Python sympy.latex函数代码示例

    def solution_statement(self):
        lines = solutions.Lines()

        if self._qp['question_type'] == 'mean':
            lines += r'$E(X) = \sum\limits_{{i=1}}^{{n}} x_{{i}} \times Pr(X = x_{{i}})$'

            lines += r'$= {expectation_of_x} = {answer}$'.format(
                expectation_of_x=expressions.discrete_expectation_x(self._qp['prob_table']),
                answer=self._qp['answer']
            )

        elif self._qp['question_type'] == 'variance':

            lines += r'$Var(X) = E(X^2) - (E(X))^2$'

            lines += r'$= [{expectation_of_x_squared}] - [{expectation_of_x}]^2$'.format(
                expectation_of_x_squared=expressions.discrete_expectation_x_squared(self._qp['prob_table']),
                expectation_of_x=expressions.discrete_expectation_x(self._qp['prob_table'])
            )

            expectation_of_x = prob_table.expectation_x(self._qp['prob_table'])
            expectation_of_x_squared = prob_table.expectation_x(self._qp['prob_table'], power=2)
            lines += r'$= {expectation_of_x_squared} - {expectation_of_x}^2 = {answer}$'.format(
                expectation_of_x_squared=sympy.latex(expectation_of_x_squared),
                expectation_of_x=sympy.latex(expectation_of_x),
                answer=sympy.latex(self._qp['answer'])
            )

        elif self._qp['question_type'] == 'mode':
            lines += r'${answer}$'.format(
                answer=prob_table.mode(self._qp['prob_table'])
            )

        return lines.write()

def relation(interval_or_relation, var=x):
    """Return LaTeX that represents an interval or a relation as a chained inequality.

    e.g. [1, 5] --> 1 < x < 5
    """
    if isinstance(interval_or_relation, (sympy.StrictLessThan, sympy.LessThan, sympy.StrictGreaterThan, sympy.GreaterThan)):
        interval = functions.relation_to_interval(interval_or_relation)
    else:
        interval = interval_or_relation

    if isinstance(interval_or_relation, sympy.Union):
        raise NotImplementedError('unions are not yet supported')

    if interval.left == -sympy.oo and interval.right == sympy.oo:
        return r'{0} < {1} < {2}'.format(sympy.latex(-sympy.oo), sympy.latex(var), sympy.latex(sympy.oo))
    elif interval.left == -sympy.oo:
        operator = r'<' if interval.right_open else r'\le'
        return r'{0} {1} {2}'.format(sympy.latex(var), operator, sympy.latex(interval.right))
    elif interval.right == sympy.oo:
        operator = r'>' if interval.left_open else r'\ge'
        return r'{0} {1} {2}'.format(sympy.latex(var), operator, sympy.latex(interval.left))
    else:
        left_operator = r'<' if interval.left_open else r'\le'
        right_operator = r'<' if interval.right_open else r'\le'
        return r'{0} {1} {2} {3} {4}'.format(
            sympy.latex(interval.left),
            left_operator,
            sympy.latex(var),
            right_operator,
            sympy.latex(interval.right)
        )

def print_latex():

    # edo_main()
    for i in range(1, 7):
        Respostas[i] = sympy.nsimplify(Respostas[i], rational=True, tolerance=0.05).evalf(prec)

    # 0- Raizes; 1- Forma Natural da respsota; 2- Resposta Natural;
    # 3- Resposta Particular; 4- Resposta Transitoria; 5- Respsota Forcada
    # 6- Resposta Completa; 7-Sinal de entrada x(t); 8 - eq
    ###
    eqDiferencialEntradaLatex = latex(Respostas[8])

    ##Perfumaria
    dif = 0.9 - 0.77
    xdif = -0.15
    font = {"family": "Sans", "weight": "normal", "size": 18}

    plt.rc("font", **font)

