement list C_i->C_coeff[i], D_i->D_coeff[i]:"
    rep_list = {}
    for i in xrange(len(C_coeff)):
        rep_list.update({'C'+str(i+1):C_coeff[i]})
    for i in xrange(len(D_coeff)):
        rep_list.update({'D'+str(i+1):D_coeff[i]})
    
    d2V_func = lambdify(field_list,d2V.subs(rep_list))

    return d2V_func

    def eval_rational(self, tol):
        """
        Return a Rational approximation to ``self`` with the tolerance ``tol``.

        This method uses bisection, which is very robust and it will always
        converge. The returned Rational instance will be at most 'tol' from the
        exact root.

        The following example first obtains Rational approximation to 1e-7
        accuracy for all roots of the 4-th order Legendre polynomial, and then
        evaluates it to 5 decimal digits (so all digits will be correct
        including rounding):

        >>> from sympy import S, legendre_poly, Symbol
        >>> x = Symbol("x")
        >>> p = legendre_poly(4, x, polys=True)
        >>> roots = [r.eval_rational(S(1)/10**7) for r in p.real_roots()]
        >>> roots = [str(r.n(5)) for r in roots]
        >>> roots
        ['-0.86114', '-0.33998', '0.33998', '0.86114']

        """

        if not self.is_real:
            raise NotImplementedError(
                "eval_rational() only works for real polynomials so far")
        func = lambdify(self.poly.gen, self.expr)
        interval = self._get_interval()
        a = Rational(str(interval.a))
        b = Rational(str(interval.b))
        return bisect(func, a, b, tol)

def f_min(y,mi,mx,stp):
	"""
	y  - form of analytical function 
	mi - plot and analyze in interval starting from this value 
	mx - plot and alalyze in interval ending with this value 
	stp- stepsize on the x axis. (with a little imagination it can be 
		considered as resolution 
	"""
	fd=[];d={}
	t=np.arange(mi,mx,stp)
	ly=lambdify(x,y)
	dy=y.diff()
	ldy=lambdify(x,dy)
	
	print 'Analitical function:    ',y
	print 'first derivative:       ',dy
	
	for i in np.arange(mi,mx,stp):
		# searhing where the first derivative is zero OR NEAR ZERO! 
		# /technically the same way can be done with lambdify 
		if -0.01 < dy.subs(x,i).evalf() < 0.01:
			yy=y.subs(x,i).evalf()
			print 'local extreme at (x,y):  (%s,  %s)' %(i,yy)
			d[yy]=i
	ix=max(d.keys())
	ixmin=min(d.keys())
	iy=d.get(ix)
	iymin=d.get(ixmin)
	print ' '	
	print 'Global minimum at (x,y): (%s,  %s) ' %(iymin,ixmin)
	print 'Global maximum at (x,y): (%s,  %s) ' %(iy,ix)
	
	plt.figure('minimi')
	o1=[];o2=[]
	for ii in np.arange(mi,mx,stp):
		o1.append(ly(ii))
		o2.append(ldy(ii))   # the plot option below 
#	plt.plot(t,ly(np.arange(mi,mx,stp)))
	plt.plot(t,o1)
#	plt.plot(t,ldy(np.arange(mi,mx,stp)))
	plt.plot(t,o2)
	plt.plot(iy,ix,'ro',iymin,ixmin,'bo')
	plt.legend(['y= %s'%y,'dy= %s' %dy, 'extreme point global max','extreme point global min'])
	plt.show()

    def _eval_evalf(self, prec):
        """Evaluate this complex root to the given precision. """
        _prec, mp.prec = mp.prec, prec

        try:
            func = lambdify(self.poly.gen, self.expr)

            interval = self._get_interval()
            if not self.is_real:
                # For complex intervals, we need to keep refining until the
                # imaginary interval is disjunct with other roots, that is,
                # until both ends get refined.
                ay = interval.ay
                by = interval.by
                while interval.ay == ay or interval.by == by:
                    interval = interval.refine()

