Python sympy.Sum() Examples

def duration(self) -> ExpressionScalar:
        step_size = self._loop_range.step.sympified_expression
        loop_index = sympy.symbols(self._loop_index)
        sum_index = sympy.symbols(self._loop_index)

        # replace loop_index with sum_index dependable expression
        body_duration = self.body.duration.sympified_expression.subs({loop_index: self._loop_range.start.sympified_expression + sum_index*step_size})

        # number of sum contributions
        step_count = sympy.ceiling((self._loop_range.stop.sympified_expression-self._loop_range.start.sympified_expression) / step_size)
        sum_start = 0
        sum_stop = sum_start + (sympy.functions.Max(step_count, 1) - 1)

        # expression used if step_count >= 0
        finite_duration_expression = sympy.Sum(body_duration, (sum_index, sum_start, sum_stop))

        duration_expression = sympy.Piecewise((0, step_count <= 0),
                                              (finite_duration_expression, True))

        return ExpressionScalar(duration_expression) 

def integral(self) -> Dict[ChannelID, ExpressionScalar]:

        step_size = self._loop_range.step.sympified_expression
        loop_index = sympy.symbols(self._loop_index)
        sum_index = sympy.symbols(self._loop_index)

        body_integrals = self.body.integral
        body_integrals = {
            c: body_integrals[c].sympified_expression.subs(
                {loop_index: self._loop_range.start.sympified_expression + sum_index*step_size}
            )
            for c in body_integrals
        }

        # number of sum contributions
        step_count = sympy.ceiling((self._loop_range.stop.sympified_expression-self._loop_range.start.sympified_expression) / step_size)
        sum_start = 0
        sum_stop = sum_start + (sympy.functions.Max(step_count, 1) - 1)

        for c in body_integrals:
            channel_integral_expr = sympy.Sum(body_integrals[c], (sum_index, sum_start, sum_stop))
            body_integrals[c] = ExpressionScalar(channel_integral_expr)

        return body_integrals 

def _needs_mul_brackets(self, expr, last=False):
        """
        Returns True if the expression needs to be wrapped in brackets when
        printed as part of a Mul, False otherwise. This is True for Add,
        but also for some container objects that would not need brackets
        when appearing last in a Mul, e.g. an Integral. ``last=True``
        specifies that this expr is the last to appear in a Mul.
        """
        from sympy import Integral, Piecewise, Product, Sum
        return expr.is_Add or (not last and
            any([expr.has(x) for x in (Integral, Piecewise, Product, Sum)])) 

def _symbol(self):
        # TODO: naive implementation
        dummy_loss = sympy.Symbol("dummy_loss")
        if self.max_iter:
            max_iter = self.max_iter
        else:
            max_iter = sympy.Symbol(sympy.latex(self.timpstep_symbol) + "_{max}")

        _symbol = sympy.Sum(dummy_loss, (self.timpstep_symbol, 1, max_iter))
        _symbol = _symbol.subs({dummy_loss: self.step_loss._symbol})
        return _symbol 

def handle_sum_or_prod(func, name):
    val      = convert_mp(func.mp())
    iter_var = convert_expr(func.subeq().equality().expr(0))
    start    = convert_expr(func.subeq().equality().expr(1))
    if func.supexpr().expr(): # ^{expr}
        end = convert_expr(func.supexpr().expr())
    else: # ^atom
        end = convert_atom(func.supexpr().atom())
        

    if name == "summation":
        return sympy.Sum(val, (iter_var, start, end))
    elif name == "product":
        return sympy.Product(val, (iter_var, start, end)) 

def _print_Mul(self, product):
        a = []  # items in the numerator
        b = []  # items that are in the denominator (if any)

        if self.order not in ('old', 'none'):
            args = product.as_ordered_factors()
        else:
            args = product.args

        # Gather terms for numerator/denominator
        for item in args:
            if item.is_commutative and item.is_Pow and item.exp.is_Rational and item.exp.is_negative:
                b.append(C.Pow(item.base, -item.exp))
            elif item.is_Rational and item is not S.Infinity:
                if item.p != 1:
                    a.append( C.Rational(item.p) )
                if item.q != 1:
                    b.append( C.Rational(item.q) )
            else:
                a.append(item)

        from sympy import Integral, Piecewise, Product, Sum

        # Convert to pretty forms. Add parens to Add instances if there
        # is more than one term in the numer/denom
        for i in xrange(0, len(a)):
            if (a[i].is_Add and len(a) > 1) or (i != len(a) - 1 and
                    isinstance(a[i], (Integral, Piecewise, Product, Sum))):
                a[i] = prettyForm(*self._print(a[i]).parens())
            else:
                a[i] = self._print(a[i])

        for i in xrange(0, len(b)):
            if (b[i].is_Add and len(b) > 1) or (i != len(b) - 1 and
                    isinstance(b[i], (Integral, Piecewise, Product, Sum))):
                b[i] = prettyForm(*self._print(b[i]).parens())
            else:
                b[i] = self._print(b[i])

        # Construct a pretty form
        if len(b) == 0:
            return prettyForm.__mul__(*a)
        else:
            if len(a) == 0:
                a.append( self._print(S.One) )
            return prettyForm.__mul__(*a)/prettyForm.__mul__(*b)

    # A helper function for _print_Pow to print x**(1/n) 

def normal_ordered_form(expr, independent=False, recursive_limit=10,
                        _recursive_depth=0):
    """Write an expression with bosonic or fermionic operators on normal
    ordered form, where each term is normally ordered. Note that this
    normal ordered form is equivalent to the original expression.

    Parameters
    ==========

    expr : expression
        The expression write on normal ordered form.

    recursive_limit : int (default 10)
        The number of allowed recursive applications of the function.

    Examples
    ========

    >>> from sympsi import Dagger
    >>> from sympsi.boson import BosonOp
    >>> from sympsi.operatorordering import normal_ordered_form
    >>> a = BosonOp("a")
    >>> normal_ordered_form(a * Dagger(a))
    1 + Dagger(a)*a
    """

    if _recursive_depth > recursive_limit:
        warnings.warn("Too many recursions, aborting")
        return expr

    if isinstance(expr, Add):
        return _normal_ordered_form_terms(expr,
                                          recursive_limit=recursive_limit,
                                          _recursive_depth=_recursive_depth,
                                          independent=independent)
    elif isinstance(expr, Mul):
        return _normal_ordered_form_factor(expr,
                                           recursive_limit=recursive_limit,
                                           _recursive_depth=_recursive_depth,
                                           independent=independent)

    elif isinstance(expr, Expectation):
        return Expectation(normal_ordered_form(expr.expression), 
                           expr.is_normal_order)
                           
    elif isinstance(expr, (Sum, Integral)):
        nargs = [normal_ordered_form(expr.function,
                                     recursive_limit=recursive_limit,
                                     _recursive_depth=_recursive_depth,
                                     independent=independent)]
        for lim in expr.limits:
            nargs.append(lim)
        return type(expr)(*nargs)

    else:
        return expr