    ##Obtendo as respostas em Latex
    RespostasEmLatex = [0] * (len(Respostas))
    raizEmLatex = [0] * (len(Respostas[0]))
    str_raizLatex = ""
    for i in range(len(Respostas[0])):
        raizEmLatex[i] = "$" + str(latex(Respostas[0][i])) + "$"
    for i in range(len(raizEmLatex)):
        rn = "r" + str(i + 1) + " = "
        rn = "$" + str(latex(rn)) + "$"
        str_raizLatex = str_raizLatex + "\t" + rn + raizEmLatex[i]
    ##print len(RespostasEmLatex)
    for i in range(len(Respostas)):
        RespostasEmLatex[i] = "$" + str(latex(Respostas[i])) + "$"
    # print RespostasEmLatex
    # xTLatex = '$' + latex(xT) +'$'
    ###Preparando para imprimir
    log_figure = plt.figure("Representacao", facecolor="white")
    ax1 = plt.axes(frameon=False)
    ax1.get_xaxis().tick_bottom()
    ax1.get_xaxis().set_visible(False)
    ax1.axes.get_yaxis().set_visible(False)
    for i in range(0, 8, 1):
        plt.axhline(0.86 - dif * i, xmin=-5, xmax=5, color="black", lw=0.2, linestyle=":")
    # log_figure.figure("Forma_Representativa:")
    plt.title("")
    plt.text(xdif, 0.89, "Eq dif: 0=" + ur"$" + eqDiferencialEntradaLatex + "$")
    plt.text(xdif, 0.89 - dif, "Forma Natural:" + ur"" + RespostasEmLatex[1])
    plt.text(xdif, 0.9 - 2 * dif, "yn(t) = " + ur"" + RespostasEmLatex[2])
    plt.text(xdif, 0.9 - 3 * dif, "ypar(t) = " + ur"" + RespostasEmLatex[3])
    plt.text(xdif, 0.9 - 4 * dif, "ytran(t) = " + ur"" + RespostasEmLatex[4])
    plt.text(xdif, 0.9 - 5 * dif, "yfor(t) = " + ur"" + RespostasEmLatex[5])
    plt.text(xdif, 0.9 - 6 * dif, "yc(t) = " + ur"" + RespostasEmLatex[6])
    plt.text(xdif, 0.9 - 7 * dif, "x(t) = " + ur"" + RespostasEmLatex[7])
    plt.text(xdif, 0.9 - 8 * dif, "Raiz(es): " + ur"" + str_raizLatex)

    plt.subplots_adjust(left=0.11, bottom=0.08, right=0.50, top=0.88, wspace=0.22, hspace=0.21)

    ##log_figure.set_size_inches(19.2,10.8)
    # log_figure.show()
    plt.show()
    return log_figure

def formula(quantity):
    """ returns error formula of quantity as latex code

    Args:
        quantity: Quantity object

    Return:
        latex code string of error formula
    """

    assert isinstance(quantity, Quantity)

    if quantity.error_formula is None:
        raise ValueError("quantity '%s' doesn't have an error formula." % quantity.name)

    formula = quantity.error_formula
    if isinstance(formula,str):
        return formula
    else:
        # replace "_err" by sigma function
        sigma = Function("\sigma")
        for var in formula.free_symbols:
            if var.name[-4:] == "_err":
                formula = formula.subs(var, sigma( Symbol(var.name[:-4], **var._assumptions)))
        latex_code = latex(sigma(quantity)) + " = " + latex(formula)

    form_button, form_code = pytex.hide_div('Formula', '$%s$' % (latex_code) , hide = False)
    latex_button, latex_code = pytex.hide_div('LaTex', latex_code)
    res = 'Error Formula for %s<div width=20px/>%s%s<hr/>%s<br>%s' % (
        '$%s$' % latex(quantity), form_button, latex_button, form_code, latex_code)

    return render_latex(res)

def baseparms_pretty_latex(delta,Pb,Pd,Kd):
    base_latex = []
    delta_b = Pb.T * delta
    delta_d = Pd.T * delta
    n_b = len(delta_b)
    n_d = len(delta_d)
    for i in range(n_b):
        _latex = latex( delta_b[i] )
        l = []
        for j in range(n_d):
            c = Kd[i,j]
            if c == -1 or c == 1:
                _latex += ' ' + ('+ ' if c > 0 else'') + latex( c * delta_d[j] )
            elif c != 0 and j not in l:
                ll = []
                for jj in range(j,n_d):
                    cc = Kd[i,jj]
                    if cc == c:
                        l.append(jj)
                        ll.append(delta_d[jj])
                p = (' \, ( ',' ) ') if (len(ll) > 1) else (' \, ','')
                ll_sum = ' + '.join( [ latex( lli ) for lli in ll] )
                _latex += ' ' + ('+ ' if c > 0 else'') + latex( c.n() ) + p[0] + ll_sum + p[1]
        base_latex.append(_latex)
    return base_latex;

    def solution_statement(self):
        lines = solutions.Lines()

        ball_combinations = itertools.combinations(self._qp['items'], self._qp['n_selections'])
        valid_total_sum_combinations = [i for i in ball_combinations if sum(i) == self._qp['sum']]

