# The Sage Preparser¶

AUTHORS:

• William Stein (2006-02-19)
• William Stein (2006-03-09)
• Fixed crash in parsing exponentials.
• Precision of real literals now determined by digits of input (like Mathematica).
• Joe Wetherell (2006-04-14)
• Bobby Moretti (2007-01-25)
• Added preliminary function assignment notation.
• Added strip_string_literals, containing_block utility functions. Arrr!
• Implicit multiplication (off by default).
• Factor out constants.
• Simplify preparser by making it modular and using regular expressions.
• Bug fixes, complex numbers, and binary input.

EXAMPLES:

Preparsing:

sage: preparse('2/3')
'Integer(2)/Integer(3)'
sage: preparse('2.5')
"RealNumber('2.5')"
sage: preparse('2^3')
'Integer(2)**Integer(3)'
sage: preparse('a^b')            # exponent
'a**b'
sage: preparse('a**b')
'a**b'
sage: preparse('G.0')            # generator
'G.gen(0)'
sage: preparse('a = 939393R')    # raw
'a = 939393'
sage: implicit_multiplication(True)
sage: preparse('a b c in L')     # implicit multiplication
'a*b*c in L'
sage: preparse('2e3x + 3exp(y)')
"RealNumber('2e3')*x + Integer(3)*exp(y)"


A string with escaped quotes in it (the point here is that the preparser doesn’t get confused by the internal quotes):

sage: ""Yes," he said."
'"Yes," he said.'
sage: s = "\"; s
'\'


A hex literal:

sage: preparse('0x2e3')
'Integer(0x2e3)'
sage: 0xA
10
sage: 0xe
14


Raw and hex work correctly:

sage: type(0xa1)
<type 'sage.rings.integer.Integer'>
sage: type(0xa1r)
<type 'int'>
sage: type(0Xa1R)
<type 'int'>


In Sage, methods can also be called on integer and real literals (note that in pure Python this would be a syntax error):

sage: 16.sqrt()
4
sage: 87.factor()
3 * 29
sage: 15.10.sqrt()
3.88587184554509
sage: preparse('87.sqrt()')
'Integer(87).sqrt()'
sage: preparse('15.10.sqrt()')
"RealNumber('15.10').sqrt()"


Note that calling methods on int literals in pure Python is a syntax error, but Sage allows this for Sage integers and reals, because users frequently request it:

sage: eval('4.__add__(3)')
Traceback (most recent call last):
...
SyntaxError: invalid syntax


Symbolic functional notation:

sage: a=10; f(theta, beta) = theta + beta; b = x^2 + theta
sage: f
(theta, beta) |--> beta + theta
sage: a
10
sage: b
x^2 + theta
sage: f(theta,theta)
2*theta

sage: a = 5; f(x,y) = x*y*sqrt(a)
sage: f
(x, y) |--> sqrt(5)*x*y


This involves an =-, but should still be turned into a symbolic expression:

sage: preparse('a(x) =- 5')
'__tmp__=var("x"); a = symbolic_expression(- Integer(5)).function(x)'
sage: f(x)=-x
sage: f(10)
-10


This involves -=, which should not be turned into a symbolic expression (of course a(x) isn’t an identifier, so this will never be valid):

sage: preparse('a(x) -= 5')
'a(x) -= Integer(5)'


Raw literals:

Raw literals are not preparsed, which can be useful from an efficiency point of view. Just like Python ints are denoted by an L, in Sage raw integer and floating literals are followed by an”r” (or “R”) for raw, meaning not preparsed.

We create a raw integer:

sage: a = 393939r
sage: a
393939
sage: type(a)
<type 'int'>


We create a raw float:

sage: z = 1.5949r
sage: z
1.5949
sage: type(z)
<type 'float'>


You can also use an upper case letter:

sage: z = 3.1415R
sage: z
3.1415
sage: type(z)
<type 'float'>


This next example illustrates how raw literals can be very useful in certain cases. We make a list of even integers up to 10000:

sage: v = [ 2*i for i in range(10000)]


This takes a noticeable fraction of a second (e.g., 0.25 seconds). After preparsing, what Python is really executing is the following:

sage: preparse('v = [ 2*i for i in range(10000)]')
'v = [ Integer(2)*i for i in range(Integer(10000))]'


