Printing¶
See the Printing section in Tutorial for introduction into printing.
This guide documents the printing system in Diofant and how it works internally.
Printer Class¶
Printing subsystem driver
Diofant’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 fallback use the emptyPrinter method for the printer.
Some more information how the single concepts work and who should use which:
The object prints itself
This was the original way of doing printing in diofant. 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 builtin diofant objects, but not that good for user defined classes where it is inconvenient to patch the printers.
Nevertheless, to get a fitting representation, the printers look for a specific method in every object, that will be called if it’s available and is then responsible for the representation. The name of that method depends on the specific printer and is defined under Printer.printmethod.
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(…), in order to dispatch, we will try calling printer methods 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, we proceed with trying Rational bases in the inheritance order.
As fallback use the emptyPrinter method for the printer.
As fallback self.emptyPrinter will be called with the expression. If not defined in the Printer subclass this will be the same as str(expr).
The main class responsible for printing is Printer
(see also its
source code):

class
diofant.printing.printer.
Printer
(settings=None)[source]¶ Generic printer
Its job is to provide infrastructure for implementing new printers easily.
Basically, if you want to implement a printer, all you have to do is:
Subclass Printer.
Define Printer.printmethod in your subclass. If a object has a method with that name, this method will be used for printing.
In your subclass, define
_print_<CLASS>
methodsFor each class you want to provide printing to, define an appropriate method how to do it. For example if you want a class FOO to be printed in its own way, define _print_FOO:
def _print_FOO(self, e): ...
this should return how FOO instance e is printed
Also, if
BAR
is a subclass ofFOO
,_print_FOO(bar)
will be called for instance ofBAR
, if no_print_BAR
is provided. Thus, usually, we don’t need to provide printing routines for every class we want to support – only generic routine has to be provided for a set of classes.A good example for this are functions  for example
PrettyPrinter
only defines_print_Function
, and there is no_print_sin
,_print_tan
, etc…On the other hand, a good printer will probably have to define separate routines for
Symbol
,Atom
,Number
,Integral
,Limit
, etc…If convenient, override
self.emptyPrinter
This callable will be called to obtain printing result as a last resort, that is when no appropriate print method was found for an expression.
Examples
Here we will overload
StrPrinter
.>>> from diofant.printing.str import StrPrinter
>>> class CustomStrPrinter(StrPrinter): ... def _print_Derivative(self, expr): ... return str(expr.args[0].func) + "'"*len(expr.args[1:]) >>> def mystr(e): ... return CustomStrPrinter().doprint(e) >>> t = Symbol('t') >>> x = Function('x')(t) >>> print(mystr(x.diff(t, 2))) x''

printmethod
= None¶
PrettyPrinter Class¶
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 nicelooking
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
diofant.printing.pretty.pretty.
PrettyPrinter
(settings=None)[source]¶ Printer, which converts an expression into 2D ASCIIart figure.

diofant.printing.pretty.pretty.
pprint
(expr, **settings)¶

diofant.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.

diofant.printing.pretty.pretty.
pretty_print
(expr, **settings)[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) – line wrapping enabled/disabled, defaults to True
 num_columns (int or None, optional) – number of columns before line breaking (default to None which reads the terminal width), useful when using Diofant without terminal.
 use_unicode (bool or None, optional) – use unicode characters, such as the Greek letter pi instead of the string pi.
 full_prec (bool or string, optional) – use full precision. Default to “auto”
 order (bool or string, optional) – set to ‘none’ for long expressions if slow; default is None
CCodePrinter¶
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))

class
diofant.printing.ccode.
CCodePrinter
(settings={})[source]¶ A printer to convert python expressions to strings of c code.