        # e.g. Pr(sum = 14) = 3! * Pr(ball1 = 3 and ball2 = 5 and ball3 = 6)
        lines += r'$Pr(\text{{sum}} = {sum}) = {sum_of_probabilities}$'.format(
            sum=self._qp['sum'],
            sum_of_probabilities=expressions.sum_combination_probabilities(valid_total_sum_combinations)
        )

        probability_of_a_single_combination = self.single_combination_probability()
        prob_instance = r'{n_valid_permutations} \times {probability_of_a_single_combination}'.format(
            n_valid_permutations=math.factorial(self._qp['n_selections']),
            probability_of_a_single_combination=sympy.latex(probability_of_a_single_combination)
        )

        # e.g. = 6 * (1/120) + 6 * (1/120)
        lines += r'$= {probabilities_sum}$'.format(
            probabilities_sum=' + '.join([prob_instance] * len(valid_total_sum_combinations))
        )

        answer = probability_of_a_single_combination * math.factorial(self._qp['n_selections']) * len(valid_total_sum_combinations)
        # e.g. = 1/20
        lines += r'$= {answer}$'.format(answer=sympy.latex(answer))

        return lines.write()

def table_groesse(expr,variables,container,name,formula=False,einheit="default"):
        (X,expr,Sexpr)=eval_expr(expr,variables,container,name)
	if einheit!="default":
		X.convert_einheit(einheit)	
        x=ur"\bigskip"
        if formula==True:
                x+=ur"\begin{equation*} "+name+" = "+sy.latex(expr)+"\end{equation*}"
                x+=ur"\begin{equation*} S"+name+" = "+sy.latex(Sexpr)+"\end{equation*}"
        s=ur""
        s2=ur""
        if X.x.dimensionality.string != "dimensionless":
                x+=ur"S"+name+" = "+sy.latex(Sexpr)+ur"\\"
        s=ur""
        s2=ur""
        if X.x.dimensionality.string != "dimensionless":
                s+=name+" in "+str(X.x.dimensionality.string)
        else: 
                s+=name
        for k in X.x.magnitude:
                s+="& %.3f " % k
                s2+="r|"
        s+=ur"\\ \hline "
        if X.Sx.dimensionality.string!= "dimensionless":
                s+="S"+name+" in "+str(X.Sx.dimensionality.string)
        else:
                s+="S"+name
        for k in X.Sx.magnitude:
                s+="& %.3f " % k
        s+=ur"\\ \hline"       
        x+=ur"""\normalsize \vspace{3 mm}
	\begin{tabular}{| l | """+s2+"""}
	\hline
        """+s+ur"""
	\end{tabular} \\ \bigskip """
	return x

 def arc_length_explain(self, start, stop, a_type = None,
                        explanation_type=None, preview = None):
     
     
     if a_type is None:
         a_type = self.a_type
         
     v = self.v_
     u = self.u
     
     start = sym.sympify(start)
     stop = sym.sympify(stop)
     
    
     if explanation_type is None:
         explanation_type = self.kwargs.get('explanation_type', 'simple')
     
     if preview is None:
         preview = self.kwargs.get('preview', False)  
    
     
     explanation = ArcLengthProb(path='arc_length/explanation', 
                 a_type = a_type, 
                 explanation_type = explanation_type,
                 preview = preview).explain()
                 
     explanation += """
         <p>
         For this problem the curve is $_C$_ is given by $_%s$_
         with the independent variable being $_%s$_ on the interval 
         $_[%s,%s]$_. So the arc length is
         $$s =\\int_{%s}^{%s} \sqrt{1+\\left(\\frac{d%s}{d%s}\\right)^2}\,d%s$$
         $$\\frac{d%s}{d%s} = %s = %s$$
         \\begin{align}
           \\sqrt{1 + \\left(%s\\right)^2} &= \\sqrt{%s} \\\\
             &= \sqrt{\\left(%s\\right)^2} = %s
         \\end{align}
         </p>
     """%tuple(map(lambda x: sym.latex(x).replace("\\log","\\ln"), 
                   [sym.Eq(v, self.v), u, start, stop, start, stop, 
                    v, u, u, v, u, 
                    self.Dv, self.dv, self.dv, 1 + (self.dv**2).expand(), 
                     self.ds, self.ds]))
     
     aa = [sym.latex(self.arc_length(start, stop,'integral')), 
           "\\left." + sym.latex(self.Ids).replace('\\log', '\\ln') +
           "\\right|_{%s=%s}^{%s=%s}"%(u, start, u, stop),
          sym.latex(self.arc_length(start, stop,'exact')).replace("\\log", "\\ln") + 
          '\\approx %.3f'%(self.arc_length(start, stop,'numeric'))]
     
