Expression of type ExprRange

from the theory of proveit.physics.quantum.circuits

import proveit
# Automation is not needed when building an expression:
proveit.defaults.automation = False # This will speed things up.
proveit.defaults.inline_pngs = False # Makes files smaller.
%load_expr # Load the stored expression as 'stored_expr'
# import Expression classes needed to build the expression
from proveit import ExprRange, IndexedVar, T, Variable, k, l, m
from proveit.logic import Disjoint
from proveit.numbers import Interval, one

# build up the expression from sub-expressions
sub_expr1 = Variable("_b", latex_format = r"{_{-}b}")
sub_expr2 = Variable("_a", latex_format = r"{_{-}a}")
expr = ExprRange(sub_expr1, ExprRange(sub_expr2, Disjoint(IndexedVar(T, [sub_expr1, sub_expr2]), Interval(one, k)), one, m), one, l).with_wrapping_at(8,16)

expr:

# check that the built expression is the same as the stored expression
assert expr == stored_expr
assert expr._style_id == stored_expr._style_id
print("Passed sanity check: expr matches stored_expr")

Passed sanity check: expr matches stored_expr

# Show the LaTeX representation of the expression for convenience if you need it.
print(stored_expr.latex())

\begin{array}{l} \textrm{disjoint}\left(T_{1, 1}, \{1~\ldotp \ldotp~k\}\right), \textrm{disjoint}\left(T_{1, 2}, \{1~\ldotp \ldotp~k\}\right), \ldots, \textrm{disjoint}\left(T_{1, m}, \{1~\ldotp \ldotp~k\}\right),  \\ \textrm{disjoint}\left(T_{2, 1}, \{1~\ldotp \ldotp~k\}\right), \textrm{disjoint}\left(T_{2, 2}, \{1~\ldotp \ldotp~k\}\right), \ldots, \textrm{disjoint}\left(T_{2, m}, \{1~\ldotp \ldotp~k\}\right),  \\ \ldots\ldots, \textrm{disjoint}\left(T_{l, 1}, \{1~\ldotp \ldotp~k\}\right), \textrm{disjoint}\left(T_{l, 2}, \{1~\ldotp \ldotp~k\}\right), \ldots, \textrm{disjoint}\left(T_{l, m}, \{1~\ldotp \ldotp~k\}\right) \end{array}

stored_expr.style_options()

name	description	default	current value	related methods
parameterization	'implicit' (default for LaTeX formatting) hides the parameter the ExprRange so the parameterization may be ambiguous (e.g., x_{1+1}, ..., x_{n+1}); 'explicit' (default for string formatting) reveals the parameterization (e.g. x_{1+1}, ..x_{k+1}.., x_{n+1}).	None	None/False	('with_explicit_parameterization', 'with_implicit_parameterization', 'with_default_parameterization_style')
front_expansion	The number of instances to display at the front of the range (e.g., before the ellipsis). Default is 2.	2	2	('with_front_expansion', 'get_front_expansion')
back_expansion	The number of instances to display at the back of the range (e.g., after the ellipsis). Default is 1.	1	1	('with_back_expansion', 'get_back_expansion')
order	The default order is 'increasing' (a_1 ... a_3) but to represent a 'decreasing' ExprRange (a_6 ... a_2) the order must be set to 'decreasing'	increasing	increasing	('with_decreasing_order', 'with_increasing_order')
wrap_positions	position(s) at which wrapping is to occur; 'n' is after the nth comma.	()	(8 16)	('with_wrapping_at',)
case_simplify	If 'True', simplify formatted instances that are ConditionalSets under proper index assumptions	False	False	('with_case_simplification',)

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	ExprRange	lambda_map: 1 start_index: 19 end_index: 2
1	Lambda	parameter: 17 body: 4
2	Variable
3	ExprTuple	17
4	ExprRange	lambda_map: 5 start_index: 19 end_index: 6
5	Lambda	parameter: 18 body: 8
6	Variable
7	ExprTuple	18
8	Operation	operator: 9 operands: 10
9	Literal
10	ExprTuple	11, 12
11	IndexedVar	variable: 13 indices: 14
12	Operation	operator: 15 operands: 16
13	Variable
14	ExprTuple	17, 18
15	Literal
16	ExprTuple	19, 20
17	Variable
18	Variable
19	Literal
20	Variable