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, N, Variable, k, m
from proveit.core_expr_types import A_1_to_m
from proveit.linear_algebra import TensorProd
from proveit.numbers import Add, Interval, one, subtract
from proveit.physics.quantum.circuits import Input, MultiQubitElem

# build up the expression from sub-expressions
sub_expr1 = Variable("_b", latex_format = r"{_{-}b}")
expr = ExprRange(sub_expr1, MultiQubitElem(element = Input(state = TensorProd(A_1_to_m), part = sub_expr1), targets = Interval(one, IndexedVar(N, m))), Add(IndexedVar(N, subtract(k, one)), one), IndexedVar(N, k)).with_wrapping_at(2,6)

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} \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& \qin{A_{1} {\otimes}  A_{2} {\otimes}  \ldots {\otimes}  A_{m}~\mbox{part}~N_{k - 1} + 1~\mbox{on}~\{1~\ldotp \ldotp~N_{m}\}} & \qw 
} \end{array},  \\ \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& \qin{A_{1} {\otimes}  A_{2} {\otimes}  \ldots {\otimes}  A_{m}~\mbox{part}~N_{k - 1} + 2~\mbox{on}~\{1~\ldotp \ldotp~N_{m}\}} & \qw 
} \end{array}, \ldots,  \\ \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& \qin{A_{1} {\otimes}  A_{2} {\otimes}  \ldots {\otimes}  A_{m}~\mbox{part}~N_{k}~\mbox{on}~\{1~\ldotp \ldotp~N_{m}\}} & \qw 
} \end{array} \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.	()	(2 6)	('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: 2 end_index: 3
1	Lambda	parameter: 20 body: 5
2	Operation	operator: 22 operands: 6
3	IndexedVar	variable: 26 index: 28
4	ExprTuple	20
5	Operation	operator: 8 operands: 9
6	ExprTuple	10, 35
7	ExprTuple	28
8	Literal
9	NamedExprs	element: 11 targets: 12
10	IndexedVar	variable: 26 index: 18
11	Operation	operator: 14 operands: 15
12	Operation	operator: 16 operands: 17
13	ExprTuple	18
14	Literal
15	NamedExprs	state: 19 part: 20
16	Literal
17	ExprTuple	35, 21
18	Operation	operator: 22 operands: 23
19	Operation	operator: 24 operands: 25
20	Variable
21	IndexedVar	variable: 26 index: 34
22	Literal
23	ExprTuple	28, 29
24	Literal
25	ExprTuple	30
26	Variable
27	ExprTuple	34
28	Variable
29	Operation	operator: 31 operand: 35
30	ExprRange	lambda_map: 33 start_index: 35 end_index: 34
31	Literal
32	ExprTuple	35
33	Lambda	parameter: 39 body: 36
34	Variable
35	Literal
36	IndexedVar	variable: 37 index: 39
37	Variable
38	ExprTuple	39
39	Variable