Expression of type ExprRange

from the theory of proveit.physics.quantum.QPE

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, U, Variable, s, t
from proveit.numbers import Add, Interval, one
from proveit.physics.quantum.QPE import QPE
from proveit.physics.quantum.circuits import Gate, MultiQubitElem

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
sub_expr2 = Add(t, s)
expr = ExprRange(sub_expr1, MultiQubitElem(element = Gate(operation = QPE(U, t), part = sub_expr1), targets = Interval(one, sub_expr2)), Add(t, one), sub_expr2)

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}{c} \Qcircuit@C=1em @R=.7em{
& & \gate{\textrm{QPE}\left(U, t\right)~\mbox{part}~t + 1~\mbox{on}~\{1~\ldotp \ldotp~t + s\}} & \qw 
} \end{array}, \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \gate{\textrm{QPE}\left(U, t\right)~\mbox{part}~t + 2~\mbox{on}~\{1~\ldotp \ldotp~t + s\}} & \qw 
} \end{array}, \ldots, \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \gate{\textrm{QPE}\left(U, t\right)~\mbox{part}~t + s~\mbox{on}~\{1~\ldotp \ldotp~t + s\}} & \qw 
} \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.	()	()	('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: 17
1	Lambda	parameter: 15 body: 4
2	Operation	operator: 20 operands: 5
3	ExprTuple	15
4	Operation	operator: 6 operands: 7
5	ExprTuple	23, 16
6	Literal
7	NamedExprs	element: 8 targets: 9
8	Operation	operator: 10 operands: 11
9	Operation	operator: 12 operands: 13
10	Literal
11	NamedExprs	operation: 14 part: 15
12	Literal
13	ExprTuple	16, 17
14	Operation	operator: 18 operands: 19
15	Variable
16	Literal
17	Operation	operator: 20 operands: 21
18	Literal
19	ExprTuple	22, 23
20	Literal
21	ExprTuple	23, 24
22	Variable
23	Variable
24	Variable