            while True:
                if self.is_real:
                    x0 = mpf(str(interval.center))
                else:
                    x0 = mpc(*map(str, interval.center))

                try:
                    root = findroot(func, x0)
                    # If the (real or complex) root is not in the 'interval',
                    # then keep refining the interval. This happens if findroot
                    # accidentally finds a different root outside of this
                    # interval because our initial estimate 'x0' was not close
                    # enough.
                    if self.is_real:
                        a = mpf(str(interval.a))
                        b = mpf(str(interval.b))
                        # This is needed due to the bug #3364:
                        a, b = min(a, b), max(a, b)
                        if not (a < root < b):
                            raise ValueError("Root not in the interval.")
                    else:
                        ax = mpf(str(interval.ax))
                        bx = mpf(str(interval.bx))
                        ay = mpf(str(interval.ay))
                        by = mpf(str(interval.by))
                        # This is needed due to the bug #3364:
                        ax, bx = min(ax, bx), max(ax, bx)
                        ay, by = min(ay, by), max(ay, by)
                        if not (ax < root.real < bx and ay < root.imag < by):
                            raise ValueError("Root not in the interval.")
                except ValueError:
                    interval = interval.refine()
                    continue
                else:
                    break
        finally:
            mp.prec = _prec

        return Float._new(root.real._mpf_, prec) + I*Float._new(root.imag._mpf_, prec)

    def solve(self, iterations=10, until=None, threshold=0.001,
              debuglist=None):
        """ Runs the solver.

            The solver will try to find a solution until one of the
            conditions is reached:
                (1) the iterations limit is reached
                    In this case a SolutionNotFoundError will be raised.
                (2) the until condition returns True

            Arguments:
                iterations: The number of iterations to run until
                    a solution is reached. (Default: 10)
                until: This is a function that determines whether or
                    not a solution is reached.  (Default: residual error)
                    This takes two parameters, the previous solution
                    vector and the current solution vector.
                threshold: If using the default end condition, this is the
                    threshold that the residuals must be less than.

            Raises:
                SolutionNotFoundError:
        """
        # pylint: disable=invalid-name
        self._validate_equations()

        current = self._get_context()
        if len(self.solutions) == 0:
            self._update_solutions({k.name: v for k, v in current.items()})

        # do we need to update the function lambdas?  This is needed
        # if the number of variables/parameters/equations change.
        if self._need_function_update:
            arg_list = [x for x in current.keys()]
            for i in xrange(len(arg_list)):
                if isinstance(arg_list[i], Symbol):
                    arg_list[i]._index = i

            private_funcs = {x[2].__name__: x[1] for x in _RT_FUNCS}

            for var in self.variables.values():
                var.equation.func = lambdify(arg_list,
                                             var.equation.expr,
                                             private_funcs)

            self._need_function_update = False

        solution = _run_solver(self.equations,
                               self.variables,
                               current,
                               max_iterations=iterations,
                               until=until,
                               threshold=threshold,
                               debuglist=debuglist)
        soln = {k.name: v for k, v in solution.items()}
        self._update_solutions(soln)

def makefunc(expr, mathmodule = "numpy", dummify=False, **kwargs):
    symbols = list(expr.atoms(sp.Symbol))
    symbols.sort(key=str)
    func = lambdify(symbols, expr, mathmodule, dummify=dummify, **kwargs)
    func.kw = symbols
    func.expr = expr
    func.kwstr = map(lambda x: x.name, symbols)
    func.dictcall = types.MethodType(dictcall, func)
    func.__doc__ = str(expr)
    return func

 def _construct(self, zet):
     if not isinstance(zet, AbstractSet):
         zet = as_abstract(zet)
     var = zet.variables
     expr = zet.expr
     func = lambdify(var, expr)
     if len(var) == 1:
         return bitmap(func, self.voxels)
     else:
         return bitmap(lambda v: func(*v), self.voxels)