If instead we use a raw 2 we get execution that is instant (0.00 seconds):

sage: v = [ 2r * i for i in range(10000r)]


Behind the scenes what happens is the following:

sage: preparse('v = [ 2r * i for i in range(10000r)]')
'v = [ 2 * i for i in range(10000)]'

class sage.misc.preparser.BackslashOperator

Implements Matlab-style backslash operator for solving systems:

A \ b


EXAMPLES:

sage: preparse("A \ matrix(QQ,2,1,[1/3,'2/3'])")
"A  * BackslashOperator() * matrix(QQ,Integer(2),Integer(1),[Integer(1)/Integer(3),'2/3'])"
sage: preparse("A \ matrix(QQ,2,1,[1/3,2*3])")
'A  * BackslashOperator() * matrix(QQ,Integer(2),Integer(1),[Integer(1)/Integer(3),Integer(2)*Integer(3)])'
sage: preparse("A \ B + C")
'A  * BackslashOperator() * B + C'
sage: preparse("A \ eval('C+D')")
"A  * BackslashOperator() * eval('C+D')"
sage: preparse("A \ x / 5")
'A  * BackslashOperator() * x / Integer(5)'
sage: preparse("A^3 \ b")
'A**Integer(3)  * BackslashOperator() * b'

sage.misc.preparser.containing_block(code, ix, delimiters=['()', '[]', '{}'], require_delim=True)

Returns the smallest range (start,end) such that code[start,end] is delimited by balanced delimiters (e.g., parentheses, brackets, and braces).

INPUT:

• code - a string
• ix - an integer; a starting position
• delimiters - a list of strings (default: [‘()’, ‘[]’, ‘{}’]); the delimiters to balance
• require_delim - a boolean (default: True); whether to raise a SyntaxError if delimiters are unbalanced

OUTPUT:

• a 2-tuple of integers

EXAMPLES:

sage: from sage.misc.preparser import containing_block
sage: s = "factor(next_prime(L[5]+1))"
sage: s[22]
'+'
sage: start, end = containing_block(s, 22); print start, end
17 25
sage: s[start:end]
'(L[5]+1)'
sage: s[20]
'5'
sage: start, end = containing_block(s, 20); s[start:end]
'[5]'
sage: start, end = containing_block(s, 20, delimiters=['()']); s[start:end]
'(L[5]+1)'
sage: start, end = containing_block(s, 10); s[start:end]
'(next_prime(L[5]+1))'

sage.misc.preparser.extract_numeric_literals(code)

Pulls out numeric literals and assigns them to global variables. This eliminates the need to re-parse and create the literals, e.g., during every iteration of a loop.

INPUT:

• code - a string; a block of code

OUTPUT:

• a (string, string:string dictionary) 2-tuple; the block with literals replaced by variable names and a mapping from names to the new variables

EXAMPLES:

sage: from sage.misc.preparser import extract_numeric_literals
sage: code, nums = extract_numeric_literals("1.2 + 5")
sage: print code
_sage_const_1p2  + _sage_const_5
sage: print nums
{'_sage_const_1p2': "RealNumber('1.2')", '_sage_const_5': 'Integer(5)'}

sage: extract_numeric_literals("[1, 1.1, 1e1, -1e-1, 1.]")[0]
'[_sage_const_1 , _sage_const_1p1 , _sage_const_1e1 , -_sage_const_1en1 , _sage_const_1p ]'

sage: extract_numeric_literals("[1.sqrt(), 1.2.sqrt(), 1r, 1.2r, R.1, R0.1, (1..5)]")[0]
'[_sage_const_1 .sqrt(), _sage_const_1p2 .sqrt(), 1 , 1.2 , R.1, R0.1, (_sage_const_1 .._sage_const_5 )]'

sage.misc.preparser.handle_encoding_declaration(contents, out)

Find a PEP 263-style Python encoding declaration in the first or second line of $$contents$$. If found, output it to $$out$$ and return $$contents$$ without the encoding line; otherwise output a default UTF-8 declaration and return $$contents$$.

