Printing System =============== See the :ref:`tutorial-printing` section in Tutorial for introduction into printing. This guide documents the printing system in SymPy and how it works internally. Printer Class ------------- .. automodule:: sympy.printing.printer The main class responsible for printing is ``Printer`` (see also its `source code `_): .. autoclass:: Printer :members: doprint, _print, set_global_settings, order .. autoattribute:: Printer.printmethod 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. .. module:: sympy.printing.pretty.pretty .. autoclass:: PrettyPrinter :members: _use_unicode, doprint .. autoattribute:: PrettyPrinter.printmethod .. autofunction:: pretty .. autofunction:: pretty_print CCodePrinter ------------ .. module:: sympy.printing.ccode This class implements C code printing (i.e. it converts Python expressions to strings of C code). Usage:: >>> from sympy.printing import print_ccode >>> from sympy.functions import sin, cos, Abs >>> from sympy.abc import x >>> print_ccode(sin(x)**2 + cos(x)**2) pow(sin(x), 2) + pow(cos(x), 2) >>> print_ccode(2*x + cos(x), assign_to="result") result = 2*x + cos(x); >>> print_ccode(Abs(x**2)) fabs(pow(x, 2)) .. autodata:: sympy.printing.ccode.known_functions .. autoclass:: sympy.printing.ccode.CCodePrinter :members: .. autoattribute:: CCodePrinter.printmethod .. autofunction:: sympy.printing.ccode.ccode .. autofunction:: sympy.printing.ccode.print_ccode 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. .. module:: sympy.printing.fcode .. autofunction:: fcode .. autofunction:: print_fcode .. autoclass:: FCodePrinter :members: .. autoattribute:: FCodePrinter.printmethod Two basic examples: >>> from sympy import * >>> x = symbols("x") >>> fcode(sqrt(1-x**2)) ' sqrt(-x**2 + 1)' >>> fcode((3 + 4*I)/(1 - conjugate(x))) ' (cmplx(3,4))/(-conjg(x) + 1)' 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 only top-level piecewise functions are supported due to the lack of a conditional operator in Fortran. Nested piecewise functions would require the introduction of temporary variables, which is a type of expression manipulation that goes beyond the scope of ``fcode``. 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 = 2.71828182845905d0) parameter (pi = 3.14159265358979d0) 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'})) -mygamma(x)**2 + 1 However, when the user_functions argument is not provided, ``fcode`` attempts to use a reasonable default and adds a comment to inform the user of the issue. >>> print(fcode(1 - gamma(x)**2)) C Not Fortran: C gamma(x) -gamma(x)**2 + 1 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 can not be translated in pure Fortran and (iii) a string of Fortran code. A few examples: >>> fcode(1 - gamma(x)**2, human=False) (set(), set([gamma(x)]), ' -gamma(x)**2 + 1') >>> fcode(1 - sin(x)**2, human=False) (set(), set(), ' -sin(x)**2 + 1') >>> fcode(x - pi**2, human=False) (set([(pi, '3.14159265358979d0')]), set(), ' x - pi**2') Gtk --- .. module:: sympy.printing.gtk You can print to a grkmathview widget using the function ``print_gtk`` located in ``sympy.printing.gtk`` (it requires to have installed gtkmatmatview 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)) .. autofunction:: print_gtk LambdaPrinter ------------- .. module:: sympy.printing.lambdarepr This classes implements printing to strings that can be used by the :py:func:`sympy.utilities.lambdify.lambdify` function. .. autoclass:: LambdaPrinter .. autoattribute:: LambdaPrinter.printmethod .. autofunction:: lambdarepr LatexPrinter ------------ .. module:: sympy.printing.latex This class implements LaTeX printing. See ``sympy.printing.latex``. .. autodata:: accepted_latex_functions .. autoclass:: LatexPrinter :members: .. autoattribute:: LatexPrinter.printmethod .. autofunction:: latex .. autofunction:: print_latex MathMLPrinter ------------- .. module:: sympy.printing.mathml This class is responsible for MathML printing. See ``sympy.printing.mathml``. More info on mathml content: http://www.w3.org/TR/MathML2/chapter4.html .. autoclass:: MathMLPrinter :members: .. autoattribute:: MathMLPrinter.printmethod .. autofunction:: mathml .. autofunction:: print_mathml PythonPrinter ------------- .. module:: sympy.printing.python 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) ReprPrinter ----------- .. module:: sympy.printing.repr This printer generates executable code. This code satisfies the identity ``eval(srepr(expr)) == expr``. .. autoclass:: ReprPrinter :members: .. autoattribute:: ReprPrinter.printmethod .. autofunction:: srepr StrPrinter ---------- .. module:: sympy.printing.str This module generates readable representations of SymPy expressions. .. autoclass:: StrPrinter :members: parenthesize, stringify, emptyPrinter .. autoattribute:: StrPrinter.printmethod .. autofunction:: sstrrepr Tree Printing ------------- .. module:: sympy.printing.tree The functions in this module create a representation of an expression as a tree. .. autofunction:: pprint_nodes .. autofunction:: print_node .. autofunction:: tree .. autofunction:: print_tree Preview ------- A useful function is ``preview``: .. module:: sympy.printing.preview .. autofunction:: preview Implementation - Helper Classes/Functions ----------------------------------------- .. module:: sympy.printing.conventions .. autofunction:: split_super_sub CodePrinter +++++++++++ .. module:: sympy.printing.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. .. autoclass:: sympy.printing.codeprinter.CodePrinter .. autoattribute:: CodePrinter.printmethod .. autoexception:: sympy.printing.codeprinter.AssignmentError Precedence ++++++++++ .. module:: sympy.printing.precedence .. autodata:: PRECEDENCE Default precedence values for some basic types. .. autodata:: PRECEDENCE_VALUES 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. .. autodata:: PRECEDENCE_FUNCTIONS 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. .. autofunction:: precedence Pretty-Printing Implementation Helpers -------------------------------------- .. module:: sympy.printing.pretty.pretty_symbology .. autofunction:: U .. autofunction:: pretty_use_unicode .. autofunction:: pretty_try_use_unicode .. autofunction:: xstr The following two functions return the Unicode version of the inputted Greek letter. .. autofunction:: g .. autofunction:: G .. autodata:: greek_letters .. autodata:: digit_2txt .. autodata:: symb_2txt The following functions return the Unicode subscript/superscript version of the character. .. autodata:: sub .. autodata:: sup The following functions return Unicode vertical objects. .. autofunction:: xobj .. autofunction:: vobj .. autofunction:: hobj The following constants are for rendering roots and fractions. .. autodata:: root .. autofunction:: VF .. autodata:: frac The following constants/functions are for rendering atoms and symbols. .. autofunction:: xsym .. autodata:: atoms_table .. autofunction:: pretty_atom .. autofunction:: pretty_symbol .. autofunction:: annotated .. automodule:: sympy.printing.pretty.stringpict .. autoclass:: stringPict :members: .. autoclass:: prettyForm :members: dotprint -------- .. autofunction:: sympy.printing.dot.dotprint