 def RelaxMethod(self):
     self.x0 = float(self.phiEditSI.text())
     self.a = self.x0
     self.b = float(self.x0EditSI.text())
     self.eps = float(self.epsEditSI.text())
     self.fexpr = parse_expr(self.fEditSI.text())
     self.f = lambdify(x, self.fexpr)
     xarg = np.linspace(self.a, self.b, np.abs(self.b-self.a)*1000)
     dfexpr = self.fexpr.diff(x)
     df = lambdify(x, dfexpr, 'numpy')
     dfa = np.fabs(df(xarg))
     M1 = np.max(dfa)
     m1 = np.min(dfa)
     tau = 2/(M1+m1)
     ro0 = (M1-m1)/(M1+m1)
     self.N = (np.floor(np.log((self.eps*(1-ro0))/(self.b-self.a))/np.log(ro0))+1).astype(np.int64)
     x1 = self.x0 + tau * self.f(self.x0)
     self.x0 = x1
     for i in range(self.N-1):
         x1 = self.x0 + tau * self.f(self.x0)
         self.x0 = x1
     self.listWidget.addItem("x = "+str(x1)+", N = "+str(self.N))

    def analyticalButtonClicked(self):
        self.derTableWidget.clear()
        self.tableWidget.clear()
        self.tableWidget.setRowCount(0)
        self.derTableWidget.setColumnCount(0)
        expr = parse_expr(self.fEdit.text())
        f = lambdify(x, expr, 'numpy')
        diff = expr.diff(x)
        diffroots = solve(diff, x)
        diffroots.insert(0, float("-inf"))
        diffroots.append(float("inf"))
        colPosition = self.derTableWidget.columnCount()
        self.derTableWidget.setRowCount(2)
        self.derTableWidget.insertColumn(colPosition)
        self.derTableWidget.setItem(0, colPosition, QTableWidgetItem("DerInterval"))
        self.derTableWidget.setItem(1, colPosition, QTableWidgetItem("Sign f(x)"))
        for i in range(len(diffroots)):
            colPosition = self.derTableWidget.columnCount()
            self.derTableWidget.insertColumn(colPosition)
            self.derTableWidget.setItem(0, colPosition, QTableWidgetItem(("%f"%(diffroots[i]))))
            self.derTableWidget.setItem(1, colPosition, QTableWidgetItem(str(sign(f(diffroots[i])))))

        xspace = np.linspace(int(diffroots[1]-100), int(diffroots[len(diffroots)-2]+100), int(diffroots[len(diffroots)-2]-diffroots[1]+201))
        #TODO: to end work with long table and algorithm with step
        dct = {}
        for i in xspace:
            dct[i] = sign(f(i))
        self.tableWidget.setColumnCount(2)
        rowCount = self.tableWidget.rowCount()
        self.tableWidget.insertRow(rowCount)
        self.tableWidget.setItem(rowCount, 0, QTableWidgetItem("x"))
        self.tableWidget.setItem(rowCount, 1, QTableWidgetItem("Sign f(x)"))
        keylist = []
        keylist = dct.keys()
        for key in sorted(keylist):
            rowCount = self.tableWidget.rowCount()
            self.tableWidget.insertRow(rowCount)
            self.tableWidget.setItem(rowCount, 0, QTableWidgetItem("%f" %key))
            self.tableWidget.setItem(rowCount, 1, QTableWidgetItem(dct[key]))

        self.derEdit.setText(str(diff))

        intervals = ''
        keylist = sorted(keylist)
        for i in range(len(keylist)-1):
            if (dct[keylist[i]] == '-' and dct[keylist[i+1]] == '+') or (dct[keylist[i]] == '+' and dct[keylist[i+1]] == '-'):
                intervals =( "%s%s" %(intervals, makeinterval(keylist[i], keylist[i+1], f)))
            elif (dct[keylist[i]] == '0'):
                intervals = ('%s{%f} and' % (intervals, keylist[i]))

