Printing System¶

See the Printing section in Tutorial for introduction into printing.

This guide documents the printing system in SymPy and how it works internally.

Printer Class¶

Printing subsystem driver

SymPy’s printing system works the following way: Any expression can be passed to a designated Printer who then is responsible to return an adequate representation of that expression.

The basic concept is the following:

Let the object print itself if it knows how.
Take the best fitting method defined in the printer.
As fall-back use the emptyPrinter method for the printer.

Which Method is Responsible for Printing?¶

The whole printing process is started by calling .doprint(expr) on the printer which you want to use. This method looks for an appropriate method which can print the given expression in the given style that the printer defines. While looking for the method, it follows these steps:

Let the object print itself if it knows how.

The printer looks for a specific method in every object. The name of that method depends on the specific printer and is defined under Printer.printmethod. For example, StrPrinter calls _sympystr and LatexPrinter calls _latex. Look at the documentation of the printer that you want to use. The name of the method is specified there.

This was the original way of doing printing in sympy. Every class had its own latex, mathml, str and repr methods, but it turned out that it is hard to produce a high quality printer, if all the methods are spread out that far. Therefore all printing code was combined into the different printers, which works great for built-in sympy objects, but not that good for user defined classes where it is inconvenient to patch the printers.
Take the best fitting method defined in the printer.
The printer loops through expr classes (class + its bases), and tries to dispatch the work to _print_<EXPR_CLASS>

e.g., suppose we have the following class hierarchy:
Basic | Atom | Number | Rational
then, for expr=Rational(...), the Printer will try to call printer methods in the order as shown in the figure below:
p._print(expr) | |-- p._print_Rational(expr) | |-- p._print_Number(expr) | |-- p._print_Atom(expr) | `-- p._print_Basic(expr)
if ._print_Rational method exists in the printer, then it is called, and the result is returned back. Otherwise, the printer tries to call ._print_Number and so on.
As a fall-back use the emptyPrinter method for the printer.

As fall-back self.emptyPrinter will be called with the expression. If not defined in the Printer subclass this will be the same as str(expr).

Example of Custom Printer¶

In the example below, we have a printer which prints the derivative of a function in a shorter form.

from sympy import Symbol
from sympy.printing.latex import LatexPrinter, print_latex
from sympy.core.function import UndefinedFunction, Function


class MyLatexPrinter(LatexPrinter):
    """Print derivative of a function of symbols in a shorter form.
    """
    def _print_Derivative(self, expr):
        function, *vars = expr.args
        if not isinstance(type(function), UndefinedFunction) or \
           not all(isinstance(i, Symbol) for i in vars):
            return super()._print_Derivative(expr)

        # If you want the printer to work correctly for nested
        # expressions then use self._print() instead of str() or latex().
        # See the example of nested modulo below in the custom printing
        # method section.
        return "{}_{{{}}}".format(
            self._print(Symbol(function.func.__name__)),
                        ''.join(self._print(i) for i in vars))


def print_my_latex(expr):
    """ Most of the printers define their own wrappers for print().
    These wrappers usually take printer settings. Our printer does not have
    any settings.
    """
    print(MyLatexPrinter().doprint(expr))


y = Symbol("y")
x = Symbol("x")
f = Function("f")
expr = f(x, y).diff(x, y)

# Print the expression using the normal latex printer and our custom
# printer.
print_latex(expr)
print_my_latex(expr)

The output of the code above is:

\frac{\partial^{2}}{\partial x\partial y}  f{\left(x,y \right)}
f_{xy}

Example of Custom Printing Method¶

In the example below, the latex printing of the modulo operator is modified. This is done by overriding the method _latex of Mod.

from sympy import Symbol, Mod, Integer
from sympy.printing.latex import print_latex


class ModOp(Mod):
    def _latex(self, printer=None):
        # Always use printer.doprint() otherwise nested expressions won't
        # work. See the example of ModOpWrong.
        a, b = [printer.doprint(i) for i in self.args]
        return r"\operatorname{Mod}{\left( %s,%s \right)}" % (a,b)


class ModOpWrong(Mod):
    def _latex(self, printer=None):
        a, b = [str(i) for i in self.args]
        return r"\operatorname{Mod}{\left( %s,%s \right)}" % (a,b)


x = Symbol('x')
m = Symbol('m')

print_latex(ModOp(x, m))
print_latex(Mod(x, m))

# Nested modulo.
print_latex(ModOp(ModOp(x, m), Integer(7)))
print_latex(ModOpWrong(ModOpWrong(x, m), Integer(7)))

The output of the code above is:

\operatorname{Mod}{\left( x,m \right)}
x\bmod{m}
\operatorname{Mod}{\left( \operatorname{Mod}{\left( x,m \right)},7 \right)}
\operatorname{Mod}{\left( ModOpWrong(x, m),7 \right)}

The main class responsible for printing is Printer (see also its source code):

class sympy.printing.printer.Printer(settings=None)[source]¶

Generic printer

Its job is to provide infrastructure for implementing new printers easily.

If you want to define your custom Printer or your custom printing method for your custom class then see the example above: printer_example .

printmethod = None¶

_print(expr, **kwargs)[source]¶

Internal dispatcher

Tries the following concepts to print an expression:

Let the object print itself if it knows how.
Take the best fitting method defined in the printer.
As fall-back use the emptyPrinter method for the printer.

doprint(expr)[source]¶: Returns printer’s representation for expr (as a string)

classmethod set_global_settings(**settings)[source]¶: Set system-wide printing settings.

PrettyPrinter Class¶

The pretty printing subsystem is implemented in sympy.printing.pretty.pretty by the PrettyPrinter class deriving from Printer. It relies on the modules sympy.printing.pretty.stringPict, and sympy.printing.pretty.pretty_symbology for rendering nice-looking formulas.

The module stringPict provides a base class stringPict and a derived class prettyForm that ease the creation and manipulation of formulas that span across multiple lines.

The module pretty_symbology provides primitives to construct 2D shapes (hline, vline, etc) together with a technique to use unicode automatically when possible.

class sympy.printing.pretty.pretty.PrettyPrinter(settings=None)[source]¶

Printer, which converts an expression into 2D ASCII-art figure.

printmethod = '_pretty'¶

sympy.printing.pretty.pretty.pretty(expr, **settings)[source]¶

Returns a string containing the prettified form of expr.

For information on keyword arguments see pretty_print function.

sympy.printing.pretty.pretty.pretty_print(expr, wrap_line=True, num_columns=None, use_unicode=None, full_prec='auto', order=None, use_unicode_sqrt_char=True, root_notation=True, mat_symbol_style='plain', imaginary_unit='i')[source]¶

Prints expr in pretty form.

pprint is just a shortcut for this function.

Parameters

expr : expression

The expression to print.

wrap_line : bool, optional (default=True)

Line wrapping enabled/disabled.

num_columns : int or None, optional (default=None)

Number of columns before line breaking (default to None which reads the terminal width), useful when using SymPy without terminal.

use_unicode : bool or None, optional (default=None)

Use unicode characters, such as the Greek letter pi instead of the string pi.

full_prec : bool or string, optional (default=”auto”)

Use full precision.

order : bool or string, optional (default=None)

Set to ‘none’ for long expressions if slow; default is None.

use_unicode_sqrt_char : bool, optional (default=True)

Use compact single-character square root symbol (when unambiguous).

root_notation : bool, optional (default=True)

Set to ‘False’ for printing exponents of the form 1/n in fractional form. By default exponent is printed in root form.

mat_symbol_style : string, optional (default=”plain”)

Set to “bold” for printing MatrixSymbols using a bold mathematical symbol face. By default the standard face is used.

imaginary_unit : string, optional (default=”i”)

Letter to use for imaginary unit when use_unicode is True. Can be “i” (default) or “j”.

C code printers¶

This class implements C code printing, i.e. it converts Python expressions to strings of C code (see also C89CodePrinter).

Usage:

>>> from sympy.printing import print_ccode
>>> from sympy.functions import sin, cos, Abs, gamma
>>> from sympy.abc import x
>>> print_ccode(sin(x)**2 + cos(x)**2, standard='C89')
pow(sin(x), 2) + pow(cos(x), 2)
>>> print_ccode(2*x + cos(x), assign_to="result", standard='C89')
result = 2*x + cos(x);
>>> print_ccode(Abs(x**2), standard='C89')
fabs(pow(x, 2))
>>> print_ccode(gamma(x**2), standard='C99')
tgamma(pow(x, 2))

sympy.printing.ccode.known_functions_C89 = {'Abs': [(<function <lambda>>, 'fabs'), (<function <lambda>>, 'abs')], 'acos': 'acos', 'asin': 'asin', 'atan': 'atan', 'atan2': 'atan2', 'ceiling': 'ceil', 'cos': 'cos', 'cosh': 'cosh', 'exp': 'exp', 'floor': 'floor', 'log': 'log', 'sin': 'sin', 'sinh': 'sinh', 'tan': 'tan', 'tanh': 'tanh'}¶

sympy.printing.ccode.known_functions_C99 = {'Abs': [(<function <lambda>>, 'fabs'), (<function <lambda>>, 'abs')], 'Cbrt': 'cbrt', 'Max': 'fmax', 'Min': 'fmin', 'acos': 'acos', 'acosh': 'acosh', 'asin': 'asin', 'asinh': 'asinh', 'atan': 'atan', 'atan2': 'atan2', 'atanh': 'atanh', 'ceiling': 'ceil', 'cos': 'cos', 'cosh': 'cosh', 'erf': 'erf', 'erfc': 'erfc', 'exp': 'exp', 'exp2': 'exp2', 'expm1': 'expm1', 'floor': 'floor', 'fma': 'fma', 'gamma': 'tgamma', 'hypot': 'hypot', 'log': 'log', 'log10': 'log10', 'log1p': 'log1p', 'log2': 'log2', 'loggamma': 'lgamma', 'sin': 'sin', 'sinh': 'sinh', 'tan': 'tan', 'tanh': 'tanh'}¶

class sympy.printing.ccode.C89CodePrinter(settings={})[source]¶

A printer to convert python expressions to strings of c code

printmethod = '_ccode'¶

indent_code(code)[source]¶: Accepts a string of code or a list of code lines

class sympy.printing.ccode.C99CodePrinter(settings={})[source]¶

printmethod = '_ccode'¶

sympy.printing.ccode.ccode(expr, assign_to=None, standard='c99', **settings)[source]¶

Converts an expr to a string of c code

Parameters

expr : Expr

A sympy expression to be converted.

assign_to : optional

When given, the argument is used as the name of the variable to which the expression is assigned. Can be a string, Symbol, MatrixSymbol, or Indexed type. This is helpful in case of line-wrapping, or for expressions that generate multi-line statements.

standard : str, optional

String specifying the standard. If your compiler supports a more modern standard you may set this to ‘c99’ to allow the printer to use more math functions. [default=’c89’].

precision : integer, optional

The precision for numbers such as pi [default=17].

user_functions : dict, optional

A dictionary where the keys are string representations of either FunctionClass or UndefinedFunction instances and the values are their desired C string representations. Alternatively, the dictionary value can be a list of tuples i.e. [(argument_test, cfunction_string)] or [(argument_test, cfunction_formater)]. See below for examples.

dereference : iterable, optional

An iterable of symbols that should be dereferenced in the printed code expression. These would be values passed by address to the function. For example, if dereference=[a], the resulting code would print (*a) instead of a.

human : bool, optional

If True, the result is a single string that may contain some constant declarations for the number symbols. If False, the same information is returned in a tuple of (symbols_to_declare, not_supported_functions, code_text). [default=True].

contract: bool, optional

If True, Indexed instances are assumed to obey tensor contraction rules and the corresponding nested loops over indices are generated. Setting contract=False will not generate loops, instead the user is responsible to provide values for the indices in the code. [default=True].

