Expression of type ExprTuple

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, ExprTuple, IndexedVar, Variable, m, t
from proveit.linear_algebra import ScalarMult, VecAdd
from proveit.numbers import Add, Exp, Interval, Mult, e, frac, i, one, pi, sqrt, two
from proveit.physics.quantum import ket0, ket1, var_ket_u, varphi
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, Output(state = ScalarMult(frac(one, sqrt(two)), VecAdd(ket0, ScalarMult(Exp(e, Mult(two, pi, i, IndexedVar(varphi, sub_expr1))), ket1)))), one, t), ExprRange(sub_expr1, MultiQubitElem(element = Output(state = var_ket_u, part = sub_expr1), targets = Interval(Add(t, one), Add(t, m))), one, m))

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{\frac{1}{\sqrt{2}} \cdot \left(\lvert 0 \rangle + \left(\mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot \varphi_{1}} \cdot \lvert 1 \rangle\right)\right)} 
} \end{array}, \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \qout{\frac{1}{\sqrt{2}} \cdot \left(\lvert 0 \rangle + \left(\mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot \varphi_{2}} \cdot \lvert 1 \rangle\right)\right)} 
} \end{array}, \ldots, \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \qout{\frac{1}{\sqrt{2}} \cdot \left(\lvert 0 \rangle + \left(\mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot \varphi_{t}} \cdot \lvert 1 \rangle\right)\right)} 
} \end{array},\begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \qout{\lvert u \rangle~\mbox{part}~1~\mbox{on}~\{t + 1~\ldotp \ldotp~t + m\}} 
} \end{array}, \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \qout{\lvert u \rangle~\mbox{part}~2~\mbox{on}~\{t + 1~\ldotp \ldotp~t + m\}} 
} \end{array}, \ldots, \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \qout{\lvert u \rangle~\mbox{part}~m~\mbox{on}~\{t + 1~\ldotp \ldotp~t + m\}} 
} \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: 50 end_index: 32
2	ExprRange	lambda_map: 4 start_index: 50 end_index: 33
3	Lambda	parameter: 59 body: 5
4	Lambda	parameter: 59 body: 6
5	Operation	operator: 14 operands: 7
6	Operation	operator: 8 operands: 9
7	NamedExprs	state: 10
8	Literal
9	NamedExprs	element: 11 targets: 12
10	Operation	operator: 36 operands: 13
11	Operation	operator: 14 operands: 15
12	Operation	operator: 16 operands: 17
13	ExprTuple	18, 19
14	Literal
15	NamedExprs	state: 20 part: 59
16	Literal
17	ExprTuple	21, 22
18	Operation	operator: 42 operands: 23
19	Operation	operator: 24 operands: 25
20	Variable
21	Operation	operator: 27 operands: 26
22	Operation	operator: 27 operands: 28
23	ExprTuple	50, 29
24	Literal
25	ExprTuple	30, 31
26	ExprTuple	32, 50
27	Literal
28	ExprTuple	32, 33
29	Operation	operator: 44 operands: 34
30	Operation	operator: 46 operand: 39
31	Operation	operator: 36 operands: 37
32	Variable
33	Variable
34	ExprTuple	53, 38
35	ExprTuple	39
36	Literal
37	ExprTuple	40, 41
38	Operation	operator: 42 operands: 43
39	Literal
40	Operation	operator: 44 operands: 45
41	Operation	operator: 46 operand: 50
42	Literal
43	ExprTuple	50, 53
44	Literal
45	ExprTuple	48, 49
46	Literal
47	ExprTuple	50
48	Literal
49	Operation	operator: 51 operands: 52
50	Literal
51	Literal
52	ExprTuple	53, 54, 55, 56
53	Literal
54	Literal
55	Literal
56	IndexedVar	variable: 57 index: 59
57	Variable
58	ExprTuple	59
59	Variable