        self.rootIntervalEdit.setText(intervals)

def index_post(name = None):
    if(request.method == 'POST'):

        default_asot = "343.822718 + x*1.8291"
        adlib_size_of_time = str(request.form.get('adlib_eq', default_asot, type=str))
        if adlib_size_of_time == "":
            adlib_size_of_time = default_asot
        sim_len = int(request.form.get('sim_len', 80, type=int))
        restr_len = int(request.form.get('restr_len', 50, type=int))
        restr = float(request.form.get('restr', 9, type=float)) / 100
        market_price = float(request.form.get('market_price', 2.89, type=float))
        feed_cost = float(request.form.get('feed_cost', 0.25, type=float))
        fac_cost = float(request.form.get('fac_cost', 0.35, type=float))
        int_rate = float(request.form.get('int_rate', 7.5, type=float)) / 100

        adlib_size_of_time += "-y"
        adlib_size_of_time = parse_expr(adlib_size_of_time)
        TIME = Symbol("x")
        SIZE = Symbol("y")
        # print solve(adlib_size_of_time, SIZE)
        # print solve(adlib_size_of_time, TIME)
        get_adlib_size = lambdify(TIME, solve(adlib_size_of_time, SIZE)[0])
        get_adlib_time = lambdify(SIZE, solve(adlib_size_of_time, TIME)[0])

        sim = simulation.Simulation(sim_len, restr_len, restr)
        sim.eqs.get_adlib_size = get_adlib_size
        sim.eqs.get_adlib_time = get_adlib_time
        sim.feed_cost = feed_cost
        sim.facility_cost = fac_cost
        sim.market_price = market_price
        sim.discount = int_rate
        
        sim.run_complete()

        graph_url = get_graph_url(sim)

        print "plot url: ", graph_url
        return render_template("output.html", ploturl = graph_url)

def _f(variables, expression):
    if not expression or expression == "None":
        return None
    elif callable(expression):
        return expression
    else:
        if len(variables) == 1 and "|" in variables[0] and Symbol is not None:
            expression = sympify(expression)
            present_variables = expression.free_symbols
            for preferred in map(Symbol, variables[0].split("|")):
                if preferred in present_variables:
                    present_variables.remove(preferred)
                    preferred = (preferred,)
                    break
            else:
                preferred = ()
            variables = *preferred, *(str(v) + "=0" for v in present_variables)
        return lambdify(variables, expression)

def isolate(alg, eps=None, fast=False):
    """Give a rational isolating interval for an algebraic number. """
    alg = sympify(alg)

    if alg.is_Rational:
        return (alg, alg)
    elif not ask(Q.real(alg)):
        raise NotImplementedError("complex algebraic numbers are not supported")

    from sympy.printing.lambdarepr import LambdaPrinter

    class IntervalPrinter(LambdaPrinter):
        """Use ``lambda`` printer but print numbers as ``mpi`` intervals. """

        def _print_Integer(self, expr):
            return "mpi('%s')" % super(IntervalPrinter, self)._print_Integer(expr)

        def _print_Rational(self, expr):
            return "mpi('%s')" % super(IntervalPrinter, self)._print_Rational(expr)

    func = lambdify((), alg, modules="mpmath", printer=IntervalPrinter())

    poly = minpoly(alg, polys=True)
    intervals = poly.intervals(sqf=True)

    dps, done = mp.dps, False

    try:
        while not done:
            alg = func()

            for a, b in intervals:
                if a <= alg.a and alg.b <= b:
                    done = True
                    break
            else:
                mp.dps *= 2
    finally:
        mp.dps = dps

    if eps is not None:
        a, b = poly.refine_root(a, b, eps=eps, fast=fast)

    return (a, b)