printmethod
= '_ccode'¶


diofant.printing.ccode.
ccode
(expr, assign_to=None, **settings)[source]¶ Converts an expr to a string of c code
Parameters:  expr (Expr) – A diofant 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
, orIndexed
type. This is helpful in case of linewrapping, or for expressions that generate multiline 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
orUndefinedFunction
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 ofa
.  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
>>> x, tau = symbols("x, tau") >>> ccode((2*tau)**Rational(7, 2)) '8*sqrt(2)*pow(tau, 7.0L/2.0L)' >>> ccode(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') >>> ccode(func(Abs(x) + ceiling(x)), user_functions=custom_functions) 'f(fabs(x) + CEIL(x))'
or if the Cfunction takes a subset of the original arguments:
>>> ccode(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 anassign_to
variable is provided an if statement is created, otherwise the ternary operator is used. Note that if thePiecewise
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.>>> expr = Piecewise((x + 1, x > 0), (x, True)) >>> print(ccode(expr, tau)) if (x > 0) { tau = x + 1; } else { tau = x; }
Support for loops is provided through
Indexed
types. Withcontract=True
these expressions will be turned into loops, whereascontract=False
will just print the assignment expression that should be looped over:>>> 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_y1) >>> e = Eq(Dy[i], (y[i+1]y[i])/(t[i+1]t[i])) >>> ccode(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 toassign_to
. Note that any expression that can be generated normally can also exist inside a Matrix:>>> mat = Matrix([x**2, Piecewise((x + 1, x > 0), (x, True)), sin(x)]) >>> A = MatrixSymbol('A', 3, 1) >>> print(ccode(mat, A)) A[0] = pow(x, 2); if (x > 0) { A[1] = x + 1; } else { A[1] = x; } A[2] = sin(x);
Fortran Printing¶
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 finetune the behavior of fcode
in such a way
that manual changes in the result are no longer needed.

diofant.printing.fcode.
fcode
(expr, assign_to=None, **settings)[source]¶ Converts an expr to a string of fortran code
Parameters:  expr (Expr) – A diofant 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
, orIndexed
type. This is helpful in case of linewrapping, or for expressions that generate multiline 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, 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.
Examples
>>> 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 anassign_to
variable is provided an if statement is created, otherwise the ternary operator is used. Note that if thePiecewise
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.>>> 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. Withcontract=True
these expressions will be turned into loops, whereascontract=False
will just print the assignment expression that should be looped over:>>> 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_y1) >>> 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 toassign_to
. Note that any expression that can be generated normally can also exist inside a Matrix:>>> 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)

class
diofant.printing.fcode.
FCodePrinter
(settings={})[source]¶ A printer to convert diofant expressions to strings of Fortran code.

printmethod
= '_fcode'¶

Two basic examples:
>>> fcode(sqrt(1x**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 toplevel 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, strict=False)))
x  9.869604401089358618834491d0
When some functions are not part of the Fortran standard, it might be desirable to introduce the names of userdefined 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 postprocessing with
source code generators that write routines with multiple instructions. The
return value is a threetuple 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(), {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')
Mathematica code printing¶
LambdaPrinter¶
This classes implements printing to strings that can be used by the
diofant.utilities.lambdify.lambdify()
function.
LatexPrinter¶
This class implements LaTeX printing. See diofant.printing.latex
.

diofant.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']¶ list() > new empty list list(iterable) > new list initialized from iterable’s items

diofant.printing.latex.
latex
(expr, **settings)[source]¶ Convert the given expression to LaTeX representation.
>>> from diofant.abc import mu, r, tau
>>> print(latex((2*tau)**Rational(7, 2))) 8 \sqrt{2} \tau^{\frac{7}{2}}
Not using a print statement for printing, results in double backslashes for latex commands since that’s the way Python escapes backslashes in strings.
>>> latex((2*tau)**Rational(7, 2)) '8 \\sqrt{2} \\tau^{\\frac{7}{2}}'
order: Any of the supported monomial orderings (currently “lex”, “grlex”, or “grevlex”) and “none”. This parameter does nothing for Mul objects. For very large expressions, set the ‘order’ keyword to ‘none’ if speed is a concern.
mode: 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.>>> 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}
itex: Specifies if itexspecific syntax is used, including emitting
$$ $$
.>>> print(latex((2*mu)**Rational(7, 2), mode='equation', itex=True)) $$8 \sqrt{2} \mu^{\frac{7}{2}}$$
fold_frac_powers: Emit “^{p/q}” instead of “^{frac{p}{q}}” for fractional powers.
>>> print(latex((2*tau)**Rational(7, 2), fold_frac_powers=True)) 8 \sqrt{2} \tau^{7/2}
fold_func_brackets: Fold function brackets where applicable.
>>> 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}}}
fold_short_frac: 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.
>>> 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
long_frac_ratio: The allowed ratio of the width of the numerator to the width of the denominator before we start breaking off long fractions. The default value is 2.
>>> 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
mul_symbol: The symbol to use for multiplication. Can be one of None, “ldot”, “dot”, or “times”.
>>> print(latex((2*tau)**sin(Rational(7, 2)), mul_symbol="times")) \left(2 \times \tau\right)^{\sin{\left (\frac{7}{2} \right )}}
inv_trig_style: How inverse trig functions should be displayed. Can be one of “abbreviated”, “full”, or “power”. Defaults to “abbreviated”.
>>> 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 )}
mat_str: 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.
>>> 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]
mat_delim: The delimiter to wrap around matrices. Can be one of “[“, “(“, or the empty string. Defaults to “[“.
>>> print(latex(Matrix(2, 1, [x, y]), mat_delim="(")) \left(\begin{matrix}x\\y\end{matrix}\right)
symbol_names: Dictionary of symbols and the custom strings they should be emitted as.
>>> print(latex(x**2, symbol_names={x: 'x_i'})) x_i^{2}
latex
also supports the builtin container types list, tuple, and dictionary.>>> print(latex([2/x, y], mode='inline')) $\left [ 2 / x, \quad y\right ]$
MathMLPrinter¶
This class is responsible for MathML printing. See diofant.printing.mathml
.
More info on mathml content: http://www.w3.org/TR/MathML2/chapter4.html
PythonPrinter¶
This class implements Python printing. Usage:
>>> print_python(5*x**3 + sin(x))
x = Symbol('x')
e = 5*x**3 + sin(x)
ReprPrinter¶
This printer generates executable code. This code satisfies the identity
eval(srepr(expr)) == expr
.
StrPrinter¶
This module generates readable representations of Diofant expressions.
Implementation  Helper Classes/Functions¶