Examples

>>> from sympy import ccode, symbols, Rational, sin, ceiling, Abs, Function
>>> x, tau = symbols("x, tau")
>>> expr = (2*tau)**Rational(7, 2)
>>> ccode(expr)
'8*M_SQRT2*pow(tau, 7.0/2.0)'
>>> ccode(expr, math_macros={})
'8*sqrt(2)*pow(tau, 7.0/2.0)'
>>> ccode(sin(x), assign_to="s")
's = sin(x);'
>>> from sympy.codegen.ast import real, float80
>>> ccode(expr, type_aliases={real: float80})
'8*M_SQRT2l*powl(tau, 7.0L/2.0L)'

Simple custom printing can be defined for certain types by passing a dictionary of {“type” : “function”} to the user_functions kwarg. Alternatively, the dictionary value can be a list of tuples i.e. [(argument_test, cfunction_string)].

>>> custom_functions = {
...   "ceiling": "CEIL",
...   "Abs": [(lambda x: not x.is_integer, "fabs"),
...           (lambda x: x.is_integer, "ABS")],
...   "func": "f"
... }
>>> func = Function('func')
>>> ccode(func(Abs(x) + ceiling(x)), standard='C89', user_functions=custom_functions)
'f(fabs(x) + CEIL(x))'

or if the C-function takes a subset of the original arguments:

>>> ccode(2**x + 3**x, standard='C99', user_functions={'Pow': [
...   (lambda b, e: b == 2, lambda b, e: 'exp2(%s)' % e),
...   (lambda b, e: b != 2, 'pow')]})
'exp2(x) + pow(3, x)'

Piecewise expressions are converted into conditionals. If an assign_to variable is provided an if statement is created, otherwise the ternary operator is used. Note that if the Piecewise lacks a default term, represented by (expr, True) then an error will be thrown. This is to prevent generating an expression that may not evaluate to anything.

>>> from sympy import Piecewise
>>> expr = Piecewise((x + 1, x > 0), (x, True))
>>> print(ccode(expr, tau, standard='C89'))
if (x > 0) {
tau = x + 1;
}
else {
tau = x;
}

Support for loops is provided through Indexed types. With contract=True these expressions will be turned into loops, whereas contract=False will just print the assignment expression that should be looped over:

>>> from sympy import Eq, IndexedBase, Idx
>>> len_y = 5
>>> y = IndexedBase('y', shape=(len_y,))
>>> t = IndexedBase('t', shape=(len_y,))
>>> Dy = IndexedBase('Dy', shape=(len_y-1,))
>>> i = Idx('i', len_y-1)
>>> e=Eq(Dy[i], (y[i+1]-y[i])/(t[i+1]-t[i]))
>>> ccode(e.rhs, assign_to=e.lhs, contract=False, standard='C89')
'Dy[i] = (y[i + 1] - y[i])/(t[i + 1] - t[i]);'

Matrices are also supported, but a MatrixSymbol of the same dimensions must be provided to assign_to. Note that any expression that can be generated normally can also exist inside a Matrix:

>>> from sympy import Matrix, MatrixSymbol
>>> mat = Matrix([x**2, Piecewise((x + 1, x > 0), (x, True)), sin(x)])
>>> A = MatrixSymbol('A', 3, 1)
>>> print(ccode(mat, A, standard='C89'))
A[0] = pow(x, 2);
if (x > 0) {
   A[1] = x + 1;
}
else {
   A[1] = x;
}
A[2] = sin(x);

sympy.printing.ccode.print_ccode(expr, **settings)[source]¶: Prints C representation of the given expression.

C++ code printers¶

This module contains printers for C++ code, i.e. functions to convert SymPy expressions to strings of C++ code.

Usage:

>>> from sympy.printing.cxxcode import cxxcode
>>> from sympy.functions import Min, gamma
>>> from sympy.abc import x
>>> print(cxxcode(Min(gamma(x) - 1, x), standard='C++11'))
std::min(x, std::tgamma(x) - 1)

class sympy.printing.cxxcode.CXX98CodePrinter(settings=None)[source]¶

printmethod = '_cxxcode'¶

class sympy.printing.cxxcode.CXX11CodePrinter(settings=None)[source]¶

printmethod = '_cxxcode'¶

sympy.printing.cxxcode.cxxcode(expr, assign_to=None, standard='c++11', **settings)[source]¶: C++ equivalent of sympy.ccode().

RCodePrinter¶

This class implements R code printing (i.e. it converts Python expressions to strings of R code).

Usage:

>>> from sympy.printing import print_rcode
>>> from sympy.functions import sin, cos, Abs
>>> from sympy.abc import x
>>> print_rcode(sin(x)**2 + cos(x)**2)
sin(x)^2 + cos(x)^2
>>> print_rcode(2*x + cos(x), assign_to="result")
result = 2*x + cos(x);
>>> print_rcode(Abs(x**2))
abs(x^2)

sympy.printing.rcode.known_functions = {'Abs': 'abs', 'Max': 'max', 'Min': 'min', 'acos': 'acos', 'acosh': 'acosh', 'asin': 'asin', 'asinh': 'asinh', 'atan': 'atan', 'atan2': 'atan2', 'atanh': 'atanh', 'beta': 'beta', 'ceiling': 'ceiling', 'cos': 'cos', 'cosh': 'cosh', 'digamma': 'digamma', 'erf': 'erf', 'exp': 'exp', 'factorial': 'factorial', 'floor': 'floor', 'gamma': 'gamma', 'log': 'log', 'sign': 'sign', 'sin': 'sin', 'sinh': 'sinh', 'tan': 'tan', 'tanh': 'tanh', 'trigamma': 'trigamma'}¶

class sympy.printing.rcode.RCodePrinter(settings={})[source]¶

A printer to convert python expressions to strings of R code

printmethod = '_rcode'¶

indent_code(code)[source]¶: Accepts a string of code or a list of code lines

sympy.printing.rcode.rcode(expr, assign_to=None, **settings)[source]¶

Converts an expr to a string of r code

Parameters

expr : Expr

A sympy expression to be converted.

assign_to : optional

When given, the argument is used as the name of the variable to which the expression is assigned. Can be a string, Symbol, MatrixSymbol, or Indexed type. This is helpful in case of line-wrapping, or for expressions that generate multi-line statements.

precision : integer, optional

The precision for numbers such as pi [default=15].

user_functions : dict, optional

A dictionary where the keys are string representations of either FunctionClass or UndefinedFunction instances and the values are their desired R string representations. Alternatively, the dictionary value can be a list of tuples i.e. [(argument_test, rfunction_string)] or [(argument_test, rfunction_formater)]. See below for examples.

human : bool, optional

If True, the result is a single string that may contain some constant declarations for the number symbols. If False, the same information is returned in a tuple of (symbols_to_declare, not_supported_functions, code_text). [default=True].

contract: bool, optional

If True, Indexed instances are assumed to obey tensor contraction rules and the corresponding nested loops over indices are generated. Setting contract=False will not generate loops, instead the user is responsible to provide values for the indices in the code. [default=True].

Examples

>>> from sympy import rcode, symbols, Rational, sin, ceiling, Abs, Function
>>> x, tau = symbols("x, tau")
>>> rcode((2*tau)**Rational(7, 2))
'8*sqrt(2)*tau^(7.0/2.0)'
>>> rcode(sin(x), assign_to="s")
's = sin(x);'

Simple custom printing can be defined for certain types by passing a dictionary of {“type” : “function”} to the user_functions kwarg. Alternatively, the dictionary value can be a list of tuples i.e. [(argument_test, cfunction_string)].

>>> custom_functions = {
...   "ceiling": "CEIL",
...   "Abs": [(lambda x: not x.is_integer, "fabs"),
...           (lambda x: x.is_integer, "ABS")],
...   "func": "f"
... }
>>> func = Function('func')
>>> rcode(func(Abs(x) + ceiling(x)), user_functions=custom_functions)
'f(fabs(x) + CEIL(x))'

or if the R-function takes a subset of the original arguments:

>>> rcode(2**x + 3**x, user_functions={'Pow': [
...   (lambda b, e: b == 2, lambda b, e: 'exp2(%s)' % e),
...   (lambda b, e: b != 2, 'pow')]})
'exp2(x) + pow(3, x)'

Piecewise expressions are converted into conditionals. If an assign_to variable is provided an if statement is created, otherwise the ternary operator is used. Note that if the Piecewise lacks a default term, represented by (expr, True) then an error will be thrown. This is to prevent generating an expression that may not evaluate to anything.

>>> from sympy import Piecewise
>>> expr = Piecewise((x + 1, x > 0), (x, True))
>>> print(rcode(expr, assign_to=tau))
tau = ifelse(x > 0,x + 1,x);

Support for loops is provided through Indexed types. With contract=True these expressions will be turned into loops, whereas contract=False will just print the assignment expression that should be looped over:

>>> from sympy import Eq, IndexedBase, Idx
>>> len_y = 5
>>> y = IndexedBase('y', shape=(len_y,))
>>> t = IndexedBase('t', shape=(len_y,))
>>> Dy = IndexedBase('Dy', shape=(len_y-1,))
>>> i = Idx('i', len_y-1)
>>> e=Eq(Dy[i], (y[i+1]-y[i])/(t[i+1]-t[i]))
>>> rcode(e.rhs, assign_to=e.lhs, contract=False)
'Dy[i] = (y[i + 1] - y[i])/(t[i + 1] - t[i]);'

Matrices are also supported, but a MatrixSymbol of the same dimensions must be provided to assign_to. Note that any expression that can be generated normally can also exist inside a Matrix:

>>> from sympy import Matrix, MatrixSymbol
>>> mat = Matrix([x**2, Piecewise((x + 1, x > 0), (x, True)), sin(x)])
>>> A = MatrixSymbol('A', 3, 1)
>>> print(rcode(mat, A))
A[0] = x^2;
A[1] = ifelse(x > 0,x + 1,x);
A[2] = sin(x);

sympy.printing.rcode.print_rcode(expr, **settings)[source]¶: Prints R representation of the given expression.

Fortran Printing¶

The fcode function translates a sympy expression into Fortran code. The main purpose is to take away the burden of manually translating long mathematical expressions. Therefore the resulting expression should also require no (or very little) manual tweaking to make it compilable. The optional arguments of fcode can be used to fine-tune the behavior of fcode in such a way that manual changes in the result are no longer needed.

sympy.printing.fcode.fcode(expr, assign_to=None, **settings)[source]¶

Converts an expr to a string of fortran code

Parameters

expr : Expr

A sympy expression to be converted.

assign_to : optional

When given, the argument is used as the name of the variable to which the expression is assigned. Can be a string, Symbol, MatrixSymbol, or Indexed type. This is helpful in case of line-wrapping, or for expressions that generate multi-line statements.

precision : integer, optional

DEPRECATED. Use type_mappings instead. The precision for numbers such as pi [default=17].

user_functions : dict, optional

A dictionary where keys are FunctionClass instances and values are their string representations. Alternatively, the dictionary value can be a list of tuples i.e. [(argument_test, cfunction_string)]. See below for examples.

human : bool, optional

If True, the result is a single string that may contain some constant declarations for the number symbols. If False, the same information is returned in a tuple of (symbols_to_declare, not_supported_functions, code_text). [default=True].

contract: bool, optional

If True, Indexed instances are assumed to obey tensor contraction rules and the corresponding nested loops over indices are generated. Setting contract=False will not generate loops, instead the user is responsible to provide values for the indices in the code. [default=True].

source_format : optional

The source format can be either ‘fixed’ or ‘free’. [default=’fixed’]

standard : integer, optional

The Fortran standard to be followed. This is specified as an integer. Acceptable standards are 66, 77, 90, 95, 2003, and 2008. Default is 77. Note that currently the only distinction internally is between standards before 95, and those 95 and after. This may change later as more features are added.

name_mangling : bool, optional

If True, then the variables that would become identical in case-insensitive Fortran are mangled by appending different number of _ at the end. If False, SymPy won’t interfere with naming of variables. [default=True]

Examples

>>> from sympy import fcode, symbols, Rational, sin, ceiling, floor
>>> x, tau = symbols("x, tau")
>>> fcode((2*tau)**Rational(7, 2))
'      8*sqrt(2.0d0)*tau**(7.0d0/2.0d0)'
>>> fcode(sin(x), assign_to="s")
'      s = sin(x)'

Custom printing can be defined for certain types by passing a dictionary of “type” : “function” to the user_functions kwarg. Alternatively, the dictionary value can be a list of tuples i.e. [(argument_test, cfunction_string)].