     # Add self.numeric / self.anti 
     
     explanation += """
         <p>
         Thus the arclength is given by
         %s
         </p>
     """%(tools.align(*aa))
     #
     return explanation

    def __str__(self):
        
        s = ""
        xi = [r'\vec i', r'\vec j', r'\vec k']
        phi = r"\phi(\vec r)"
        
        for key in sorted(self.stateMap.keys()):
            s += self.beginTable()

            qNums = str(self.stateMap[key]).strip("]").strip("[")
            
            genericFactor = self.genericFactor(self.stateMap[key])            
            
            s += "$\phi_{%d} \\rightarrow \phi_{%s}$\\\\\n" % (key, qNums)
            s += "\hline\n"
            s += "$%s$ & $%s$\\\\\n" % (phi, latex(self.orbitals[key]/genericFactor))
            s += "\hline\n"
         
            for i in range(self.dim):
                s+= "$%s\cdot \\nabla %s$ & $%s$\\\\\n" % \
                        (xi[i], phi, latex(self.gradients[key][i]/genericFactor))
           
            s += "\hline\n"
            s += "$\\nabla^2 %s$ & $%s$\\\\\n" % (phi, latex(self.Laplacians[key]/genericFactor))
            s += self.endTable(caption="Orbital expressions %s : %s. Factor $%s$ is omitted." % \
                                (self.__class__.__name__, qNums, latex(genericFactor)))
            
            if (key+1)%self.figsPrPage == 0:
                s += "\\clearpage\n"
            
        return s

def print_latex():



        # 0- Raizes; 1- Forma Natural da respsota; 2- Resposta Natural;
        # 3- Resposta Particular; 4- Resposta Transitoria; 5- Respsota Forcada
        # 6- Resposta Completa
        # 7-Sinal de entrada x(t)

        ##Perfumaria
        dif = 0.9 -0.75
        xdif = -0.15

        font = {'family' : 'Arial',
		'weight' : 'normal',
		'size'   : 18}

        plt.rc('font', **font)
        #plt.rc('text', usetex=True)

        ##Obtendo as respostas em Latex
        RespostasEmLatex = [0]*(len(Respostas))
        #print len(RespostasEmLatex)
        for i in range(len(Respostas)):RespostasEmLatex[i] = '$'+str(latex(Respostas[i])) +'$'

        ## Tratamento Inicial para as raizes:
        #replace(a, old, new[, count])
        #r'$\left( \begin{array}{ll} 2 & 3 \\ 4 & 5 \end{array} \right)$'
        #$\begin{bmatrix}-1.5, & 1.0\end{bmatrix}$
        #\begin{Bmatrix} x & y \\ z & v \end{Bmatrix}
        #print RespostasEmLatex[0]
        #RespostasEmLatex[0]= RespostasEmLatex[0].replace("bmatrix","Bmatrix")
        #RespostasEmLatex[0]= RespostasEmLatex[0].replace("}$","})$",1)
        #print RespostasEmLatex[0]

        ####


        #print RespostasEmLatex
        xTLatex = '$' + latex(xT) +'$'
        ###Preparando para imprimir
        log_figure = plt.figure("Representacao",facecolor='white')
        ax1 = plt.axes(frameon = False)
        ax1.get_xaxis().tick_bottom()
        ax1.get_xaxis().set_visible(False)
        ax1.axes.get_yaxis().set_visible(False)
        for i in range(0,7,1):plt.axhline(dif*i,xmin = -5,xmax = 5, color = 'black',lw =1.5, linestyle = ':')
        #log_figure.figure("Forma_Representativa:")
        plt.title('')
        #print RespostasEmLatex[0]
        #plt.text(xdif,0.05,'Raizes:'+str(Respostas[0]))
        plt.text(xdif,0.9,'Forma Natural:'+ur''+RespostasEmLatex[1])
        plt.text(xdif,0.9-dif,'yn(t) = '+ur''+RespostasEmLatex[2])
        plt.text(xdif,0.9-2*dif,'ypar(t) = '+ur''+RespostasEmLatex[3])
        plt.text(xdif,0.9-3*dif,'ytran(t) = '+ur''+RespostasEmLatex[4])
        plt.text(xdif,0.9-4*dif,'yfor(t) = '+ur''+RespostasEmLatex[5])
        plt.text(xdif,0.9-5*dif,'yc(t) = '+ur''+RespostasEmLatex[6])
        plt.text(xdif,0.9-6*dif,'x(t) = '+ur''+xTLatex)

        log_figure.show()