EXAMPLES:

sage: from sage.misc.preparser import handle_encoding_declaration
sage: import sys
sage: c1='# -*- coding: latin-1 -*-\nimport os, sys\n...'
sage: c2='# -*- coding: iso-8859-15 -*-\nimport os, sys\n...'
sage: c3='# -*- coding: ascii -*-\nimport os, sys\n...'
sage: c4='import os, sys\n...'
sage: handle_encoding_declaration(c1, sys.stdout)
# -*- coding: latin-1 -*-
'import os, sys\n...'
sage: handle_encoding_declaration(c2, sys.stdout)
# -*- coding: iso-8859-15 -*-
'import os, sys\n...'
sage: handle_encoding_declaration(c3, sys.stdout)
# -*- coding: ascii -*-
'import os, sys\n...'
sage: handle_encoding_declaration(c4, sys.stdout)
# -*- coding: utf-8 -*-
'import os, sys\n...'


TESTS:

These are some of the tests listed in PEP 263:

sage: contents = '#!/usr/bin/python\n# -*- coding: latin-1 -*-\nimport os, sys'
sage: handle_encoding_declaration(contents, sys.stdout)
# -*- coding: latin-1 -*-
'#!/usr/bin/python\nimport os, sys'

sage: contents = '# This Python file uses the following encoding: utf-8\nimport os, sys'
sage: handle_encoding_declaration(contents, sys.stdout)
# This Python file uses the following encoding: utf-8
'import os, sys'

sage: contents = '#!/usr/local/bin/python\n# coding: latin-1\nimport os, sys'
sage: handle_encoding_declaration(contents, sys.stdout)
# coding: latin-1
'#!/usr/local/bin/python\nimport os, sys'


Two hash marks are okay; this shows up in SageTeX-generated scripts:

sage: contents = '## -*- coding: utf-8 -*-\nimport os, sys\nprint x'
sage: handle_encoding_declaration(contents, sys.stdout)
## -*- coding: utf-8 -*-
'import os, sys\nprint x'


When the encoding declaration doesn’t match the specification, we spit out a default UTF-8 encoding.

Incorrect coding line:

sage: contents = '#!/usr/local/bin/python\n# latin-1\nimport os, sys'
sage: handle_encoding_declaration(contents, sys.stdout)
# -*- coding: utf-8 -*-
'#!/usr/local/bin/python\n# latin-1\nimport os, sys'


Encoding declaration not on first or second line:

sage: contents ='#!/usr/local/bin/python\n#\n# -*- coding: latin-1 -*-\nimport os, sys'
sage: handle_encoding_declaration(contents, sys.stdout)
# -*- coding: utf-8 -*-
'#!/usr/local/bin/python\n#\n# -*- coding: latin-1 -*-\nimport os, sys'


We don’t check for legal encoding names; that’s Python’s job:

sage: contents ='#!/usr/local/bin/python\n# -*- coding: utf-42 -*-\nimport os, sys'
sage: handle_encoding_declaration(contents, sys.stdout)
# -*- coding: utf-42 -*-
'#!/usr/local/bin/python\nimport os, sys'


NOTES:

PEP 263: http://www.python.org/dev/peps/pep-0263/

PEP 263 says that Python will interpret a UTF-8 byte order mark
as a declaration of UTF-8 encoding, but I don't think we do
that; this function only sees a Python string so it can't
account for a BOM.

We default to UTF-8 encoding even though PEP 263 says that
Python files should default to ASCII.

Also see http://docs.python.org/ref/encodings.html.


AUTHORS:

- Lars Fischer
- Dan Drake (2010-12-08, rewrite for ticket #10440)

sage.misc.preparser.implicit_mul(code, level=5)

Inserts *’s to make implicit multiplication explicit.