>>> custom_functions = {
...   "ceiling": "CEIL",
...   "floor": [(lambda x: not x.is_integer, "FLOOR1"),
...             (lambda x: x.is_integer, "FLOOR2")]
... }
>>> fcode(floor(x) + ceiling(x), user_functions=custom_functions)
'      CEIL(x) + FLOOR1(x)'

Piecewise expressions are converted into conditionals. If an assign_to variable is provided an if statement is created, otherwise the ternary operator is used. Note that if the Piecewise lacks a default term, represented by (expr, True) then an error will be thrown. This is to prevent generating an expression that may not evaluate to anything.

>>> from sympy import Piecewise
>>> expr = Piecewise((x + 1, x > 0), (x, True))
>>> print(fcode(expr, tau))
      if (x > 0) then
         tau = x + 1
      else
         tau = x
      end if

Support for loops is provided through Indexed types. With contract=True these expressions will be turned into loops, whereas contract=False will just print the assignment expression that should be looped over:

>>> from sympy import Eq, IndexedBase, Idx
>>> len_y = 5
>>> y = IndexedBase('y', shape=(len_y,))
>>> t = IndexedBase('t', shape=(len_y,))
>>> Dy = IndexedBase('Dy', shape=(len_y-1,))
>>> i = Idx('i', len_y-1)
>>> e=Eq(Dy[i], (y[i+1]-y[i])/(t[i+1]-t[i]))
>>> fcode(e.rhs, assign_to=e.lhs, contract=False)
'      Dy(i) = (y(i + 1) - y(i))/(t(i + 1) - t(i))'

Matrices are also supported, but a MatrixSymbol of the same dimensions must be provided to assign_to. Note that any expression that can be generated normally can also exist inside a Matrix:

>>> from sympy import Matrix, MatrixSymbol
>>> mat = Matrix([x**2, Piecewise((x + 1, x > 0), (x, True)), sin(x)])
>>> A = MatrixSymbol('A', 3, 1)
>>> print(fcode(mat, A))
      A(1, 1) = x**2
         if (x > 0) then
      A(2, 1) = x + 1
         else
      A(2, 1) = x
         end if
      A(3, 1) = sin(x)

sympy.printing.fcode.print_fcode(expr, **settings)[source]¶

Prints the Fortran representation of the given expression.

See fcode for the meaning of the optional arguments.

class sympy.printing.fcode.FCodePrinter(settings={})[source]¶

A printer to convert sympy expressions to strings of Fortran code

printmethod = '_fcode'¶

indent_code(code)[source]¶: Accepts a string of code or a list of code lines

Two basic examples:

>>> from sympy import *
>>> x = symbols("x")
>>> fcode(sqrt(1-x**2))
'      sqrt(1 - x**2)'
>>> fcode((3 + 4*I)/(1 - conjugate(x)))
'      (cmplx(3,4))/(1 - conjg(x))'

An example where line wrapping is required:

>>> expr = sqrt(1-x**2).series(x,n=20).removeO()
>>> print(fcode(expr))
      -715.0d0/65536.0d0*x**18 - 429.0d0/32768.0d0*x**16 - 33.0d0/
     @ 2048.0d0*x**14 - 21.0d0/1024.0d0*x**12 - 7.0d0/256.0d0*x**10 -
     @ 5.0d0/128.0d0*x**8 - 1.0d0/16.0d0*x**6 - 1.0d0/8.0d0*x**4 - 1.0d0
     @ /2.0d0*x**2 + 1

In case of line wrapping, it is handy to include the assignment so that lines are wrapped properly when the assignment part is added.

>>> print(fcode(expr, assign_to="var"))
      var = -715.0d0/65536.0d0*x**18 - 429.0d0/32768.0d0*x**16 - 33.0d0/
     @ 2048.0d0*x**14 - 21.0d0/1024.0d0*x**12 - 7.0d0/256.0d0*x**10 -
     @ 5.0d0/128.0d0*x**8 - 1.0d0/16.0d0*x**6 - 1.0d0/8.0d0*x**4 - 1.0d0
     @ /2.0d0*x**2 + 1

For piecewise functions, the assign_to option is mandatory:

>>> print(fcode(Piecewise((x,x<1),(x**2,True)), assign_to="var"))
      if (x < 1) then
        var = x
      else
        var = x**2
      end if

Note that by default only top-level piecewise functions are supported due to the lack of a conditional operator in Fortran 77. Inline conditionals can be supported using the merge function introduced in Fortran 95 by setting of the kwarg standard=95:

>>> print(fcode(Piecewise((x,x<1),(x**2,True)), standard=95))
      merge(x, x**2, x < 1)

Loops are generated if there are Indexed objects in the expression. This also requires use of the assign_to option.

>>> A, B = map(IndexedBase, ['A', 'B'])
>>> m = Symbol('m', integer=True)
>>> i = Idx('i', m)
>>> print(fcode(2*B[i], assign_to=A[i]))
    do i = 1, m
        A(i) = 2*B(i)
    end do

Repeated indices in an expression with Indexed objects are interpreted as summation. For instance, code for the trace of a matrix can be generated with

>>> print(fcode(A[i, i], assign_to=x))
      x = 0
      do i = 1, m
          x = x + A(i, i)
      end do

By default, number symbols such as pi and E are detected and defined as Fortran parameters. The precision of the constants can be tuned with the precision argument. Parameter definitions are easily avoided using the N function.

>>> print(fcode(x - pi**2 - E))
      parameter (E = 2.7182818284590452d0)
      parameter (pi = 3.1415926535897932d0)
      x - pi**2 - E
>>> print(fcode(x - pi**2 - E, precision=25))
      parameter (E = 2.718281828459045235360287d0)
      parameter (pi = 3.141592653589793238462643d0)
      x - pi**2 - E
>>> print(fcode(N(x - pi**2, 25)))
      x - 9.869604401089358618834491d0

When some functions are not part of the Fortran standard, it might be desirable to introduce the names of user-defined functions in the Fortran expression.

>>> print(fcode(1 - gamma(x)**2, user_functions={'gamma': 'mygamma'}))
      1 - mygamma(x)**2

However, when the user_functions argument is not provided, fcode will generate code which assumes that a function of the same name will be provided by the user. A comment will be added to inform the user of the issue:

>>> print(fcode(1 - gamma(x)**2))
C     Not supported in Fortran:
C     gamma
      1 - gamma(x)**2

The printer can be configured to omit these comments:

>>> print(fcode(1 - gamma(x)**2, allow_unknown_functions=True))
      1 - gamma(x)**2

By default the output is human readable code, ready for copy and paste. With the option human=False, the return value is suitable for post-processing with source code generators that write routines with multiple instructions. The return value is a three-tuple containing: (i) a set of number symbols that must be defined as ‘Fortran parameters’, (ii) a list functions that cannot be translated in pure Fortran and (iii) a string of Fortran code. A few examples:

>>> fcode(1 - gamma(x)**2, human=False)
(set(), {gamma(x)}, '      1 - gamma(x)**2')
>>> fcode(1 - sin(x)**2, human=False)
(set(), set(), '      1 - sin(x)**2')
>>> fcode(x - pi**2, human=False)
({(pi, '3.1415926535897932d0')}, set(), '      x - pi**2')

Mathematica code printing¶

sympy.printing.mathematica.known_functions = {'Max': [(<function <lambda>>, 'Max')], 'Min': [(<function <lambda>>, 'Min')], 'acos': [(<function <lambda>>, 'ArcCos')], 'acosh': [(<function <lambda>>, 'ArcCosh')], 'acoth': [(<function <lambda>>, 'ArcCoth')], 'acsch': [(<function <lambda>>, 'ArcCsch')], 'asech': [(<function <lambda>>, 'ArcSech')], 'asin': [(<function <lambda>>, 'ArcSin')], 'asinh': [(<function <lambda>>, 'ArcSinh')], 'atan': [(<function <lambda>>, 'ArcTan')], 'atanh': [(<function <lambda>>, 'ArcTanh')], 'conjugate': [(<function <lambda>>, 'Conjugate')], 'cos': [(<function <lambda>>, 'Cos')], 'cosh': [(<function <lambda>>, 'Cosh')], 'cot': [(<function <lambda>>, 'Cot')], 'coth': [(<function <lambda>>, 'Coth')], 'csch': [(<function <lambda>>, 'Csch')], 'exp': [(<function <lambda>>, 'Exp')], 'log': [(<function <lambda>>, 'Log')], 'sech': [(<function <lambda>>, 'Sech')], 'sin': [(<function <lambda>>, 'Sin')], 'sinh': [(<function <lambda>>, 'Sinh')], 'tan': [(<function <lambda>>, 'Tan')], 'tanh': [(<function <lambda>>, 'Tanh')]}¶

class sympy.printing.mathematica.MCodePrinter(settings={})[source]¶

A printer to convert python expressions to strings of the Wolfram’s Mathematica code

printmethod = '_mcode'¶

sympy.printing.mathematica.mathematica_code(expr, **settings)[source]¶

Converts an expr to a string of the Wolfram Mathematica code

Examples

>>> from sympy import mathematica_code as mcode, symbols, sin
>>> x = symbols('x')
>>> mcode(sin(x).series(x).removeO())
'(1/120)*x^5 - 1/6*x^3 + x'

Javascript Code printing¶

sympy.printing.jscode.known_functions = {'Abs': 'Math.abs', 'Max': 'Math.max', 'Min': 'Math.min', 'acos': 'Math.acos', 'acosh': 'Math.acosh', 'asin': 'Math.asin', 'asinh': 'Math.asinh', 'atan': 'Math.atan', 'atan2': 'Math.atan2', 'atanh': 'Math.atanh', 'ceiling': 'Math.ceil', 'cos': 'Math.cos', 'cosh': 'Math.cosh', 'exp': 'Math.exp', 'floor': 'Math.floor', 'log': 'Math.log', 'sign': 'Math.sign', 'sin': 'Math.sin', 'sinh': 'Math.sinh', 'tan': 'Math.tan', 'tanh': 'Math.tanh'}¶

class sympy.printing.jscode.JavascriptCodePrinter(settings={})[source]¶

“A Printer to convert python expressions to strings of javascript code

printmethod = '_javascript'¶

indent_code(code)[source]¶: Accepts a string of code or a list of code lines

sympy.printing.jscode.jscode(expr, assign_to=None, **settings)[source]¶

Converts an expr to a string of javascript code

Parameters

expr : Expr

A sympy expression to be converted.

assign_to : optional

When given, the argument is used as the name of the variable to which the expression is assigned. Can be a string, Symbol, MatrixSymbol, or Indexed type. This is helpful in case of line-wrapping, or for expressions that generate multi-line statements.

precision : integer, optional

The precision for numbers such as pi [default=15].

user_functions : dict, optional

A dictionary where keys are FunctionClass instances and values are their string representations. Alternatively, the dictionary value can be a list of tuples i.e. [(argument_test, js_function_string)]. See below for examples.

human : bool, optional

If True, the result is a single string that may contain some constant declarations for the number symbols. If False, the same information is returned in a tuple of (symbols_to_declare, not_supported_functions, code_text). [default=True].

contract: bool, optional

If True, Indexed instances are assumed to obey tensor contraction rules and the corresponding nested loops over indices are generated. Setting contract=False will not generate loops, instead the user is responsible to provide values for the indices in the code. [default=True].

Examples

>>> from sympy import jscode, symbols, Rational, sin, ceiling, Abs
>>> x, tau = symbols("x, tau")
>>> jscode((2*tau)**Rational(7, 2))
'8*Math.sqrt(2)*Math.pow(tau, 7/2)'
>>> jscode(sin(x), assign_to="s")
's = Math.sin(x);'

Custom printing can be defined for certain types by passing a dictionary of “type” : “function” to the user_functions kwarg. Alternatively, the dictionary value can be a list of tuples i.e. [(argument_test, js_function_string)].

>>> custom_functions = {
...   "ceiling": "CEIL",
...   "Abs": [(lambda x: not x.is_integer, "fabs"),
...           (lambda x: x.is_integer, "ABS")]
... }
>>> jscode(Abs(x) + ceiling(x), user_functions=custom_functions)
'fabs(x) + CEIL(x)'

Piecewise expressions are converted into conditionals. If an assign_to variable is provided an if statement is created, otherwise the ternary operator is used. Note that if the Piecewise lacks a default term, represented by (expr, True) then an error will be thrown. This is to prevent generating an expression that may not evaluate to anything.

