Formatting utilities

This module defines helper functions that are not class methods.

AUTHORS:

  • Eric Gourgoulhon, Michal Bejger (2014-2015): initial version

  • Joris Vankerschaver (2010): for the function is_atomic()

  • Michael Jung (2020): extended usage of is_atomic()

class sage.tensor.modules.format_utilities.FormattedExpansion(txt=None, latex=None)[source]

Bases: SageObject

Helper class for displaying tensor expansions.

EXAMPLES:

sage: from sage.tensor.modules.format_utilities import FormattedExpansion
sage: f = FormattedExpansion('v', r'\tilde v')
sage: f
v
sage: latex(f)
\tilde v
sage: f = FormattedExpansion('x/2', r'\frac{x}{2}')
sage: f
x/2
sage: latex(f)
\frac{x}{2}

>>> from sage.all import *
>>> from sage.tensor.modules.format_utilities import FormattedExpansion
>>> f = FormattedExpansion('v', r'\tilde v')
>>> f
v
>>> latex(f)
\tilde v
>>> f = FormattedExpansion('x/2', r'\frac{x}{2}')
>>> f
x/2
>>> latex(f)
\frac{x}{2}

from sage.tensor.modules.format_utilities import FormattedExpansion
f = FormattedExpansion('v', r'\tilde v')
f
latex(f)
f = FormattedExpansion('x/2', r'\frac{x}{2}')
f
latex(f)
sage.tensor.modules.format_utilities.format_mul_latex(name1, operator, name2)[source]

Helper function for LaTeX names of results of multiplication or tensor product.

EXAMPLES:

sage: from sage.tensor.modules.format_utilities import format_mul_latex
sage: format_mul_latex('a', '*', 'b')
'a*b'
sage: format_mul_latex('a+b', '*', 'c')
'\\left(a+b\\right)*c'
sage: format_mul_latex('a', '*', 'b+c')
'a*\\left(b+c\\right)'
sage: format_mul_latex('a+b', '*', 'c+d')
'\\left(a+b\\right)*\\left(c+d\\right)'
sage: format_mul_latex(None, '*', 'b')
sage: format_mul_latex('a', '*', None)

>>> from sage.all import *
>>> from sage.tensor.modules.format_utilities import format_mul_latex
>>> format_mul_latex('a', '*', 'b')
'a*b'
>>> format_mul_latex('a+b', '*', 'c')
'\\left(a+b\\right)*c'
>>> format_mul_latex('a', '*', 'b+c')
'a*\\left(b+c\\right)'
>>> format_mul_latex('a+b', '*', 'c+d')
'\\left(a+b\\right)*\\left(c+d\\right)'
>>> format_mul_latex(None, '*', 'b')
>>> format_mul_latex('a', '*', None)

from sage.tensor.modules.format_utilities import format_mul_latex
format_mul_latex('a', '*', 'b')
format_mul_latex('a+b', '*', 'c')
format_mul_latex('a', '*', 'b+c')
format_mul_latex('a+b', '*', 'c+d')
format_mul_latex(None, '*', 'b')
format_mul_latex('a', '*', None)
sage.tensor.modules.format_utilities.format_mul_txt(name1, operator, name2)[source]

Helper function for text-formatted names of results of multiplication or tensor product.

EXAMPLES:

sage: from sage.tensor.modules.format_utilities import format_mul_txt
sage: format_mul_txt('a', '*', 'b')
'a*b'
sage: format_mul_txt('a+b', '*', 'c')
'(a+b)*c'
sage: format_mul_txt('a', '*', 'b+c')
'a*(b+c)'
sage: format_mul_txt('a+b', '*', 'c+d')
'(a+b)*(c+d)'
sage: format_mul_txt(None, '*', 'b')
sage: format_mul_txt('a', '*', None)

>>> from sage.all import *
>>> from sage.tensor.modules.format_utilities import format_mul_txt
>>> format_mul_txt('a', '*', 'b')
'a*b'
>>> format_mul_txt('a+b', '*', 'c')
'(a+b)*c'
>>> format_mul_txt('a', '*', 'b+c')
'a*(b+c)'
>>> format_mul_txt('a+b', '*', 'c+d')
'(a+b)*(c+d)'
>>> format_mul_txt(None, '*', 'b')
>>> format_mul_txt('a', '*', None)

from sage.tensor.modules.format_utilities import format_mul_txt
format_mul_txt('a', '*', 'b')
format_mul_txt('a+b', '*', 'c')
format_mul_txt('a', '*', 'b+c')
format_mul_txt('a+b', '*', 'c+d')
format_mul_txt(None, '*', 'b')
format_mul_txt('a', '*', None)
sage.tensor.modules.format_utilities.format_unop_latex(operator, name)[source]

Helper function for LaTeX names of results of unary operator.