INPUT:

• code – a string; the code with missing *’s
• level – an integer (default: 5); how aggressive to be in placing *’s
• 0 - Do nothing
• 1 - Numeric followed by alphanumeric
• 2 - Closing parentheses followed by alphanumeric
• 3 - Spaces between alphanumeric
• 10 - Adjacent parentheses (may mangle call statements)

OUTPUT:

• a string

EXAMPLES:

sage: from sage.misc.preparser import implicit_mul
sage: implicit_mul('(2x^2-4x+3)a0')
'(2*x^2-4*x+3)*a0'
sage: implicit_mul('a b c in L')
'a*b*c in L'
sage: implicit_mul('1r + 1e3 + 5exp(2)')
'1r + 1e3 + 5*exp(2)'
sage: implicit_mul('f(a)(b)', level=10)
'f(a)*(b)'

sage.misc.preparser.implicit_multiplication(level=None)

Turns implicit multiplication on or off, optionally setting a specific level. Returns the current level if no argument is given.

INPUT:

EXAMPLES:

sage: implicit_multiplication(True)
sage: implicit_multiplication()
5
sage: preparse('2x')
'Integer(2)*x'
sage: implicit_multiplication(False)
sage: preparse('2x')
'2x'

sage.misc.preparser.in_quote()

x.__init__(...) initializes x; see help(type(x)) for signature

Returns whether a file can be loaded into Sage. This checks only whether its name ends in one of the supported extensions .py, .pyx, .sage, .spyx, and .m. Note: load() assumes the latter signifies a Magma file.

INPUT:

• filename - a string

OUTPUT:

• a boolean

EXAMPLES:

sage: sage.misc.preparser.is_loadable_filename('foo.bar')
False
False
True
True


Return True if s is a non-empty string of alphabetic characters or a non-empty string of digits or just a single _

EXAMPLES:

sage: from sage.misc.preparser import isalphadigit_
True
True
True
False


Executes a file in the scope given by globals. The filename itself is also evaluated in the scope. If the name starts with http://, it is treated as a URL and downloaded.

Note

For Cython files, the situation is more complicated – the module is first compiled to a temporary module t and executed via:

from t import *


INPUT:

• filename – a string; a .py, .sage, .pyx, etc., filename, URL, or expression that evaluates to one
• globals – a string:object dictionary; the context in which to evaluate the filename and exec its contents
• attach – a boolean (default: False); whether to add the file to the list of attached files

EXAMPLES:

Note that .py files are not preparsed:

sage: t = tmp_filename(ext='.py')
sage: open(t,'w').write("print 'hi', 2/3; z = -2/7")
sage: z = 1
hi 0
sage: z
-1


A .sage file is preparsed:

sage: t = tmp_filename(ext='.sage')
sage: open(t,'w').write("print 'hi', 2/3; z = -2/7")
sage: z = 1
hi 2/3
sage: z
-2/7


Cython files are not preparsed:

sage: t = tmp_filename(ext='.pyx')
sage: open(t,'w').write("print 'hi', 2/3; z = -2/7")
sage: z = 1
Compiling ...
hi 0
sage: z
-1


If the file isn’t a Cython, Python, or a Sage file, a ValueError is raised:

sage: sage.misc.preparser.load('a.foo',globals())
Traceback (most recent call last):
...
ValueError: argument (='a.foo') to load or attach must have extension py, pyx, sage, spyx, or m


A filename given as an expression get evaluated. This ensures that load DATA+'foo.sage' works in the Notebook, say:

sage: t=tmp_filename(ext='.py'); open(t,'w').write("print 'hello world'")
hello world


We load a file given at a remote URL:

sage: sage.misc.preparser.load('http://wstein.org/loadtest.py', globals())  # optional - internet
hi from the net
5


We can load files using secure http (https):

sage: sage.misc.preparser.load('https://github.com/jasongrout/minimum_rank/raw/minimum_rank_1_0_0/minrank.py', globals())  # optional - internet


We attach a file:

sage: t = tmp_filename(ext='.py')
sage: open(t,'w').write("print 'hello world'")
hello world
sage: t in attached_files()
True


You can’t attach remote URLs (yet):

sage: sage.misc.preparser.load('http://wstein.org/loadtest.py', globals(), attach=True)  # optional - internet
Traceback (most recent call last):
...
NotImplementedError: you can't attach a URL


The default search path for loading and attaching files is the current working directory, i.e., '.'. But you can modify the path with load_attach_path():

sage: sage.misc.attached_files.reset(); reset_load_attach_path()
['.']
sage: t_dir = tmp_dir()
sage: fullpath = os.path.join(t_dir, 'test.py')
sage: open(fullpath, 'w').write("print 37 * 3")
sage: attach('test.py')
111
sage: sage.misc.attached_files.reset(); reset_load_attach_path() # clean up


or by setting the environment variable SAGE_LOAD_ATTACH_PATH to a colon-separated list before starting Sage:

$export SAGE_LOAD_ATTACH_PATH="/path/to/my/library:/path/to/utils"$ sage
['.', '/path/to/my/library', '/path/to/utils']


Make sure that load handles filenames with spaces in the name or path:

sage: t = tmp_filename(ext=' b.sage'); open(t,'w').write("print 2")
2


Encodes a load or attach command as valid Python code.

INPUT:

• filename - a string; the argument to the load or attach command

OUTPUT:

• a string

EXAMPLES:

sage: sage.misc.preparser.load_wrap('foo.py', True)
sage: sage.misc.preparser.base64.b64decode("Zm9vLnNhZ2U=")
'foo.sage'

sage.misc.preparser.parse_ellipsis(code, preparse_step=True)

Preparses [0,2,..,n] notation.

INPUT:

• code - a string
• preparse_step - a boolean (default: True)

OUTPUT:

• a string

EXAMPLES:

sage: from sage.misc.preparser import parse_ellipsis
sage: parse_ellipsis("[1,2,..,n]")
'(ellipsis_range(1,2,Ellipsis,n))'
sage: parse_ellipsis("for i in (f(x) .. L[10]):")
'for i in (ellipsis_iter(f(x) ,Ellipsis, L[10])):'
sage: [1.0..2.0]
[1.00000000000000, 2.00000000000000]

sage.misc.preparser.preparse(line, reset=True, do_time=False, ignore_prompts=False, numeric_literals=True)

Preparses a line of input.

INPUT:

• line - a string
• reset - a boolean (default: True)
• do_time - a boolean (default: False)
• ignore_prompts - a boolean (default: False)
• numeric_literals - a boolean (default: True)

OUTPUT:

• a string

EXAMPLES:

sage: preparse("ZZ.<x> = ZZ['x']")
"ZZ = ZZ['x']; (x,) = ZZ._first_ngens(1)"
sage: preparse("ZZ.<x> = ZZ['y']")
"ZZ = ZZ['y']; (x,) = ZZ._first_ngens(1)"
sage: preparse("ZZ.<x,y> = ZZ[]")
"ZZ = ZZ['x, y']; (x, y,) = ZZ._first_ngens(2)"
sage: preparse("ZZ.<x,y> = ZZ['u,v']")
"ZZ = ZZ['u,v']; (x, y,) = ZZ._first_ngens(2)"
sage: preparse("ZZ.<x> = QQ[2^(1/3)]")
'ZZ = QQ[Integer(2)**(Integer(1)/Integer(3))]; (x,) = ZZ._first_ngens(1)'
sage: QQ[2^(1/3)]
Number Field in a with defining polynomial x^3 - 2

sage: preparse("a^b")
'a**b'
sage: preparse("a^^b")
'a^b'
sage: 8^1
8
sage: 8^^1
9
sage: 9^^1
8

sage: preparse("A \ B")
'A  * BackslashOperator() * B'
sage: preparse("A^2 \ B + C")
'A**Integer(2)  * BackslashOperator() * B + C'
sage: preparse("a \\ b \\") # There is really only one backslash here, it's just being escaped.
'a  * BackslashOperator() * b \\'

sage: preparse("time R.<x> = ZZ[]", do_time=True)
'__time__=misc.cputime(); __wall__=misc.walltime(); R = ZZ[\'x\']; print "Time: CPU %.2f s, Wall: %.2f s"%(misc.cputime(__time__), misc.walltime(__wall__)); (x,) = R._first_ngens(1)'

sage.misc.preparser.preparse_calculus(code)

Supports calculus-like function assignment, e.g., transforms:

f(x,y,z) = sin(x^3 - 4*y) + y^x


into:

__tmp__=var("x,y,z")
f = symbolic_expression(sin(x**3 - 4*y) + y**x).function(x,y,z)


AUTHORS:

• Bobby Moretti
• Initial version - 02/2007
• William Stein
• Make variables become defined if they aren’t already defined.
• Rewrite using regular expressions (01/2009)

EXAMPLES:

sage: preparse("f(x) = x^3-x")
'__tmp__=var("x"); f = symbolic_expression(x**Integer(3)-x).function(x)'
sage: preparse("f(u,v) = u - v")
'__tmp__=var("u,v"); f = symbolic_expression(u - v).function(u,v)'
sage: preparse("f(x) =-5")
'__tmp__=var("x"); f = symbolic_expression(-Integer(5)).function(x)'
sage: preparse("f(x) -= 5")
'f(x) -= Integer(5)'
sage: preparse("f(x_1, x_2) = x_1^2 - x_2^2")
'__tmp__=var("x_1,x_2"); f = symbolic_expression(x_1**Integer(2) - x_2**Integer(2)).function(x_1,x_2)'


For simplicity, this function assumes all statements begin and end with a semicolon:

sage: from sage.misc.preparser import preparse_calculus
sage: preparse_calculus(";f(t,s)=t^2;")
';__tmp__=var("t,s"); f = symbolic_expression(t^2).function(t,s);'
sage: preparse_calculus(";f( t , s ) = t^2;")
';__tmp__=var("t,s"); f = symbolic_expression(t^2).function(t,s);'


TESTS:

The arguments in the definition must be symbolic variables #10747:

sage: preparse_calculus(";f(_sage_const_)=x;")
Traceback (most recent call last):
...
ValueError: Argument names should be valid python identifiers.


Although preparse_calculus returns something for f(1)=x, when preparsing a file an exception is raised because it is invalid python:

sage: preparse_calculus(";f(1)=x;")
';__tmp__=var("1"); f = symbolic_expression(x).function(1);'

sage: from sage.misc.preparser import preparse_file
sage: preparse_file("f(1)=x")
Traceback (most recent call last):
...
ValueError: Argument names should be valid python identifiers.

sage: from sage.misc.preparser import preparse_file
sage: preparse_file("f(x,1)=2")
Traceback (most recent call last):
...
ValueError: Argument names should be valid python identifiers.

sage.misc.preparser.preparse_file(contents, globals=None, numeric_literals=True)

Preparses input, attending to numeric literals and load/attach file directives.

Note

Temporarily, if @parallel is in the input, then numeric_literals is always set to False.

INPUT:

• contents - a string
• globals - dict or None (default: None); if given, then arguments to load/attach are evaluated in the namespace of this dict.
• numeric_literals - bool (default: True), whether to factor out wrapping of integers and floats, so they don’t get created repeatedly inside loops

OUTPUT:

• a string

TESTS:

sage: from sage.misc.preparser import preparse_file
sage: lots_of_numbers = "[%s]" % ", ".join(str(i) for i in range(3000))
sage: _ = preparse_file(lots_of_numbers)
sage: print preparse_file("type(100r), type(100)")
_sage_const_100 = Integer(100)
type(100 ), type(_sage_const_100 )

sage.misc.preparser.preparse_file_named(name)

Preparse file named code{name} (presumably a .sage file), outputting to a temporary file. Returns name of temporary file.

sage.misc.preparser.preparse_file_named_to_stream(name, out)

Preparse file named code{name} (presumably a .sage file), outputting to stream code{out}.

sage.misc.preparser.preparse_generators(code)

Parses generator syntax, converting:

obj.<gen0,gen1,...,genN> = objConstructor(...)


into:

obj = objConstructor(..., names=("gen0", "gen1", ..., "genN"))
(gen0, gen1, ..., genN,) = obj.gens()


and:

obj.<gen0,gen1,...,genN> = R[interior]


into:

obj = R[interior]; (gen0, gen1, ..., genN,) = obj.gens()


INPUT:

• code - a string

OUTPUT:

• a string

LIMITATIONS:

• The entire constructor must be on one line.