>>> from sympy import Piecewise
>>> expr = Piecewise((x + 1, x > 0), (x, True))
>>> print(jscode(expr, tau))
if (x > 0) {
   tau = x + 1;
}
else {
   tau = x;
}

Support for loops is provided through Indexed types. With contract=True these expressions will be turned into loops, whereas contract=False will just print the assignment expression that should be looped over:

>>> from sympy import Eq, IndexedBase, Idx
>>> len_y = 5
>>> y = IndexedBase('y', shape=(len_y,))
>>> t = IndexedBase('t', shape=(len_y,))
>>> Dy = IndexedBase('Dy', shape=(len_y-1,))
>>> i = Idx('i', len_y-1)
>>> e=Eq(Dy[i], (y[i+1]-y[i])/(t[i+1]-t[i]))
>>> jscode(e.rhs, assign_to=e.lhs, contract=False)
'Dy[i] = (y[i + 1] - y[i])/(t[i + 1] - t[i]);'

Matrices are also supported, but a MatrixSymbol of the same dimensions must be provided to assign_to. Note that any expression that can be generated normally can also exist inside a Matrix:

>>> from sympy import Matrix, MatrixSymbol
>>> mat = Matrix([x**2, Piecewise((x + 1, x > 0), (x, True)), sin(x)])
>>> A = MatrixSymbol('A', 3, 1)
>>> print(jscode(mat, A))
A[0] = Math.pow(x, 2);
if (x > 0) {
   A[1] = x + 1;
}
else {
   A[1] = x;
}
A[2] = Math.sin(x);

Julia code printing¶

sympy.printing.julia.known_fcns_src1 = ['sin', 'cos', 'tan', 'cot', 'sec', 'csc', 'asin', 'acos', 'atan', 'acot', 'asec', 'acsc', 'sinh', 'cosh', 'tanh', 'coth', 'sech', 'csch', 'asinh', 'acosh', 'atanh', 'acoth', 'asech', 'acschsinc', 'atan2', 'sign', 'floor', 'log', 'exp', 'cbrt', 'sqrt', 'erf', 'erfc', 'erfi', 'factorial', 'gamma', 'digamma', 'trigamma', 'polygamma', 'beta', 'airyai', 'airyaiprime', 'airybi', 'airybiprime', 'besselj', 'bessely', 'besseli', 'besselk', 'erfinv', 'erfcinv']¶

Built-in mutable sequence.

If no argument is given, the constructor creates a new empty list. The argument must be an iterable if specified.

sympy.printing.julia.known_fcns_src2 = {'Abs': 'abs', 'ceiling': 'ceil', 'conjugate': 'conj', 'hankel1': 'hankelh1', 'hankel2': 'hankelh2', 'im': 'imag', 're': 'real'}¶

class sympy.printing.julia.JuliaCodePrinter(settings={})[source]¶

A printer to convert expressions to strings of Julia code.

printmethod = '_julia'¶

indent_code(code)[source]¶: Accepts a string of code or a list of code lines

sympy.printing.julia.julia_code(expr, assign_to=None, **settings)[source]¶

Converts $expr$ to a string of Julia code.

Parameters

expr : Expr

A sympy expression to be converted.

assign_to : optional

When given, the argument is used as the name of the variable to which the expression is assigned. Can be a string, Symbol, MatrixSymbol, or Indexed type. This can be helpful for expressions that generate multi-line statements.

precision : integer, optional

The precision for numbers such as pi [default=16].

user_functions : dict, optional

A dictionary where keys are FunctionClass instances and values are their string representations. Alternatively, the dictionary value can be a list of tuples i.e. [(argument_test, cfunction_string)]. See below for examples.

human : bool, optional

If True, the result is a single string that may contain some constant declarations for the number symbols. If False, the same information is returned in a tuple of (symbols_to_declare, not_supported_functions, code_text). [default=True].

contract: bool, optional

If True, Indexed instances are assumed to obey tensor contraction rules and the corresponding nested loops over indices are generated. Setting contract=False will not generate loops, instead the user is responsible to provide values for the indices in the code. [default=True].

inline: bool, optional

If True, we try to create single-statement code instead of multiple statements. [default=True].

Examples

>>> from sympy import julia_code, symbols, sin, pi
>>> x = symbols('x')
>>> julia_code(sin(x).series(x).removeO())
'x.^5/120 - x.^3/6 + x'

>>> from sympy import Rational, ceiling, Abs
>>> x, y, tau = symbols("x, y, tau")
>>> julia_code((2*tau)**Rational(7, 2))
'8*sqrt(2)*tau.^(7/2)'

Note that element-wise (Hadamard) operations are used by default between symbols. This is because its possible in Julia to write “vectorized” code. It is harmless if the values are scalars.

>>> julia_code(sin(pi*x*y), assign_to="s")
's = sin(pi*x.*y)'

If you need a matrix product “*” or matrix power “^”, you can specify the symbol as a MatrixSymbol.

>>> from sympy import Symbol, MatrixSymbol
>>> n = Symbol('n', integer=True, positive=True)
>>> A = MatrixSymbol('A', n, n)
>>> julia_code(3*pi*A**3)
'(3*pi)*A^3'

This class uses several rules to decide which symbol to use a product. Pure numbers use “*”, Symbols use “.*” and MatrixSymbols use “*”. A HadamardProduct can be used to specify componentwise multiplication “.*” of two MatrixSymbols. There is currently there is no easy way to specify scalar symbols, so sometimes the code might have some minor cosmetic issues. For example, suppose x and y are scalars and A is a Matrix, then while a human programmer might write “(x^2*y)*A^3”, we generate:

>>> julia_code(x**2*y*A**3)
'(x.^2.*y)*A^3'

Matrices are supported using Julia inline notation. When using assign_to with matrices, the name can be specified either as a string or as a MatrixSymbol. The dimensions must align in the latter case.

>>> from sympy import Matrix, MatrixSymbol
>>> mat = Matrix([[x**2, sin(x), ceiling(x)]])
>>> julia_code(mat, assign_to='A')
'A = [x.^2 sin(x) ceil(x)]'

Piecewise expressions are implemented with logical masking by default. Alternatively, you can pass “inline=False” to use if-else conditionals. Note that if the Piecewise lacks a default term, represented by (expr, True) then an error will be thrown. This is to prevent generating an expression that may not evaluate to anything.

>>> from sympy import Piecewise
>>> pw = Piecewise((x + 1, x > 0), (x, True))
>>> julia_code(pw, assign_to=tau)
'tau = ((x > 0) ? (x + 1) : (x))'

Note that any expression that can be generated normally can also exist inside a Matrix:

>>> mat = Matrix([[x**2, pw, sin(x)]])
>>> julia_code(mat, assign_to='A')
'A = [x.^2 ((x > 0) ? (x + 1) : (x)) sin(x)]'

Custom printing can be defined for certain types by passing a dictionary of “type” : “function” to the user_functions kwarg. Alternatively, the dictionary value can be a list of tuples i.e., [(argument_test, cfunction_string)]. This can be used to call a custom Julia function.

>>> from sympy import Function
>>> f = Function('f')
>>> g = Function('g')
>>> custom_functions = {
...   "f": "existing_julia_fcn",
...   "g": [(lambda x: x.is_Matrix, "my_mat_fcn"),
...         (lambda x: not x.is_Matrix, "my_fcn")]
... }
>>> mat = Matrix([[1, x]])
>>> julia_code(f(x) + g(x) + g(mat), user_functions=custom_functions)
'existing_julia_fcn(x) + my_fcn(x) + my_mat_fcn([1 x])'

Support for loops is provided through Indexed types. With contract=True these expressions will be turned into loops, whereas contract=False will just print the assignment expression that should be looped over:

>>> from sympy import Eq, IndexedBase, Idx, ccode
>>> len_y = 5
>>> y = IndexedBase('y', shape=(len_y,))
>>> t = IndexedBase('t', shape=(len_y,))
>>> Dy = IndexedBase('Dy', shape=(len_y-1,))
>>> i = Idx('i', len_y-1)
>>> e = Eq(Dy[i], (y[i+1]-y[i])/(t[i+1]-t[i]))
>>> julia_code(e.rhs, assign_to=e.lhs, contract=False)
'Dy[i] = (y[i + 1] - y[i])./(t[i + 1] - t[i])'

Octave (and Matlab) Code printing¶

sympy.printing.octave.known_fcns_src1 = ['sin', 'cos', 'tan', 'cot', 'sec', 'csc', 'asin', 'acos', 'acot', 'atan', 'atan2', 'asec', 'acsc', 'sinh', 'cosh', 'tanh', 'coth', 'csch', 'sech', 'asinh', 'acosh', 'atanh', 'acoth', 'asech', 'acsch', 'erfc', 'erfi', 'erf', 'erfinv', 'erfcinv', 'besseli', 'besselj', 'besselk', 'bessely', 'bernoulli', 'beta', 'euler', 'exp', 'factorial', 'floor', 'fresnelc', 'fresnels', 'gamma', 'harmonic', 'log', 'polylog', 'sign', 'zeta']¶

Built-in mutable sequence.

If no argument is given, the constructor creates a new empty list. The argument must be an iterable if specified.

sympy.printing.octave.known_fcns_src2 = {'Abs': 'abs', 'Chi': 'coshint', 'Ci': 'cosint', 'DiracDelta': 'dirac', 'Heaviside': 'heaviside', 'LambertW': 'lambertw', 'Max': 'max', 'Min': 'min', 'RisingFactorial': 'pochhammer', 'Shi': 'sinhint', 'Si': 'sinint', 'arg': 'angle', 'ceiling': 'ceil', 'chebyshevt': 'chebyshevT', 'chebyshevu': 'chebyshevU', 'conjugate': 'conj', 'im': 'imag', 'laguerre': 'laguerreL', 'li': 'logint', 'loggamma': 'gammaln', 'polygamma': 'psi', 're': 'real'}¶

class sympy.printing.octave.OctaveCodePrinter(settings={})[source]¶

A printer to convert expressions to strings of Octave/Matlab code.

printmethod = '_octave'¶

indent_code(code)[source]¶: Accepts a string of code or a list of code lines

sympy.printing.octave.octave_code(expr, assign_to=None, **settings)[source]¶

Converts $expr$ to a string of Octave (or Matlab) code.

The string uses a subset of the Octave language for Matlab compatibility.

Parameters

expr : Expr

A sympy expression to be converted.

assign_to : optional

When given, the argument is used as the name of the variable to which the expression is assigned. Can be a string, Symbol, MatrixSymbol, or Indexed type. This can be helpful for expressions that generate multi-line statements.

precision : integer, optional

The precision for numbers such as pi [default=16].

user_functions : dict, optional

A dictionary where keys are FunctionClass instances and values are their string representations. Alternatively, the dictionary value can be a list of tuples i.e. [(argument_test, cfunction_string)]. See below for examples.

human : bool, optional

If True, the result is a single string that may contain some constant declarations for the number symbols. If False, the same information is returned in a tuple of (symbols_to_declare, not_supported_functions, code_text). [default=True].

contract: bool, optional

If True, Indexed instances are assumed to obey tensor contraction rules and the corresponding nested loops over indices are generated. Setting contract=False will not generate loops, instead the user is responsible to provide values for the indices in the code. [default=True].

inline: bool, optional

If True, we try to create single-statement code instead of multiple statements. [default=True].

Examples

>>> from sympy import octave_code, symbols, sin, pi
>>> x = symbols('x')
>>> octave_code(sin(x).series(x).removeO())
'x.^5/120 - x.^3/6 + x'

>>> from sympy import Rational, ceiling, Abs
>>> x, y, tau = symbols("x, y, tau")
>>> octave_code((2*tau)**Rational(7, 2))
'8*sqrt(2)*tau.^(7/2)'

Note that element-wise (Hadamard) operations are used by default between symbols. This is because its very common in Octave to write “vectorized” code. It is harmless if the values are scalars.

>>> octave_code(sin(pi*x*y), assign_to="s")
's = sin(pi*x.*y);'

If you need a matrix product “*” or matrix power “^”, you can specify the symbol as a MatrixSymbol.