diofant.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.
>>> 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 codeprinting functionality, and additionally lists a number of functions that cannot be easily translated to C or Fortran.
Precedence¶
A module providing information about the necessity of brackets
PrettyPrinting Implementation Helpers¶

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

diofant.printing.pretty.pretty_symbology.
pretty_use_unicode
(flag=None)[source]¶ Set whether prettyprinter should use unicode by default
The following two functions return the Unicode version of the inputted Greek letter.

diofant.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']¶ list() > new empty list list(iterable) > new list initialized from iterable’s items
The following functions return Unicode vertical objects.

diofant.printing.pretty.pretty_symbology.
xobj
(symb, length)[source]¶ Construct spatial object of given length.
return: [] of equallength strings

diofant.printing.pretty.pretty_symbology.
vobj
(symb, height)[source]¶ Construct vertical object of a given height
see: xobj

diofant.printing.pretty.pretty_symbology.
hobj
(symb, width)[source]¶ Construct horizontal object of a given width
see: xobj
The following functions are for rendering atoms and symbols.

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

diofant.printing.pretty.pretty_symbology.
pretty_symbol
(symb_name)[source]¶ return pretty representation of a symbol

diofant.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
diofant.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 diofant.printing.pretty.pretty_symbology import pretty_use_unicode >>> f = pretty_use_unicode(flag=False) >>> print(stringPict("x+3").below(stringPict.LINE, '3')[0]) x+3  3

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

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 diofant.printing.pretty.pretty_symbology import pretty_use_unicode >>> f = pretty_use_unicode(flag=False) >>> print(stringPict("10").right(" + ", stringPict("1\r\r2", 1))[0]) 1 10 +  2

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.


class
diofant.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)
dotprint¶

diofant.printing.dot.
dotprint
(expr, styles=[(<class 'diofant.core.basic.Basic'>, {'shape': 'ellipse', 'color': 'blue'}), (<class 'diofant.core.expr.Expr'>, {'color': 'black'})], atom=<function <lambda>>, maxdepth=None, repeat=True, labelfunc=<class 'str'>, **kwargs)[source]¶ DOT description of a Diofant 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 islambda x: not isinstance(x, Basic)
. Another good choice islambda 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
withrepeat=True
, it will have two nodes forx
and withrepeat=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 isstr
. Another good option is
repr
. For example withstr
, the leaf nodes ofx + 1
are labeled,x
and1
. Withrepr
, they are labeledSymbol('x')
andInteger(1)
.
Additional keyword arguments are included as styles for the graph.
Examples
>>> print(dotprint(x + 2)) digraph{ <BLANKLINE> # Graph style "bgcolor"="transparent" "ordering"="out" "rankdir"="TD" <BLANKLINE> ######### # Nodes # ######### <BLANKLINE> "Add(Symbol('x'), Integer(2))_()" ["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(Symbol('x'), Integer(2))_()" > "Integer(2)_(0,)"; "Add(Symbol('x'), Integer(2))_()" > "Symbol('x')_(1,)"; }