EXAMPLES:

sage: from sage.tensor.modules.format_utilities import format_unop_latex
sage: format_unop_latex('-', 'a')
'-a'
sage: format_unop_latex('-', 'a+b')
'-\\left(a+b\\right)'
sage: format_unop_latex('-', '(a+b)')
'-(a+b)'
sage: format_unop_latex('-', None)

>>> from sage.all import *
>>> from sage.tensor.modules.format_utilities import format_unop_latex
>>> format_unop_latex('-', 'a')
'-a'
>>> format_unop_latex('-', 'a+b')
'-\\left(a+b\\right)'
>>> format_unop_latex('-', '(a+b)')
'-(a+b)'
>>> format_unop_latex('-', None)

from sage.tensor.modules.format_utilities import format_unop_latex
format_unop_latex('-', 'a')
format_unop_latex('-', 'a+b')
format_unop_latex('-', '(a+b)')
format_unop_latex('-', None)
sage.tensor.modules.format_utilities.format_unop_txt(operator, name)[source]

Helper function for text-formatted names of results of unary operator.

EXAMPLES:

sage: from sage.tensor.modules.format_utilities import format_unop_txt
sage: format_unop_txt('-', 'a')
'-a'
sage: format_unop_txt('-', 'a+b')
'-(a+b)'
sage: format_unop_txt('-', '(a+b)')
'-(a+b)'
sage: format_unop_txt('-', None)

>>> from sage.all import *
>>> from sage.tensor.modules.format_utilities import format_unop_txt
>>> format_unop_txt('-', 'a')
'-a'
>>> format_unop_txt('-', 'a+b')
'-(a+b)'
>>> format_unop_txt('-', '(a+b)')
'-(a+b)'
>>> format_unop_txt('-', None)

from sage.tensor.modules.format_utilities import format_unop_txt
format_unop_txt('-', 'a')
format_unop_txt('-', 'a+b')
format_unop_txt('-', '(a+b)')
format_unop_txt('-', None)
sage.tensor.modules.format_utilities.is_atomic(expr, sep=['+', '-'])[source]

Helper function to check whether some LaTeX expression is atomic.

Adapted from method _is_atomic() of class DifferentialFormFormatter written by Joris Vankerschaver (2010) and modified by Michael Jung (2020).

INPUT:

  • expr – string representing the expression (e.g. LaTeX string)

  • sep – (default: ['+', '-']) a list of strings representing the operations (e.g. LaTeX strings)

OUTPUT:

  • True if the operations are enclosed in parentheses and False otherwise.

EXAMPLES:

sage: from sage.tensor.modules.format_utilities import is_atomic
sage: is_atomic("2*x")
True
sage: is_atomic("2+x")
False
sage: is_atomic("(2+x)")
True

>>> from sage.all import *
>>> from sage.tensor.modules.format_utilities import is_atomic
>>> is_atomic("2*x")
True
>>> is_atomic("2+x")
False
>>> is_atomic("(2+x)")
True

from sage.tensor.modules.format_utilities import is_atomic
is_atomic("2*x")
is_atomic("2+x")
is_atomic("(2+x)")

Moreover the separator can be changed:

sage: is_atomic("a*b", sep=['*'])
False
sage: is_atomic("(a*b)", sep=['*'])
True
sage: is_atomic("a mod b", sep=['mod'])
False
sage: is_atomic("(a mod b)", sep=['mod'])
True

>>> from sage.all import *
>>> is_atomic("a*b", sep=['*'])
False
>>> is_atomic("(a*b)", sep=['*'])
True
>>> is_atomic("a mod b", sep=['mod'])
False
>>> is_atomic("(a mod b)", sep=['mod'])
True

is_atomic("a*b", sep=['*'])
is_atomic("(a*b)", sep=['*'])
is_atomic("a mod b", sep=['mod'])
is_atomic("(a mod b)", sep=['mod'])
sage.tensor.modules.format_utilities.is_atomic_wedge_latex(expression)[source]

Helper function to check whether LaTeX-formatted expression is atomic in terms of wedge products.