>>> from sympy import Symbol, MatrixSymbol
>>> n = Symbol('n', integer=True, positive=True)
>>> A = MatrixSymbol('A', n, n)
>>> octave_code(3*pi*A**3)
'(3*pi)*A^3'

This class uses several rules to decide which symbol to use a product. Pure numbers use “*”, Symbols use “.*” and MatrixSymbols use “*”. A HadamardProduct can be used to specify componentwise multiplication “.*” of two MatrixSymbols. There is currently there is no easy way to specify scalar symbols, so sometimes the code might have some minor cosmetic issues. For example, suppose x and y are scalars and A is a Matrix, then while a human programmer might write “(x^2*y)*A^3”, we generate:

>>> octave_code(x**2*y*A**3)
'(x.^2.*y)*A^3'

Matrices are supported using Octave inline notation. When using assign_to with matrices, the name can be specified either as a string or as a MatrixSymbol. The dimensions must align in the latter case.

>>> from sympy import Matrix, MatrixSymbol
>>> mat = Matrix([[x**2, sin(x), ceiling(x)]])
>>> octave_code(mat, assign_to='A')
'A = [x.^2 sin(x) ceil(x)];'

Piecewise expressions are implemented with logical masking by default. Alternatively, you can pass “inline=False” to use if-else conditionals. Note that if the Piecewise lacks a default term, represented by (expr, True) then an error will be thrown. This is to prevent generating an expression that may not evaluate to anything.

>>> from sympy import Piecewise
>>> pw = Piecewise((x + 1, x > 0), (x, True))
>>> octave_code(pw, assign_to=tau)
'tau = ((x > 0).*(x + 1) + (~(x > 0)).*(x));'

Note that any expression that can be generated normally can also exist inside a Matrix:

>>> mat = Matrix([[x**2, pw, sin(x)]])
>>> octave_code(mat, assign_to='A')
'A = [x.^2 ((x > 0).*(x + 1) + (~(x > 0)).*(x)) sin(x)];'

Custom printing can be defined for certain types by passing a dictionary of “type” : “function” to the user_functions kwarg. Alternatively, the dictionary value can be a list of tuples i.e., [(argument_test, cfunction_string)]. This can be used to call a custom Octave function.

>>> from sympy import Function
>>> f = Function('f')
>>> g = Function('g')
>>> custom_functions = {
...   "f": "existing_octave_fcn",
...   "g": [(lambda x: x.is_Matrix, "my_mat_fcn"),
...         (lambda x: not x.is_Matrix, "my_fcn")]
... }
>>> mat = Matrix([[1, x]])
>>> octave_code(f(x) + g(x) + g(mat), user_functions=custom_functions)
'existing_octave_fcn(x) + my_fcn(x) + my_mat_fcn([1 x])'

Support for loops is provided through Indexed types. With contract=True these expressions will be turned into loops, whereas contract=False will just print the assignment expression that should be looped over:

>>> from sympy import Eq, IndexedBase, Idx, ccode
>>> len_y = 5
>>> y = IndexedBase('y', shape=(len_y,))
>>> t = IndexedBase('t', shape=(len_y,))
>>> Dy = IndexedBase('Dy', shape=(len_y-1,))
>>> i = Idx('i', len_y-1)
>>> e = Eq(Dy[i], (y[i+1]-y[i])/(t[i+1]-t[i]))
>>> octave_code(e.rhs, assign_to=e.lhs, contract=False)
'Dy(i) = (y(i + 1) - y(i))./(t(i + 1) - t(i));'

Rust code printing¶

sympy.printing.rust.known_functions = {'': 'ln_1p', 'Abs': 'abs', 'Max': 'max', 'Min': 'min', 'Pow': [(<function <lambda>>, 'recip', 2), (<function <lambda>>, 'sqrt', 2), (<function <lambda>>, 'sqrt().recip', 2), (<function <lambda>>, 'cbrt', 2), (<function <lambda>>, 'exp2', 3), (<function <lambda>>, 'powi', 1), (<function <lambda>>, 'powf', 1)], 'acos': 'acos', 'acosh': 'acosh', 'asin': 'asin', 'asinh': 'asinh', 'atan': 'atan', 'atan2': 'atan2', 'atanh': 'atanh', 'ceiling': 'ceil', 'cos': 'cos', 'cosh': 'cosh', 'exp': [(<function <lambda>>, 'exp', 2)], 'floor': 'floor', 'log': 'ln', 'sign': 'signum', 'sin': 'sin', 'sinh': 'sinh', 'tan': 'tan', 'tanh': 'tanh'}¶

class sympy.printing.rust.RustCodePrinter(settings={})[source]¶

A printer to convert python expressions to strings of Rust code

printmethod = '_rust_code'¶

indent_code(code)[source]¶: Accepts a string of code or a list of code lines

sympy.printing.rust.rust_code(expr, assign_to=None, **settings)[source]¶

Converts an expr to a string of Rust code

Parameters

expr : Expr

A sympy expression to be converted.

assign_to : optional

When given, the argument is used as the name of the variable to which the expression is assigned. Can be a string, Symbol, MatrixSymbol, or Indexed type. This is helpful in case of line-wrapping, or for expressions that generate multi-line statements.

precision : integer, optional

The precision for numbers such as pi [default=15].

user_functions : dict, optional

A dictionary where the keys are string representations of either FunctionClass or UndefinedFunction instances and the values are their desired C string representations. Alternatively, the dictionary value can be a list of tuples i.e. [(argument_test, cfunction_string)]. See below for examples.

dereference : iterable, optional

An iterable of symbols that should be dereferenced in the printed code expression. These would be values passed by address to the function. For example, if dereference=[a], the resulting code would print (*a) instead of a.

human : bool, optional

If True, the result is a single string that may contain some constant declarations for the number symbols. If False, the same information is returned in a tuple of (symbols_to_declare, not_supported_functions, code_text). [default=True].

contract: bool, optional

If True, Indexed instances are assumed to obey tensor contraction rules and the corresponding nested loops over indices are generated. Setting contract=False will not generate loops, instead the user is responsible to provide values for the indices in the code. [default=True].

Examples

>>> from sympy import rust_code, symbols, Rational, sin, ceiling, Abs, Function
>>> x, tau = symbols("x, tau")
>>> rust_code((2*tau)**Rational(7, 2))
'8*1.4142135623731*tau.powf(7_f64/2.0)'
>>> rust_code(sin(x), assign_to="s")
's = x.sin();'

Simple custom printing can be defined for certain types by passing a dictionary of {“type” : “function”} to the user_functions kwarg. Alternatively, the dictionary value can be a list of tuples i.e. [(argument_test, cfunction_string)].

>>> custom_functions = {
...   "ceiling": "CEIL",
...   "Abs": [(lambda x: not x.is_integer, "fabs", 4),
...           (lambda x: x.is_integer, "ABS", 4)],
...   "func": "f"
... }
>>> func = Function('func')
>>> rust_code(func(Abs(x) + ceiling(x)), user_functions=custom_functions)
'(fabs(x) + x.CEIL()).f()'

Piecewise expressions are converted into conditionals. If an assign_to variable is provided an if statement is created, otherwise the ternary operator is used. Note that if the Piecewise lacks a default term, represented by (expr, True) then an error will be thrown. This is to prevent generating an expression that may not evaluate to anything.

>>> from sympy import Piecewise
>>> expr = Piecewise((x + 1, x > 0), (x, True))
>>> print(rust_code(expr, tau))
tau = if (x > 0) {
    x + 1
} else {
    x
};

Support for loops is provided through Indexed types. With contract=True these expressions will be turned into loops, whereas contract=False will just print the assignment expression that should be looped over:

>>> from sympy import Eq, IndexedBase, Idx
>>> len_y = 5
>>> y = IndexedBase('y', shape=(len_y,))
>>> t = IndexedBase('t', shape=(len_y,))
>>> Dy = IndexedBase('Dy', shape=(len_y-1,))
>>> i = Idx('i', len_y-1)
>>> e=Eq(Dy[i], (y[i+1]-y[i])/(t[i+1]-t[i]))
>>> rust_code(e.rhs, assign_to=e.lhs, contract=False)
'Dy[i] = (y[i + 1] - y[i])/(t[i + 1] - t[i]);'

Matrices are also supported, but a MatrixSymbol of the same dimensions must be provided to assign_to. Note that any expression that can be generated normally can also exist inside a Matrix:

>>> from sympy import Matrix, MatrixSymbol
>>> mat = Matrix([x**2, Piecewise((x + 1, x > 0), (x, True)), sin(x)])
>>> A = MatrixSymbol('A', 3, 1)
>>> print(rust_code(mat, A))
A = [x.powi(2), if (x > 0) {
    x + 1
} else {
    x
}, x.sin()];

Theano Code printing¶

class sympy.printing.theanocode.TheanoPrinter(*args, **kwargs)[source]¶

Code printer which creates Theano symbolic expression graphs.

Parameters: cache : dict

Cache dictionary to use (see cache). If None (default) will use the global cache. To create a printer which does not depend on or alter global state pass an empty dictionary. Note: the dictionary is not copied on initialization of the printer and will be updated in-place, so using the same dict object when creating multiple printers or making multiple calls to theano_code() or theano_function() means the cache is shared between all these applications.

Attributes

cache

(dict) A cache of Theano variables which have been created for Sympy symbol-like objects (e.g. sympy.core.symbol.Symbol or sympy.matrices.expressions.MatrixSymbol). This is used to ensure that all references to a given symbol in an expression (or multiple expressions) are printed as the same Theano variable, which is created only once. Symbols are differentiated only by name and type. The format of the cache’s contents should be considered opaque to the user.

printmethod = '_theano'¶

doprint(expr, dtypes=None, broadcastables=None)[source]¶

Convert a Sympy expression to a Theano graph variable.

The dtypes and broadcastables arguments are used to specify the data type, dimension, and broadcasting behavior of the Theano variables corresponding to the free symbols in expr. Each is a mapping from Sympy symbols to the value of the corresponding argument to theano.tensor.Tensor().

See the corresponding documentation page for more information on broadcasting in Theano.

Parameters

expr : sympy.core.expr.Expr

Sympy expression to print.

dtypes : dict

Mapping from Sympy symbols to Theano datatypes to use when creating new Theano variables for those symbols. Corresponds to the dtype argument to theano.tensor.Tensor(). Defaults to 'floatX' for symbols not included in the mapping.

broadcastables : dict

Mapping from Sympy symbols to the value of the broadcastable argument to theano.tensor.Tensor() to use when creating Theano variables for those symbols. Defaults to the empty tuple for symbols not included in the mapping (resulting in a scalar).

Returns

theano.gof.graph.Variable

A variable corresponding to the expression’s value in a Theano symbolic expression graph.

See also

theano.tensor.Tensor

sympy.printing.theanocode.theano_code(expr, cache=None, **kwargs)[source]¶

Convert a Sympy expression into a Theano graph variable.

Parameters

expr : sympy.core.expr.Expr

Sympy expression object to convert.

cache : dict

Cached Theano variables (see TheanoPrinter.cache). Defaults to the module-level global cache.

dtypes : dict

Passed to TheanoPrinter.doprint().

broadcastables : dict

Passed to TheanoPrinter.doprint().

Returns

theano.gof.graph.Variable

A variable corresponding to the expression’s value in a Theano symbolic expression graph.

sympy.printing.theanocode.theano_function(inputs, outputs, scalar=False, **kwargs)[source]¶

Create a Theano function from SymPy expressions.

The inputs and outputs are converted to Theano variables using theano_code() and then passed to theano.function().

Parameters

inputs

Sequence of symbols which constitute the inputs of the function.

outputs

Sequence of expressions which constitute the outputs(s) of the function. The free symbols of each expression must be a subset of inputs.

scalar : bool

Convert 0-dimensional arrays in output to scalars. This will return a Python wrapper function around the Theano function object.

cache : dict

Cached Theano variables (see TheanoPrinter.cache). Defaults to the module-level global cache.

dtypes : dict

Passed to TheanoPrinter.doprint().

broadcastables : dict

Passed to TheanoPrinter.doprint().

dims : dict

Alternative to broadcastables argument. Mapping from elements of inputs to integers indicating the dimension of their associated arrays/tensors. Overrides broadcastables argument if given.

dim : int

Another alternative to the broadcastables argument. Common number of dimensions to use for all arrays/tensors. theano_function([x, y], [...], dim=2) is equivalent to using broadcastables={x: (False, False), y: (False, False)}.