AUTHORS:

• 2006-04-14: Joe Wetherell (jlwether@alum.mit.edu)
• Initial version.
• 2006-04-17: William Stein
• Improvements to allow multiple statements.
• 2006-05-01: William
• Fix bug that Joe found.
• 2006-10-31: William
• Fix so obj doesn’t have to be mutated.
• Rewrite using regular expressions

TESTS:

sage: from sage.misc.preparser import preparse, preparse_generators


Vanilla:

sage: preparse("R.<x> = ZZ['x']")
"R = ZZ['x']; (x,) = R._first_ngens(1)"
sage: preparse("R.<x,y> = ZZ['x,y']")
"R = ZZ['x,y']; (x, y,) = R._first_ngens(2)"


No square brackets:

sage: preparse("R.<x> = PolynomialRing(ZZ, 'x')")
"R = PolynomialRing(ZZ, 'x', names=('x',)); (x,) = R._first_ngens(1)"
sage: preparse("R.<x,y> = PolynomialRing(ZZ, 'x,y')")
"R = PolynomialRing(ZZ, 'x,y', names=('x', 'y',)); (x, y,) = R._first_ngens(2)"


Names filled in:

sage: preparse("R.<x> = ZZ[]")
"R = ZZ['x']; (x,) = R._first_ngens(1)"
sage: preparse("R.<x,y> = ZZ[]")
"R = ZZ['x, y']; (x, y,) = R._first_ngens(2)"


Names given not the same as generator names:

sage: preparse("R.<x> = ZZ['y']")
"R = ZZ['y']; (x,) = R._first_ngens(1)"
sage: preparse("R.<x,y> = ZZ['u,v']")
"R = ZZ['u,v']; (x, y,) = R._first_ngens(2)"


Number fields:

sage: preparse("K.<a> = QQ[2^(1/3)]")
'K = QQ[Integer(2)**(Integer(1)/Integer(3))]; (a,) = K._first_ngens(1)'
sage: preparse("K.<a, b> = QQ[2^(1/3), 2^(1/2)]")
'K = QQ[Integer(2)**(Integer(1)/Integer(3)), Integer(2)**(Integer(1)/Integer(2))]; (a, b,) = K._first_ngens(2)'


Just the .<> notation:

sage: preparse("R.<x> = ZZx")
'R = ZZx; (x,) = R._first_ngens(1)'
sage: preparse("R.<x, y> = a+b")
'R = a+b; (x, y,) = R._first_ngens(2)'
sage: preparse("A.<x,y,z>=FreeAlgebra(ZZ,3)")
"A = FreeAlgebra(ZZ,Integer(3), names=('x', 'y', 'z',)); (x, y, z,) = A._first_ngens(3)"


Ensure we don’t eat too much:

sage: preparse("R.<x, y> = ZZ;2")
'R = ZZ; (x, y,) = R._first_ngens(2);Integer(2)'
sage: preparse("R.<x, y> = ZZ['x,y'];2")
"R = ZZ['x,y']; (x, y,) = R._first_ngens(2);Integer(2)"
sage: preparse("F.<b>, f, g = S.field_extension()")
"F, f, g  = S.field_extension(names=('b',)); (b,) = F._first_ngens(1)"


For simplicity, this function assumes all statements begin and end with a semicolon:

sage: preparse_generators(";  R.<x>=ZZ[];")
";  R = ZZ['x']; (x,) = R._first_ngens(1);"

sage: preparse_generators('R.<x> = ')
'R.<x> = '

sage.misc.preparser.preparse_numeric_literals(code, extract=False)

This preparses numerical literals into their Sage counterparts, e.g. Integer, RealNumber, and ComplexNumber.

INPUT:

• code - a string; a code block to preparse
• extract - a boolean (default: False); whether to create names for the literals and return a dictionary of name-construction pairs

OUTPUT:

• a string or (string, string:string dictionary) 2-tuple; the preparsed block and, if extract is True, the name-construction mapping

