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 ExprTuple, t
from proveit.linear_algebra import ScalarMult, VecAdd
from proveit.numbers import Add, Exp, Interval, Mult, Neg, e, frac, i, one, pi, sqrt, two, zero
from proveit.physics.quantum import ket0, ket1
from proveit.physics.quantum.QPE import _phase
from proveit.physics.quantum.circuits import MultiQubitElem, Output

# build up the expression from sub-expressions
sub_expr1 = Output(state = ScalarMult(frac(one, sqrt(two)), VecAdd(ket0, ScalarMult(Exp(e, Mult(two, pi, i, Exp(two, Neg(Add(Neg(t), one))), _phase)), ket1))), part = one)
expr = ExprTuple(MultiQubitElem(element = sub_expr1, targets = Interval(Add(zero, one), one)), MultiQubitElem(element = sub_expr1, targets = Interval(one, one)))

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 2^{-\left(-t + 1\right)} \cdot \varphi} \cdot \lvert 1 \rangle\right)\right)~\mbox{part}~1~\mbox{on}~\{0 + 1~\ldotp \ldotp~1\}} 
} \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 2^{-\left(-t + 1\right)} \cdot \varphi} \cdot \lvert 1 \rangle\right)\right)~\mbox{part}~1~\mbox{on}~\{1~\ldotp \ldotp~1\}} 
} \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	Operation	operator: 4 operands: 3
2	Operation	operator: 4 operands: 5
3	NamedExprs	element: 7 targets: 6
4	Literal
5	NamedExprs	element: 7 targets: 8
6	Operation	operator: 12 operands: 9
7	Operation	operator: 10 operands: 11
8	Operation	operator: 12 operands: 13
9	ExprTuple	14, 56
10	Literal
11	NamedExprs	state: 15 part: 56
12	Literal
13	ExprTuple	56, 56
14	Operation	operator: 53 operands: 16
15	Operation	operator: 28 operands: 17
16	ExprTuple	31, 56
17	ExprTuple	18, 19
18	Operation	operator: 34 operands: 20
19	Operation	operator: 21 operands: 22
20	ExprTuple	56, 23
21	Literal
22	ExprTuple	24, 25
23	Operation	operator: 47 operands: 26
24	Operation	operator: 37 operand: 31
25	Operation	operator: 28 operands: 29
26	ExprTuple	49, 30
27	ExprTuple	31
28	Literal
29	ExprTuple	32, 33
30	Operation	operator: 34 operands: 35
31	Literal
32	Operation	operator: 47 operands: 36
33	Operation	operator: 37 operand: 56
34	Literal
35	ExprTuple	56, 49
36	ExprTuple	39, 40
37	Literal
38	ExprTuple	56
39	Literal
40	Operation	operator: 41 operands: 42
41	Literal
42	ExprTuple	49, 43, 44, 45, 46
43	Literal
44	Literal
45	Operation	operator: 47 operands: 48
46	Literal
47	Literal
48	ExprTuple	49, 50
49	Literal
50	Operation	operator: 57 operand: 52
51	ExprTuple	52
52	Operation	operator: 53 operands: 54
53	Literal
54	ExprTuple	55, 56
55	Operation	operator: 57 operand: 59
56	Literal
57	Literal
58	ExprTuple	59
59	Variable