Returns

callable

A callable object which takes values of inputs as positional arguments and returns an output array for each of the expressions in outputs. If outputs is a single expression the function will return a Numpy array, if it is a list of multiple expressions the function will return a list of arrays. See description of the squeeze argument above for the behavior when a single output is passed in a list. The returned object will either be an instance of theano.compile.function_module.Function or a Python wrapper function around one. In both cases, the returned value will have a theano_function attribute which points to the return value of theano.function().

Examples

>>> from sympy.abc import x, y, z
>>> from sympy.printing.theanocode import theano_function

A simple function with one input and one output:

>>> f1 = theano_function([x], [x**2 - 1], scalar=True)
>>> f1(3)
8.0

A function with multiple inputs and one output:

>>> f2 = theano_function([x, y, z], [(x**z + y**z)**(1/z)], scalar=True)
>>> f2(3, 4, 2)
5.0

A function with multiple inputs and multiple outputs:

>>> f3 = theano_function([x, y], [x**2 + y**2, x**2 - y**2], scalar=True)
>>> f3(2, 3)
[13.0, -5.0]

See also

theano.function, dim_handling

Gtk¶

You can print to a gtkmathview widget using the function print_gtk located in sympy.printing.gtk (it requires to have installed gtkmathview and libgtkmathview-bin in some systems).

GtkMathView accepts MathML, so this rendering depends on the MathML representation of the expression.

Usage:

from sympy import *
print_gtk(x**2 + 2*exp(x**3))

sympy.printing.gtk.print_gtk(x, start_viewer=True)[source]¶

Print to Gtkmathview, a gtk widget capable of rendering MathML.

Needs libgtkmathview-bin

LambdaPrinter¶

This classes implements printing to strings that can be used by the sympy.utilities.lambdify.lambdify() function.

class sympy.printing.lambdarepr.LambdaPrinter(settings=None)[source]¶

This printer converts expressions into strings that can be used by lambdify.

printmethod = '_lambdacode'¶

sympy.printing.lambdarepr.lambdarepr(expr, **settings)[source]¶: Returns a string usable for lambdifying.

LatexPrinter¶

This class implements LaTeX printing. See sympy.printing.latex.

sympy.printing.latex.accepted_latex_functions = ['arcsin', 'arccos', 'arctan', 'sin', 'cos', 'tan', 'sinh', 'cosh', 'tanh', 'sqrt', 'ln', 'log', 'sec', 'csc', 'cot', 'coth', 're', 'im', 'frac', 'root', 'arg']¶

Built-in mutable sequence.

If no argument is given, the constructor creates a new empty list. The argument must be an iterable if specified.

class sympy.printing.latex.LatexPrinter(settings=None)[source]¶

printmethod = '_latex'¶

sympy.printing.latex.latex(expr, fold_frac_powers=False, fold_func_brackets=False, fold_short_frac=None, inv_trig_style='abbreviated', itex=False, ln_notation=False, long_frac_ratio=None, mat_delim='[', mat_str=None, mode='plain', mul_symbol=None, order=None, symbol_names=None, root_notation=True, mat_symbol_style='plain', imaginary_unit='i', gothic_re_im=False)[source]¶

Convert the given expression to LaTeX string representation.

Parameters

fold_frac_powers : boolean, optional

Emit ^{p/q} instead of ^{\frac{p}{q}} for fractional powers.

fold_func_brackets : boolean, optional

Fold function brackets where applicable.

fold_short_frac : boolean, optional

Emit p / q instead of \frac{p}{q} when the denominator is simple enough (at most two terms and no powers). The default value is True for inline mode, False otherwise.

inv_trig_style : string, optional

How inverse trig functions should be displayed. Can be one of abbreviated, full, or power. Defaults to abbreviated.

itex : boolean, optional

Specifies if itex-specific syntax is used, including emitting $$...$$.

ln_notation : boolean, optional

If set to True, \ln is used instead of default \log.

long_frac_ratio : float or None, optional

The allowed ratio of the width of the numerator to the width of the denominator before the printer breaks off long fractions. If None (the default value), long fractions are not broken up.

mat_delim : string, optional

The delimiter to wrap around matrices. Can be one of [, (, or the empty string. Defaults to [.

mat_str : string, optional

Which matrix environment string to emit. smallmatrix, matrix, array, etc. Defaults to smallmatrix for inline mode, matrix for matrices of no more than 10 columns, and array otherwise.

mode: string, optional

Specifies how the generated code will be delimited. mode can be one of plain, inline, equation or equation*. If mode is set to plain, then the resulting code will not be delimited at all (this is the default). If mode is set to inline then inline LaTeX $...$ will be used. If mode is set to equation or equation*, the resulting code will be enclosed in the equation or equation* environment (remember to import amsmath for equation*), unless the itex option is set. In the latter case, the $$...$$ syntax is used.

mul_symbol : string or None, optional

The symbol to use for multiplication. Can be one of None, ldot, dot, or times.

order: string, optional

Any of the supported monomial orderings (currently lex, grlex, or grevlex), old, and none. This parameter does nothing for Mul objects. Setting order to old uses the compatibility ordering for Add defined in Printer. For very large expressions, set the order keyword to none if speed is a concern.

symbol_names : dictionary of strings mapped to symbols, optional

Dictionary of symbols and the custom strings they should be emitted as.

root_notation : boolean, optional

If set to False, exponents of the form 1/n are printed in fractonal form. Default is True, to print exponent in root form.

mat_symbol_style : string, optional

Can be either plain (default) or bold. If set to bold, a MatrixSymbol A will be printed as \mathbf{A}, otherwise as A.

imaginary_unit : string, optional

String to use for the imaginary unit. Defined options are “i” (default) and “j”. Adding “r” or “t” in front gives \mathrm or \text, so “ri” leads to \mathrm{i} which gives $\mathrm{i}$.

gothic_re_im : boolean, optional

If set to True, $\Re$ and $\Im$ is used for re and im, respectively. The default is False leading to $\operatorname{re}$ and $\operatorname{im}$.

Notes

Not using a print statement for printing, results in double backslashes for latex commands since that’s the way Python escapes backslashes in strings.

>>> from sympy import latex, Rational
>>> from sympy.abc import tau
>>> latex((2*tau)**Rational(7,2))
'8 \\sqrt{2} \\tau^{\\frac{7}{2}}'
>>> print(latex((2*tau)**Rational(7,2)))
8 \sqrt{2} \tau^{\frac{7}{2}}

Examples

>>> from sympy import latex, pi, sin, asin, Integral, Matrix, Rational, log
>>> from sympy.abc import x, y, mu, r, tau

Basic usage:

>>> print(latex((2*tau)**Rational(7,2)))
8 \sqrt{2} \tau^{\frac{7}{2}}

mode and itex options:

>>> print(latex((2*mu)**Rational(7,2), mode='plain'))
8 \sqrt{2} \mu^{\frac{7}{2}}
>>> print(latex((2*tau)**Rational(7,2), mode='inline'))
$8 \sqrt{2} \tau^{7 / 2}$
>>> print(latex((2*mu)**Rational(7,2), mode='equation*'))
\begin{equation*}8 \sqrt{2} \mu^{\frac{7}{2}}\end{equation*}
>>> print(latex((2*mu)**Rational(7,2), mode='equation'))
\begin{equation}8 \sqrt{2} \mu^{\frac{7}{2}}\end{equation}
>>> print(latex((2*mu)**Rational(7,2), mode='equation', itex=True))
$$8 \sqrt{2} \mu^{\frac{7}{2}}$$
>>> print(latex((2*mu)**Rational(7,2), mode='plain'))
8 \sqrt{2} \mu^{\frac{7}{2}}
>>> print(latex((2*tau)**Rational(7,2), mode='inline'))
$8 \sqrt{2} \tau^{7 / 2}$
>>> print(latex((2*mu)**Rational(7,2), mode='equation*'))
\begin{equation*}8 \sqrt{2} \mu^{\frac{7}{2}}\end{equation*}
>>> print(latex((2*mu)**Rational(7,2), mode='equation'))
\begin{equation}8 \sqrt{2} \mu^{\frac{7}{2}}\end{equation}
>>> print(latex((2*mu)**Rational(7,2), mode='equation', itex=True))
$$8 \sqrt{2} \mu^{\frac{7}{2}}$$

Fraction options:

>>> print(latex((2*tau)**Rational(7,2), fold_frac_powers=True))
8 \sqrt{2} \tau^{7/2}
>>> print(latex((2*tau)**sin(Rational(7,2))))
\left(2 \tau\right)^{\sin{\left(\frac{7}{2} \right)}}
>>> print(latex((2*tau)**sin(Rational(7,2)), fold_func_brackets=True))
\left(2 \tau\right)^{\sin {\frac{7}{2}}}
>>> print(latex(3*x**2/y))
\frac{3 x^{2}}{y}
>>> print(latex(3*x**2/y, fold_short_frac=True))
3 x^{2} / y
>>> print(latex(Integral(r, r)/2/pi, long_frac_ratio=2))
\frac{\int r\, dr}{2 \pi}
>>> print(latex(Integral(r, r)/2/pi, long_frac_ratio=0))
\frac{1}{2 \pi} \int r\, dr

Multiplication options:

>>> print(latex((2*tau)**sin(Rational(7,2)), mul_symbol="times"))
\left(2 \times \tau\right)^{\sin{\left(\frac{7}{2} \right)}}

Trig options:

>>> print(latex(asin(Rational(7,2))))
\operatorname{asin}{\left(\frac{7}{2} \right)}
>>> print(latex(asin(Rational(7,2)), inv_trig_style="full"))
\arcsin{\left(\frac{7}{2} \right)}
>>> print(latex(asin(Rational(7,2)), inv_trig_style="power"))
\sin^{-1}{\left(\frac{7}{2} \right)}

Matrix options:

>>> print(latex(Matrix(2, 1, [x, y])))
\left[\begin{matrix}x\\y\end{matrix}\right]
>>> print(latex(Matrix(2, 1, [x, y]), mat_str = "array"))
\left[\begin{array}{c}x\\y\end{array}\right]
>>> print(latex(Matrix(2, 1, [x, y]), mat_delim="("))
\left(\begin{matrix}x\\y\end{matrix}\right)

Custom printing of symbols:

>>> print(latex(x**2, symbol_names={x: 'x_i'}))
x_i^{2}

Logarithms:

>>> print(latex(log(10)))
\log{\left(10 \right)}
>>> print(latex(log(10), ln_notation=True))
\ln{\left(10 \right)}

latex() also supports the builtin container types list, tuple, and dictionary.

>>> print(latex([2/x, y], mode='inline'))
$\left[ 2 / x, \  y\right]$

sympy.printing.latex.print_latex(expr, **settings)[source]¶: Prints LaTeX representation of the given expression. Takes the same settings as latex().

MathMLPrinter¶

This class is responsible for MathML printing. See sympy.printing.mathml.

More info on mathml : http://www.w3.org/TR/MathML2

class sympy.printing.mathml.MathMLPrinterBase(settings=None)[source]¶: Contains common code required for MathMLContentPrinter and MathMLPresentationPrinter.

class sympy.printing.mathml.MathMLContentPrinter(settings=None)[source]¶

Prints an expression to the Content MathML markup language.

References: https://www.w3.org/TR/MathML2/chapter4.html

printmethod = '_mathml_content'¶

mathml_tag(e)[source]¶: Returns the MathML tag for an expression.

class sympy.printing.mathml.MathMLPresentationPrinter(settings=None)[source]¶

Prints an expression to the Presentation MathML markup language.

References: https://www.w3.org/TR/MathML2/chapter3.html

printmethod = '_mathml_presentation'¶

mathml_tag(e)[source]¶: Returns the MathML tag for an expression.

sympy.printing.mathml.mathml(expr, printer='content', **settings)[source]¶: Returns the MathML representation of expr. If printer is presentation then prints Presentation MathML else prints content MathML.

sympy.printing.mathml.print_mathml(expr, printer='content', **settings)[source]¶

Prints a pretty representation of the MathML code for expr. If printer is presentation then prints Presentation MathML else prints content MathML.

