.. module:: diofant.printing
See the :ref:`tutorial-printing` section in Tutorial for introduction into printing.
This guide documents the printing system in Diofant and how it works internally.
.. automodule:: diofant.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
The pretty printing subsystem is implemented in diofant.printing.pretty.pretty
by the PrettyPrinter class deriving from Printer. It relies on
the modules diofant.printing.pretty.stringPict, and
diofant.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.
.. automodule:: diofant.printing.pretty.pretty :members:
.. module:: diofant.printing.ccode
This class implements C code printing (i.e. it converts Python expressions to strings of C code).
Usage:
>>> 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))
.. autoclass:: CCodePrinter :members: .. autoattribute:: CCodePrinter.printmethod
.. autofunction:: ccode
The fcode function translates a diofant 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:: diofant.printing.fcode
.. autofunction:: fcode
.. autoclass:: FCodePrinter :members: .. autoattribute:: FCodePrinter.printmethod
Two basic examples:
>>> 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 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 = 2.71828182845905d0) 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 supported in Fortran: C gamma -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 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)}, ' -gamma(x)**2 + 1') >>> fcode(1 - sin(x)**2, human=False) (set(), set(), ' -sin(x)**2 + 1') >>> fcode(x - pi**2, human=False) ({(pi, '3.14159265358979d0')}, set(), ' x - pi**2')
.. module:: diofant.printing.mathematica
.. autoclass:: diofant.printing.mathematica.MCodePrinter :members: .. autoattribute:: MCodePrinter.printmethod
.. autofunction:: diofant.printing.mathematica.mathematica_code
.. module:: diofant.printing.lambdarepr
This classes implements printing to strings that can be used by the :py:func:`diofant.utilities.lambdify.lambdify` function.
.. autoclass:: LambdaPrinter .. autoattribute:: LambdaPrinter.printmethod
.. autofunction:: lambdarepr
.. module:: diofant.printing.latex
This class implements LaTeX printing. See diofant.printing.latex.
.. autodata:: accepted_latex_functions
.. autoclass:: LatexPrinter :members: .. autoattribute:: LatexPrinter.printmethod
.. autofunction:: latex
.. module:: diofant.printing.mathml
This class is responsible for MathML printing. See diofant.printing.mathml.
More info on mathml content: http://www.w3.org/TR/MathML2/chapter4.html
.. autoclass:: MathMLPrinter :members: .. autoattribute:: MathMLPrinter.printmethod
.. autofunction:: mathml
.. module:: diofant.printing.python
This class implements Python printing. Usage:
>>> print(python(5*x**3 + sin(x)))
x = Symbol('x')
e = 5*x**3 + sin(x)
.. module:: diofant.printing.repr
This printer generates executable code. This code satisfies the identity
eval(srepr(expr)) == expr.
.. autoclass:: ReprPrinter :members: .. autoattribute:: ReprPrinter.printmethod
.. autofunction:: srepr
.. module:: diofant.printing.str
This module generates readable representations of Diofant expressions.
.. autoclass:: StrPrinter :members: parenthesize, stringify, emptyPrinter .. autoattribute:: StrPrinter.printmethod
.. autofunction:: sstr
.. autofunction:: sstrrepr
.. module:: diofant.printing.conventions
.. autofunction:: split_super_sub
.. module:: diofant.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:: diofant.printing.codeprinter.CodePrinter .. autoattribute:: CodePrinter.printmethod
.. autoexception:: diofant.printing.codeprinter.AssignmentError
.. automodule:: diofant.printing.precedence
.. module:: diofant.printing.pretty.pretty_symbology
.. autofunction:: U
.. autofunction:: pretty_use_unicode
The following two functions return the Unicode version of the inputted Greek letter.
.. autofunction:: g
.. autofunction:: G
.. autodata:: greek_letters
The following functions return Unicode vertical objects.
.. autofunction:: xobj
.. autofunction:: vobj
.. autofunction:: hobj
The following functions are for rendering atoms and symbols.
.. autofunction:: xsym
.. autofunction:: pretty_atom
.. autofunction:: pretty_symbol
.. autofunction:: annotated
.. automodule:: diofant.printing.pretty.stringpict
.. autoclass:: stringPict :members:
.. autoclass:: prettyForm :members:
.. autofunction:: diofant.printing.dot.dotprint