Expression of type ExprTuple

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, ExprTuple, Variable, s, t
from proveit.numbers import Add, Interval, Mod, Mult, Round, one
from proveit.physics.quantum import NumKet, var_ket_u
from proveit.physics.quantum.QPE import phase, two_pow_t
from proveit.physics.quantum.circuits import MultiQubitElem, Output

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
expr = ExprTuple(ExprRange(sub_expr1, MultiQubitElem(element = Output(state = NumKet(Mod(Round(Mult(two_pow_t, phase)), two_pow_t), t), part = sub_expr1), targets = Interval(one, t)), one, t), ExprRange(sub_expr1, MultiQubitElem(element = Output(state = var_ket_u, part = sub_expr1), targets = Interval(Add(t, one), Add(t, s))), one, s))

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())

\left(\begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \qout{\lvert round\left(2^{t} \cdot \varphi\right) ~\textup{mod}~ 2^{t} \rangle_{t}~\mbox{part}~1~\mbox{on}~\{1~\ldotp \ldotp~t\}} 
} \end{array}, \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \qout{\lvert round\left(2^{t} \cdot \varphi\right) ~\textup{mod}~ 2^{t} \rangle_{t}~\mbox{part}~2~\mbox{on}~\{1~\ldotp \ldotp~t\}} 
} \end{array}, \ldots, \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \qout{\lvert round\left(2^{t} \cdot \varphi\right) ~\textup{mod}~ 2^{t} \rangle_{t}~\mbox{part}~t~\mbox{on}~\{1~\ldotp \ldotp~t\}} 
} \end{array},\begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \qout{\lvert u \rangle~\mbox{part}~1~\mbox{on}~\{t + 1~\ldotp \ldotp~t + s\}} 
} \end{array}, \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \qout{\lvert u \rangle~\mbox{part}~2~\mbox{on}~\{t + 1~\ldotp \ldotp~t + s\}} 
} \end{array}, \ldots, \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \qout{\lvert u \rangle~\mbox{part}~s~\mbox{on}~\{t + 1~\ldotp \ldotp~t + s\}} 
} \end{array}\right)

stored_expr.style_options()

name	description	default	current value	related methods
wrap_positions	position(s) at which wrapping is to occur; 'n' is after the nth comma.	()	()	('with_wrapping_at',)
justification	if any wrap positions are set, justify to the 'left', 'center', or 'right'	left	left	('with_justification',)

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	ExprTuple	1, 2
1	ExprRange	lambda_map: 3 start_index: 32 end_index: 47
2	ExprRange	lambda_map: 4 start_index: 32 end_index: 33
3	Lambda	parameter: 23 body: 5
4	Lambda	parameter: 23 body: 7
5	Operation	operator: 9 operands: 8
6	ExprTuple	23
7	Operation	operator: 9 operands: 10
8	NamedExprs	element: 11 targets: 12
9	Literal
10	NamedExprs	element: 13 targets: 14
11	Operation	operator: 17 operands: 15
12	Operation	operator: 19 operands: 16
13	Operation	operator: 17 operands: 18
14	Operation	operator: 19 operands: 20
15	NamedExprs	state: 21 part: 23
16	ExprTuple	32, 47
17	Literal
18	NamedExprs	state: 22 part: 23
19	Literal
20	ExprTuple	24, 25
21	Operation	operator: 26 operands: 27
22	Variable
23	Variable
24	Operation	operator: 29 operands: 28
25	Operation	operator: 29 operands: 30
26	Literal
27	ExprTuple	31, 47
28	ExprTuple	47, 32
29	Literal
30	ExprTuple	47, 33
31	Operation	operator: 34 operands: 35
32	Literal
33	Variable
34	Literal
35	ExprTuple	36, 42
36	Operation	operator: 37 operand: 39
37	Literal
38	ExprTuple	39
39	Operation	operator: 40 operands: 41
40	Literal
41	ExprTuple	42, 43
42	Operation	operator: 44 operands: 45
43	Variable
44	Literal
45	ExprTuple	46, 47
46	Literal
47	Variable