Examples

>>> ##
>>> from sympy.printing.mathml import print_mathml
>>> from sympy.abc import x
>>> print_mathml(x+1) #doctest: +NORMALIZE_WHITESPACE
<apply>
    <plus/>
    <ci>x</ci>
    <cn>1</cn>
</apply>
>>> print_mathml(x+1, printer='presentation')
<mrow>
    <mi>x</mi>
    <mo>+</mo>
    <mn>1</mn>
</mrow>

PythonCodePrinter¶

Python code printers

This module contains python code printers for plain python as well as NumPy & SciPy enabled code.

class sympy.printing.pycode.MpmathPrinter(settings=None)[source]¶: Lambda printer for mpmath which maintains precision for floats

class sympy.printing.pycode.NumPyPrinter(settings=None)[source]¶: Numpy printer which handles vectorized piecewise functions, logical operators, etc.

sympy.printing.pycode.pycode(expr, **settings)[source]¶

Converts an expr to a string of Python code

Parameters

expr : Expr

A SymPy expression.

fully_qualified_modules : bool

Whether or not to write out full module names of functions (math.sin vs. sin). default: True.

Examples

>>> from sympy import tan, Symbol
>>> from sympy.printing.pycode import pycode
>>> pycode(tan(Symbol('x')) + 1)
'math.tan(x) + 1'

PythonPrinter¶

This class implements Python printing. Usage:

>>> from sympy import print_python, sin
>>> from sympy.abc import x

>>> print_python(5*x**3 + sin(x))
x = Symbol('x')
e = 5*x**3 + sin(x)

srepr¶

This printer generates executable code. This code satisfies the identity eval(srepr(expr)) == expr.

srepr() gives more low level textual output than repr()

Example:

>>> repr(5*x**3 + sin(x))
'5*x**3 + sin(x)'

>>> srepr(5*x**3 + sin(x))
"Add(Mul(Integer(5), Pow(Symbol('x'), Integer(3))), sin(Symbol('x')))"

srepr() gives the repr form, which is what repr() would normally give but for SymPy we don’t actually use srepr() for __repr__ because it’s is so verbose, it is unlikely that anyone would want it called by default. Another reason is that lists call repr on their elements, like print([a, b, c]) calls repr(a), repr(b), repr(c). So if we used srepr for `` __repr__`` any list with SymPy objects would include the srepr form, even if we used str() or print().

class sympy.printing.repr.ReprPrinter(settings=None)[source]¶

printmethod = '_sympyrepr'¶

emptyPrinter(expr)[source]¶: The fallback printer.

reprify(args, sep)[source]¶: Prints each item in $args$ and joins them with $sep$.

sympy.printing.repr.srepr(expr, **settings)[source]¶: return expr in repr form

StrPrinter¶

This module generates readable representations of SymPy expressions.

class sympy.printing.str.StrPrinter(settings=None)[source]¶

printmethod = '_sympystr'¶

sympy.printing.str.sstrrepr(expr, **settings)[source]¶

return expr in mixed str/repr form

i.e. strings are returned in repr form with quotes, and everything else is returned in str form.

This function could be useful for hooking into sys.displayhook

Tree Printing¶

The functions in this module create a representation of an expression as a tree.

sympy.printing.tree.pprint_nodes(subtrees)[source]¶

Prettyprints systems of nodes.

Examples

>>> from sympy.printing.tree import pprint_nodes
>>> print(pprint_nodes(["a", "b1\nb2", "c"]))
+-a
+-b1
| b2
+-c

sympy.printing.tree.print_node(node)[source]¶

Returns information about the “node”.

This includes class name, string representation and assumptions.

sympy.printing.tree.tree(node)[source]¶

Returns a tree representation of “node” as a string.

It uses print_node() together with pprint_nodes() on node.args recursively.

See also

print_tree

sympy.printing.tree.print_tree(node)[source]¶

Prints a tree representation of “node”.

Examples

>>> from sympy.printing import print_tree
>>> from sympy import Symbol
>>> x = Symbol('x', odd=True)
>>> y = Symbol('y', even=True)
>>> print_tree(y**x)
Pow: y**x
+-Symbol: y
| algebraic: True
| commutative: True
| complex: True
| even: True
| hermitian: True
| imaginary: False
| integer: True
| irrational: False
| noninteger: False
| odd: False
| rational: True
| real: True
| transcendental: False
+-Symbol: x
  algebraic: True
  commutative: True
  complex: True
  even: False
  hermitian: True
  imaginary: False
  integer: True
  irrational: False
  noninteger: False
  nonzero: True
  odd: True
  rational: True
  real: True
  transcendental: False
  zero: False

See also

tree

Preview¶

A useful function is preview:

sympy.printing.preview.preview(expr, output='png', viewer=None, euler=True, packages=(), filename=None, outputbuffer=None, preamble=None, dvioptions=None, outputTexFile=None, **latex_settings)[source]¶

View expression or LaTeX markup in PNG, DVI, PostScript or PDF form.

If the expr argument is an expression, it will be exported to LaTeX and then compiled using the available TeX distribution. The first argument, ‘expr’, may also be a LaTeX string. The function will then run the appropriate viewer for the given output format or use the user defined one. By default png output is generated.

By default pretty Euler fonts are used for typesetting (they were used to typeset the well known “Concrete Mathematics” book). For that to work, you need the ‘eulervm.sty’ LaTeX style (in Debian/Ubuntu, install the texlive-fonts-extra package). If you prefer default AMS fonts or your system lacks ‘eulervm’ LaTeX package then unset the ‘euler’ keyword argument.

To use viewer auto-detection, lets say for ‘png’ output, issue

>>> from sympy import symbols, preview, Symbol
>>> x, y = symbols("x,y")

>>> preview(x + y, output='png')

This will choose ‘pyglet’ by default. To select a different one, do

>>> preview(x + y, output='png', viewer='gimp')

The ‘png’ format is considered special. For all other formats the rules are slightly different. As an example we will take ‘dvi’ output format. If you would run

>>> preview(x + y, output='dvi')

then ‘view’ will look for available ‘dvi’ viewers on your system (predefined in the function, so it will try evince, first, then kdvi and xdvi). If nothing is found you will need to set the viewer explicitly.

>>> preview(x + y, output='dvi', viewer='superior-dvi-viewer')

This will skip auto-detection and will run user specified ‘superior-dvi-viewer’. If ‘view’ fails to find it on your system it will gracefully raise an exception.

You may also enter ‘file’ for the viewer argument. Doing so will cause this function to return a file object in read-only mode, if ‘filename’ is unset. However, if it was set, then ‘preview’ writes the genereted file to this filename instead.

There is also support for writing to a BytesIO like object, which needs to be passed to the ‘outputbuffer’ argument.

>>> from io import BytesIO
>>> obj = BytesIO()
>>> preview(x + y, output='png', viewer='BytesIO',
...         outputbuffer=obj)

The LaTeX preamble can be customized by setting the ‘preamble’ keyword argument. This can be used, e.g., to set a different font size, use a custom documentclass or import certain set of LaTeX packages.

>>> preamble = "\\documentclass[10pt]{article}\n" \
...            "\\usepackage{amsmath,amsfonts}\\begin{document}"
>>> preview(x + y, output='png', preamble=preamble)

If the value of ‘output’ is different from ‘dvi’ then command line options can be set (‘dvioptions’ argument) for the execution of the ‘dvi’+output conversion tool. These options have to be in the form of a list of strings (see subprocess.Popen).

Additional keyword args will be passed to the latex call, e.g., the symbol_names flag.

>>> phidd = Symbol('phidd')
>>> preview(phidd, symbol_names={phidd:r'\ddot{\varphi}'})

For post-processing the generated TeX File can be written to a file by passing the desired filename to the ‘outputTexFile’ keyword argument. To write the TeX code to a file named “sample.tex” and run the default png viewer to display the resulting bitmap, do

>>> preview(x + y, outputTexFile="sample.tex")

Implementation - Helper Classes/Functions¶

sympy.printing.conventions.split_super_sub(text)[source]¶

Split a symbol name into a name, superscripts and subscripts

The first part of the symbol name is considered to be its actual ‘name’, followed by super- and subscripts. Each superscript is preceded with a “^” character or by “__”. Each subscript is preceded by a “_” character. The three return values are the actual name, a list with superscripts and a list with subscripts.

Examples

>>> from sympy.printing.conventions import split_super_sub
>>> split_super_sub('a_x^1')
('a', ['1'], ['x'])
>>> split_super_sub('var_sub1__sup_sub2')
('var', ['sup'], ['sub1', 'sub2'])

CodePrinter¶

This class is a base class for other classes that implement code-printing functionality, and additionally lists a number of functions that cannot be easily translated to C or Fortran.

class sympy.printing.codeprinter.Assignment[source]¶

Represents variable assignment for code generation.

Parameters

lhs : Expr

Sympy object representing the lhs of the expression. These should be singular objects, such as one would use in writing code. Notable types include Symbol, MatrixSymbol, MatrixElement, and Indexed. Types that subclass these types are also supported.

rhs : Expr

Sympy object representing the rhs of the expression. This can be any type, provided its shape corresponds to that of the lhs. For example, a Matrix type can be assigned to MatrixSymbol, but not to Symbol, as the dimensions will not align.

Examples

>>> from sympy import symbols, MatrixSymbol, Matrix
>>> from sympy.codegen.ast import Assignment
>>> x, y, z = symbols('x, y, z')
>>> Assignment(x, y)
Assignment(x, y)
>>> Assignment(x, 0)
Assignment(x, 0)
>>> A = MatrixSymbol('A', 1, 3)
>>> mat = Matrix([x, y, z]).T
>>> Assignment(A, mat)
Assignment(A, Matrix([[x, y, z]]))
>>> Assignment(A[0, 1], x)
Assignment(A[0, 1], x)

class sympy.printing.codeprinter.CodePrinter(settings=None)[source]¶

The base class for code-printing subclasses.

printmethod = '_sympystr'¶

exception sympy.printing.codeprinter.AssignmentError[source]¶: Raised if an assignment variable for a loop is missing.

Precedence¶

sympy.printing.precedence.PRECEDENCE = {'Add': 40, 'And': 30, 'Atom': 1000, 'BitwiseAnd': 38, 'BitwiseOr': 36, 'Func': 70, 'Lambda': 1, 'Mul': 50, 'Not': 100, 'Or': 20, 'Pow': 60, 'Relational': 35, 'Xor': 10}¶: Default precedence values for some basic types.

sympy.printing.precedence.PRECEDENCE_VALUES = {'Add': 40, 'And': 30, 'Equality': 50, 'Equivalent': 10, 'Function': 70, 'HadamardProduct': 50, 'Implies': 10, 'KroneckerProduct': 50, 'MatAdd': 40, 'MatPow': 60, 'NegativeInfinity': 40, 'Not': 100, 'Or': 20, 'Pow': 60, 'Relational': 35, 'Sub': 40, 'TensAdd': 40, 'TensMul': 50, 'Unequality': 50, 'Xor': 10}¶: A dictionary assigning precedence values to certain classes. These values are treated like they were inherited, so not every single class has to be named here.

sympy.printing.precedence.PRECEDENCE_FUNCTIONS = {'Float': <function precedence_Float>, 'FracElement': <function precedence_FracElement>, 'Integer': <function precedence_Integer>, 'Mul': <function precedence_Mul>, 'PolyElement': <function precedence_PolyElement>, 'Rational': <function precedence_Rational>, 'UnevaluatedExpr': <function precedence_UnevaluatedExpr>}¶: Sometimes it’s not enough to assign a fixed precedence value to a class. Then a function can be inserted in this dictionary that takes an instance of this class as argument and returns the appropriate precedence value.

sympy.printing.precedence.precedence(item)[source]¶: Returns the precedence of a given object.