EXAMPLES:

sage: from sage.misc.preparser import preparse_numeric_literals
sage: preparse_numeric_literals("5")
'Integer(5)'
sage: preparse_numeric_literals("5j")
"ComplexNumber(0, '5')"
sage: preparse_numeric_literals("5jr")
'5J'
sage: preparse_numeric_literals("5l")
'5l'
sage: preparse_numeric_literals("5L")
'5L'
sage: preparse_numeric_literals("1.5")
"RealNumber('1.5')"
sage: preparse_numeric_literals("1.5j")
"ComplexNumber(0, '1.5')"
sage: preparse_numeric_literals(".5j")
"ComplexNumber(0, '.5')"
sage: preparse_numeric_literals("5e9j")
"ComplexNumber(0, '5e9')"
sage: preparse_numeric_literals("5.")
"RealNumber('5.')"
sage: preparse_numeric_literals("5.j")
"ComplexNumber(0, '5.')"
sage: preparse_numeric_literals("5.foo()")
'Integer(5).foo()'
sage: preparse_numeric_literals("5.5.foo()")
"RealNumber('5.5').foo()"
sage: preparse_numeric_literals("5.5j.foo()")
"ComplexNumber(0, '5.5').foo()"
sage: preparse_numeric_literals("5j.foo()")
"ComplexNumber(0, '5').foo()"
sage: preparse_numeric_literals("1.exp()")
'Integer(1).exp()'
sage: preparse_numeric_literals("1e+10")
"RealNumber('1e+10')"
sage: preparse_numeric_literals("0x0af")
'Integer(0x0af)'
sage: preparse_numeric_literals("0x10.sqrt()")
'Integer(0x10).sqrt()'
sage: preparse_numeric_literals('0o100')
"Integer('100', 8)"
sage: preparse_numeric_literals('0b111001')
"Integer('111001', 2)"
sage: preparse_numeric_literals('0xe')
'Integer(0xe)'
sage: preparse_numeric_literals('0xEAR')
'0xEA'
sage: preparse_numeric_literals('0x1012Fae')
'Integer(0x1012Fae)'

sage.misc.preparser.strip_prompts(line)

Removes leading sage: and >>> prompts so that pasting of examples from the documentation works.

INPUT:

• line - a string to process

OUTPUT:

• a string stripped of leading prompts

EXAMPLES:

sage: from sage.misc.preparser import strip_prompts
sage: strip_prompts("sage: 2 + 2")
'2 + 2'
sage: strip_prompts(">>>   3 + 2")
'3 + 2'
sage: strip_prompts("  2 + 4")
'  2 + 4'

sage.misc.preparser.strip_string_literals(code, state=None)

Returns a string with all literal quotes replaced with labels and a dictionary of labels for re-substitution. This makes parsing easier.

INPUT:

• code - a string; the input
• state - a 2-tuple (default: None); state with which to continue processing, e.g., across multiple calls to this function

OUTPUT:

• a 3-tuple of the processed code, the dictionary of labels, and any accumulated state

EXAMPLES:

sage: from sage.misc.preparser import strip_string_literals
sage: s, literals, state = strip_string_literals(r'''['a', "b", 'c', "d\""]''')
sage: s
'[%(L1)s, %(L2)s, %(L3)s, %(L4)s]'
sage: literals
{'L1': "'a'", 'L2': '"b"', 'L3': "'c'", 'L4': '"d\\""'}
sage: print s % literals
['a', "b", 'c', "d\""]
sage: print strip_string_literals(r'-"\\\""-"\\"-')[0]
-%(L1)s-%(L2)s-


Triple-quotes are handled as well:

sage: s, literals, state = strip_string_literals("[a, '''b''', c, '']")
sage: s
'[a, %(L1)s, c, %(L2)s]'
sage: print s % literals
[a, '''b''', c, '']


sage: s, literals, state = strip_string_literals("code '#' # ccc 't'"); s
'code %(L1)s #%(L2)s'
sage: s % literals
"code '#' # ccc 't'"


A state is returned so one can break strings across multiple calls to this function:

sage: s, literals, state = strip_string_literals('s = "some'); s
's = %(L1)s'
sage: s, literals, state = strip_string_literals('thing" * 5', state); s
'%(L1)s * 5'


TESTS:

Even for raw strings, a backslash can escape a following quote:

sage: s, literals, state = strip_string_literals(r"r'somethin\' funny'"); s
'r%(L1)s'
sage: dep_regex = r'^ *(?:(?:cimport +([\w\. ,]+))|(?:from +(\w+) +cimport)|(?:include *[\'"]([^\'"]+)[\'"])|(?:cdef *extern *from *[\'"]([^\'"]+)[\'"]))' # Ticket 5821


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