Adapted from method _is_atomic() of class DifferentialFormFormatter written by Joris Vankerschaver (2010) and modified by Michael Jung (2020).

INPUT:

  • expression – string representing the LaTeX expression

OUTPUT:

  • True if wedge products are enclosed in parentheses and False otherwise.

EXAMPLES:

sage: from sage.tensor.modules.format_utilities import is_atomic_wedge_latex
sage: is_atomic_wedge_latex(r"a")
True
sage: is_atomic_wedge_latex(r"a\wedge b")
False
sage: is_atomic_wedge_latex(r"(a\wedge b)")
True
sage: is_atomic_wedge_latex(r"(a\wedge b)\wedge c")
False
sage: is_atomic_wedge_latex(r"((a\wedge b)\wedge c)")
True
sage: is_atomic_wedge_latex(r"(a\wedge b\wedge c)")
True
sage: is_atomic_wedge_latex(r"\omega\wedge\theta")
False
sage: is_atomic_wedge_latex(r"(\omega\wedge\theta)")
True
sage: is_atomic_wedge_latex(r"\omega\wedge(\theta+a)")
False

>>> from sage.all import *
>>> from sage.tensor.modules.format_utilities import is_atomic_wedge_latex
>>> is_atomic_wedge_latex(r"a")
True
>>> is_atomic_wedge_latex(r"a\wedge b")
False
>>> is_atomic_wedge_latex(r"(a\wedge b)")
True
>>> is_atomic_wedge_latex(r"(a\wedge b)\wedge c")
False
>>> is_atomic_wedge_latex(r"((a\wedge b)\wedge c)")
True
>>> is_atomic_wedge_latex(r"(a\wedge b\wedge c)")
True
>>> is_atomic_wedge_latex(r"\omega\wedge\theta")
False
>>> is_atomic_wedge_latex(r"(\omega\wedge\theta)")
True
>>> is_atomic_wedge_latex(r"\omega\wedge(\theta+a)")
False

from sage.tensor.modules.format_utilities import is_atomic_wedge_latex
is_atomic_wedge_latex(r"a")
is_atomic_wedge_latex(r"a\wedge b")
is_atomic_wedge_latex(r"(a\wedge b)")
is_atomic_wedge_latex(r"(a\wedge b)\wedge c")
is_atomic_wedge_latex(r"((a\wedge b)\wedge c)")
is_atomic_wedge_latex(r"(a\wedge b\wedge c)")
is_atomic_wedge_latex(r"\omega\wedge\theta")
is_atomic_wedge_latex(r"(\omega\wedge\theta)")
is_atomic_wedge_latex(r"\omega\wedge(\theta+a)")
sage.tensor.modules.format_utilities.is_atomic_wedge_txt(expression)[source]

Helper function to check whether some text-formatted expression is atomic in terms of wedge products.

Adapted from method _is_atomic() of class DifferentialFormFormatter written by Joris Vankerschaver (2010) and modified by Michael Jung (2020).

INPUT:

  • expression – string representing the text-formatted expression

OUTPUT:

  • True if wedge products are enclosed in parentheses and False otherwise.

EXAMPLES:

sage: from sage.tensor.modules.format_utilities import is_atomic_wedge_txt
sage: is_atomic_wedge_txt("a")
True
sage: is_atomic_wedge_txt(r"a∧b")
False
sage: is_atomic_wedge_txt(r"(a∧b)")
True
sage: is_atomic_wedge_txt(r"(a∧b)∧c")
False
sage: is_atomic_wedge_txt(r"(a∧b∧c)")
True

>>> from sage.all import *
>>> from sage.tensor.modules.format_utilities import is_atomic_wedge_txt
>>> is_atomic_wedge_txt("a")
True
>>> is_atomic_wedge_txt(r"a∧b")
False
>>> is_atomic_wedge_txt(r"(a∧b)")
True
>>> is_atomic_wedge_txt(r"(a∧b)∧c")
False
>>> is_atomic_wedge_txt(r"(a∧b∧c)")
True

from sage.tensor.modules.format_utilities import is_atomic_wedge_txt
is_atomic_wedge_txt("a")
is_atomic_wedge_txt(r"a∧b")
is_atomic_wedge_txt(r"(a∧b)")
is_atomic_wedge_txt(r"(a∧b)∧c")
is_atomic_wedge_txt(r"(a∧b∧c)")