    def visit_Call(self, node):
        buffer = []
        fname = node.func.id

        # Only apply to lowercase names (i.e. functions, not classes)
        if fname in self.__class__.EXCEPTIONS:
            node.func.id = self.__class__.EXCEPTIONS[fname].__name__
            self.latex = sympy.latex(self.evaluator.eval_node(node))
        else:
            result = self.format(fname, node)
            if result:
                self.latex = result
            elif fname[0].islower() and fname not in OTHER_SYMPY_FUNCTIONS:
                buffer.append("\\mathrm{%s}" % fname.replace('_', '\\_'))
                buffer.append('(')

                latexes = []
                for arg in node.args:
                    if isinstance(arg, ast.Call) and arg.func.id[0].lower() == arg.func.id[0]:
                        latexes.append(self.visit_Call(arg))
                    else:
                        latexes.append(sympy.latex(self.evaluator.eval_node(arg)))

                buffer.append(', '.join(latexes))
                buffer.append(')')

                self.latex = ''.join(buffer)
            else:
                self.latex = sympy.latex(self.evaluator.eval_node(node))
        return self.latex

    def solution_statement(self):
        lines = solutions.Lines()

        derivative = self._qp['equation'].diff()
        lines += r'''$y = {equation}, y' = {derivative}$'''.format(
            equation=sympy.latex(self._qp['equation']),
            derivative=sympy.latex(derivative)
        )

        original_y_coordinate = self._qp['equation'].subs({x: self._qp['location']})
        lines += r'$y({original_x_coordinate}) = {original_y_coordinate}$'.format(
            original_x_coordinate=self._qp['location'],
            original_y_coordinate=original_y_coordinate
        )

        derivative_at_original_location = derivative.subs({x: self._qp['location']})
        lines += r'''$y'({original_x_coordinate}) = {derivative_at_original_location}$'''.format(
            original_x_coordinate=self._qp['location'],
            derivative_at_original_location=sympy.latex(derivative_at_original_location)
        )

        unevaluated_approximation_of_answer = noevals.noevalAdd(original_y_coordinate, noevals.noevalMul(self._qp['delta'], derivative_at_original_location))
        answer = original_y_coordinate + self._qp['delta'] * derivative_at_original_location
        lines += r'$\therefore y({new_x_coordinate}) \approx {unevaluated_approximation_of_answer} = {answer}$'.format(
            new_x_coordinate=self._qp['new_location'],
            unevaluated_approximation_of_answer=noevals.latex(unevaluated_approximation_of_answer),
            answer=sympy.latex(answer)
        )

        return lines.write()

def simplex_table_to_tex_solution_only(table):
    solution = ''
    var, target = table.solution
    for i in range(table.amount_of_vars):
        solution += "$x_{" + "{0:<2}".format(i) + "} = " + latex(var[i]) + '$\\\\'
    solution += '$\Psi = ' + latex(target) + '$'
    return solution

    def formula(self, quantity, adjust=True):
        """ returns error formula of quantity as latex code

        Args:
            quantity: name of quantity or Quantity object
            adjust: if True, replaces "_err" suffix by "\sigma" function and adds equals sign in front

        Return:
            latex code string of error formula
        """

        quantity = quantities.parse_expr(quantity, self.data)
        assert isinstance(quantity, quantities.Quantity)

        if quantity.error_formula is None:
            raise ValueError("quantity '%s' doesn't have an error formula.")

        formula = quantity.error_formula
        if isinstance(formula,str):
            return formula
        else:
            # replace "_err" by sigma function
            if adjust:
                sigma = Function("\sigma")
                for var in formula.free_symbols:
                    if var.name[-4:] == "_err":
                        formula = formula.subs(var, sigma( Symbol(var.name[:-4], **var._assumptions)))
                return latex(sigma(quantity)) + " = " + latex(formula)
            return formula

def simplex_table_to_tex_table_only(table):
    ret = """\\begin{tabular}{|c|"""
    ret += ("c|"*(table.amount_of_vars + 1))
    ret += "} \\hline"

    ret += " & \\T \\B $ "
    for j in range(table.amount_of_vars):
        ret += "$&$"
        ret += "x_{"+"{0:<2}".format(j) +"}"
    ret += "$\\\\ \\hline "

    for i in range(table.amount_of_equations):
        ret += "$x_{" + "{0:<2}".format(table.basis[i]) + "}$"
        ret += "& \\T \\B $ "
        ret += latex(table.free[i])
        for j in range(table.amount_of_vars):
            ret += "$&$"
            ret += latex(table.limits[i][j])
        ret += "$\\\\ \\hline "

    ret += "$\Psi$ & $"
    ret += latex(table.target_free)
    for j in range(table.amount_of_vars):
        ret += "$&\\T \\B$"
        ret += latex(table.target[j])
    ret += "$\\\\ \\hline "

    ret += """\\end{tabular}"""
    return ret