Pretty-Printing Implementation Helpers¶

sympy.printing.pretty.pretty_symbology.U(name)[source]¶: unicode character by name or None if not found

sympy.printing.pretty.pretty_symbology.pretty_use_unicode(flag=None)[source]¶: Set whether pretty-printer should use unicode by default

sympy.printing.pretty.pretty_symbology.pretty_try_use_unicode()[source]¶: See if unicode output is available and leverage it if possible

sympy.printing.pretty.pretty_symbology.xstr(*args)[source]¶: call str or unicode depending on current mode

The following two functions return the Unicode version of the inputted Greek letter.

sympy.printing.pretty.pretty_symbology.g(l)¶

sympy.printing.pretty.pretty_symbology.G(l)¶

sympy.printing.pretty.pretty_symbology.greek_letters = ['alpha', 'beta', 'gamma', 'delta', 'epsilon', 'zeta', 'eta', 'theta', 'iota', 'kappa', 'lamda', 'mu', 'nu', 'xi', 'omicron', 'pi', 'rho', 'sigma', 'tau', 'upsilon', 'phi', 'chi', 'psi', 'omega']¶

Built-in mutable sequence.

If no argument is given, the constructor creates a new empty list. The argument must be an iterable if specified.

sympy.printing.pretty.pretty_symbology.digit_2txt = {'0': 'ZERO', '1': 'ONE', '2': 'TWO', '3': 'THREE', '4': 'FOUR', '5': 'FIVE', '6': 'SIX', '7': 'SEVEN', '8': 'EIGHT', '9': 'NINE'}¶

sympy.printing.pretty.pretty_symbology.symb_2txt = {'(': 'LEFT PARENTHESIS', ')': 'RIGHT PARENTHESIS', '+': 'PLUS SIGN', '-': 'MINUS', '=': 'EQUALS SIGN', '[': 'LEFT SQUARE BRACKET', ']': 'RIGHT SQUARE BRACKET', 'int': 'INTEGRAL', 'sum': 'SUMMATION', '{': 'LEFT CURLY BRACKET', '{}': 'CURLY BRACKET', '}': 'RIGHT CURLY BRACKET'}¶

The following functions return the Unicode subscript/superscript version of the character.

sympy.printing.pretty.pretty_symbology.sub = {'(': '₍', ')': '₎', '+': '₊', '-': '₋', '0': '₀', '1': '₁', '2': '₂', '3': '₃', '4': '₄', '5': '₅', '6': '₆', '7': '₇', '8': '₈', '9': '₉', '=': '₌', 'a': 'ₐ', 'beta': 'ᵦ', 'chi': 'ᵪ', 'e': 'ₑ', 'gamma': 'ᵧ', 'h': 'ₕ', 'i': 'ᵢ', 'k': 'ₖ', 'l': 'ₗ', 'm': 'ₘ', 'n': 'ₙ', 'o': 'ₒ', 'p': 'ₚ', 'phi': 'ᵩ', 'r': 'ᵣ', 'rho': 'ᵨ', 's': 'ₛ', 't': 'ₜ', 'u': 'ᵤ', 'v': 'ᵥ', 'x': 'ₓ'}¶

sympy.printing.pretty.pretty_symbology.sup = {'(': '⁽', ')': '⁾', '+': '⁺', '-': '⁻', '0': '⁰', '1': '¹', '2': '²', '3': '³', '4': '⁴', '5': '⁵', '6': '⁶', '7': '⁷', '8': '⁸', '9': '⁹', '=': '⁼', 'i': 'ⁱ', 'n': 'ⁿ'}¶

The following functions return Unicode vertical objects.

sympy.printing.pretty.pretty_symbology.xobj(symb, length)[source]¶

Construct spatial object of given length.

return: [] of equal-length strings

sympy.printing.pretty.pretty_symbology.vobj(symb, height)[source]¶

Construct vertical object of a given height

see: xobj

sympy.printing.pretty.pretty_symbology.hobj(symb, width)[source]¶

Construct horizontal object of a given width

see: xobj

The following constants are for rendering roots and fractions.

sympy.printing.pretty.pretty_symbology.root = {2: '√', 3: '∛', 4: '∜'}¶

sympy.printing.pretty.pretty_symbology.VF(txt)¶

sympy.printing.pretty.pretty_symbology.frac = {(1, 2): '½', (1, 3): '⅓', (1, 4): '¼', (1, 5): '⅕', (1, 6): '⅙', (1, 8): '⅛', (2, 3): '⅔', (2, 5): '⅖', (3, 4): '¾', (3, 5): '⅗', (3, 8): '⅜', (4, 5): '⅘', (5, 6): '⅚', (5, 8): '⅝', (7, 8): '⅞'}¶

The following constants/functions are for rendering atoms and symbols.

sympy.printing.pretty.pretty_symbology.xsym(sym)[source]¶: get symbology for a ‘character’

sympy.printing.pretty.pretty_symbology.atoms_table = {'Complexes': 'ℂ', 'EmptySet': '∅', 'Exp1': 'ℯ', 'ImaginaryUnit': 'ⅈ', 'Infinity': '∞', 'Integers': 'ℤ', 'Intersection': '∩', 'Naturals': 'ℕ', 'Naturals0': 'ℕ₀', 'NegativeInfinity': '-∞', 'Pi': 'π', 'Reals': 'ℝ', 'Ring': '∘', 'SymmetricDifference': '∆', 'Union': '∪'}¶

sympy.printing.pretty.pretty_symbology.pretty_atom(atom_name, default=None, printer=None)[source]¶: return pretty representation of an atom

sympy.printing.pretty.pretty_symbology.pretty_symbol(symb_name, bold_name=False)[source]¶: return pretty representation of a symbol

sympy.printing.pretty.pretty_symbology.annotated(letter)[source]¶

Return a stylised drawing of the letter letter, together with information on how to put annotations (super- and subscripts to the left and to the right) on it.

See pretty.py functions _print_meijerg, _print_hyper on how to use this information.

Prettyprinter by Jurjen Bos. (I hate spammers: mail me at pietjepuk314 at the reverse of ku.oc.oohay). All objects have a method that create a “stringPict”, that can be used in the str method for pretty printing.

Updates by Jason Gedge (email <my last name> at cs mun ca)

terminal_string() method
minor fixes and changes (mostly to prettyForm)

TODO:

Allow left/center/right alignment options for above/below and top/center/bottom alignment options for left/right

class sympy.printing.pretty.stringpict.stringPict(s, baseline=0)[source]¶

An ASCII picture. The pictures are represented as a list of equal length strings.

above(*args)[source]¶: Put pictures above this picture. Returns string, baseline arguments for stringPict. Baseline is baseline of bottom picture.

below(*args)[source]¶

Put pictures under this picture. Returns string, baseline arguments for stringPict. Baseline is baseline of top picture

Examples

>>> from sympy.printing.pretty.stringpict import stringPict
>>> print(stringPict("x+3").below(
...       stringPict.LINE, '3')[0]) #doctest: +NORMALIZE_WHITESPACE
x+3
---
 3

height()[source]¶: The height of the picture in characters.

left(*args)[source]¶: Put pictures (left to right) at left. Returns string, baseline arguments for stringPict.

leftslash()[source]¶: Precede object by a slash of the proper size.

static next(*args)[source]¶: Put a string of stringPicts next to each other. Returns string, baseline arguments for stringPict.

parens(left='(', right=')', ifascii_nougly=False)[source]¶

Put parentheses around self. Returns string, baseline arguments for stringPict.

left or right can be None or empty string which means ‘no paren from that side’

render(*args, **kwargs)[source]¶

Return the string form of self.

Unless the argument line_break is set to False, it will break the expression in a form that can be printed on the terminal without being broken up.

right(*args)[source]¶

Put pictures next to this one. Returns string, baseline arguments for stringPict. (Multiline) strings are allowed, and are given a baseline of 0.

Examples

>>> from sympy.printing.pretty.stringpict import stringPict
>>> print(stringPict("10").right(" + ",stringPict("1\r-\r2",1))[0])
     1
10 + -
     2

root(n=None)[source]¶: Produce a nice root symbol. Produces ugly results for big n inserts.

static stack(*args)[source]¶: Put pictures on top of each other, from top to bottom. Returns string, baseline arguments for stringPict. The baseline is the baseline of the second picture. Everything is centered. Baseline is the baseline of the second picture. Strings are allowed. The special value stringPict.LINE is a row of ‘-‘ extended to the width.

terminal_width()[source]¶: Return the terminal width if possible, otherwise return 0.

width()[source]¶: The width of the picture in characters.

class sympy.printing.pretty.stringpict.prettyForm(s, baseline=0, binding=0, unicode=None)[source]¶

Extension of the stringPict class that knows about basic math applications, optimizing double minus signs.

“Binding” is interpreted as follows:

ATOM this is an atom: never needs to be parenthesized
FUNC this is a function application: parenthesize if added (?)
DIV  this is a division: make wider division if divided
POW  this is a power: only parenthesize if exponent
MUL  this is a multiplication: parenthesize if powered
ADD  this is an addition: parenthesize if multiplied or powered
NEG  this is a negative number: optimize if added, parenthesize if
     multiplied or powered
OPEN this is an open object: parenthesize if added, multiplied, or
     powered (example: Piecewise)

static apply(function, *args)[source]¶: Functions of one or more variables.

dotprint¶

sympy.printing.dot.dotprint(expr, styles=((<class 'sympy.core.basic.Basic'>, {'color': 'blue', 'shape': 'ellipse'}), (<class 'sympy.core.expr.Expr'>, {'color': 'black'})), atom=<function <lambda>>, maxdepth=None, repeat=True, labelfunc=<class 'str'>, **kwargs)[source]¶

DOT description of a SymPy expression tree

Options are

styles: Styles for different classes. The default is:

[(Basic, {'color': 'blue', 'shape': 'ellipse'}),
(Expr, {'color': 'black'})]``

atom: Function used to determine if an arg is an atom. The default is: lambda x: not isinstance(x, Basic). Another good choice is lambda x: not x.args.

maxdepth: The maximum depth. The default is None, meaning no limit.

repeat: Whether to different nodes for separate common subexpressions.: The default is True. For example, for x + x*y with repeat=True, it will have two nodes for x and with repeat=False, it will have one (warning: even if it appears twice in the same object, like Pow(x, x), it will still only appear only once. Hence, with repeat=False, the number of arrows out of an object might not equal the number of args it has).
labelfunc: How to label leaf nodes. The default is str. Another: good option is srepr. For example with str, the leaf nodes of x + 1 are labeled, x and 1. With srepr, they are labeled Symbol('x') and Integer(1).

Additional keyword arguments are included as styles for the graph.

Examples

>>> from sympy.printing.dot import dotprint
>>> from sympy.abc import x
>>> print(dotprint(x+2)) # doctest: +NORMALIZE_WHITESPACE
digraph{
<BLANKLINE>
# Graph style
"ordering"="out"
"rankdir"="TD"
<BLANKLINE>
#########
# Nodes #
#########
<BLANKLINE>
"Add(Integer(2), Symbol(x))_()" ["color"="black", "label"="Add", "shape"="ellipse"];
"Integer(2)_(0,)" ["color"="black", "label"="2", "shape"="ellipse"];
"Symbol(x)_(1,)" ["color"="black", "label"="x", "shape"="ellipse"];
<BLANKLINE>
#########
# Edges #
#########
<BLANKLINE>
"Add(Integer(2), Symbol(x))_()" -> "Integer(2)_(0,)";
"Add(Integer(2), Symbol(x))_()" -> "Symbol(x)_(1,)";
}

Printing System¶

Printer Class¶

Which Method is Responsible for Printing?¶

Example of Custom Printer¶

Example of Custom Printing Method¶

PrettyPrinter Class¶

C code printers¶

C++ code printers¶

RCodePrinter¶

Fortran Printing¶

Mathematica code printing¶

Javascript Code printing¶

Julia code printing¶

Octave (and Matlab) Code printing¶

Rust code printing¶

Theano Code printing¶

Gtk¶

LambdaPrinter¶

LatexPrinter¶

MathMLPrinter¶

PythonCodePrinter¶

PythonPrinter¶

srepr¶

StrPrinter¶

Tree Printing¶

Preview¶

Implementation - Helper Classes/Functions¶

CodePrinter¶

Precedence¶

Pretty-Printing Implementation Helpers¶

dotprint¶

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