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, k, t
from proveit.linear_algebra import ScalarMult, TensorProd, VecAdd, VecSum
from proveit.numbers import Add, Exp, Interval, Mult, e, i, one, pi, subtract, two, zero
from proveit.physics.quantum import NumKet, ket0, ket1
from proveit.physics.quantum.QPE import _phase, two_pow_t

# build up the expression from sub-expressions
sub_expr1 = [k]
sub_expr2 = Exp(e, Mult(two, pi, i, _phase, k))
sub_expr3 = VecSum(index_or_indices = sub_expr1, summand = ScalarMult(sub_expr2, NumKet(k, t)), domain = Interval(zero, subtract(two_pow_t, one)))
expr = ExprTuple(VecSum(index_or_indices = sub_expr1, summand = ScalarMult(sub_expr2, NumKet(k, Add(t, one))), domain = Interval(zero, subtract(Mult(two, two_pow_t), one))), VecAdd(TensorProd(ket0, sub_expr3), ScalarMult(Exp(e, Mult(two, pi, i, _phase, two_pow_t)), TensorProd(ket1, sub_expr3))))

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(\sum_{k=0}^{\left(2 \cdot 2^{t}\right) - 1} \left(\mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot \varphi \cdot k} \cdot \lvert k \rangle_{t + 1}\right), \left(\lvert 0 \rangle {\otimes} \left(\sum_{k=0}^{2^{t} - 1} \left(\mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot \varphi \cdot k} \cdot \lvert k \rangle_{t}\right)\right)\right) + \left(\mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot \varphi \cdot 2^{t}} \cdot \left(\lvert 1 \rangle {\otimes} \left(\sum_{k=0}^{2^{t} - 1} \left(\mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot \varphi \cdot k} \cdot \lvert k \rangle_{t}\right)\right)\right)\right)\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: 32 operand: 6
2	Operation	operator: 4 operands: 5
3	ExprTuple	6
4	Literal
5	ExprTuple	7, 8
6	Lambda	parameter: 68 body: 9
7	Operation	operator: 21 operands: 10
8	Operation	operator: 45 operands: 11
9	Conditional	value: 12 condition: 13
10	ExprTuple	14, 27
11	ExprTuple	15, 16
12	Operation	operator: 45 operands: 17
13	Operation	operator: 47 operands: 18
14	Operation	operator: 31 operand: 59
15	Operation	operator: 71 operands: 20
16	Operation	operator: 21 operands: 22
17	ExprTuple	49, 23
18	ExprTuple	68, 24
19	ExprTuple	59
20	ExprTuple	57, 25
21	Literal
22	ExprTuple	26, 27
23	Operation	operator: 53 operands: 28
24	Operation	operator: 55 operands: 29
25	Operation	operator: 61 operands: 30
26	Operation	operator: 31 operand: 77
27	Operation	operator: 32 operand: 36
28	ExprTuple	68, 34
29	ExprTuple	59, 35
30	ExprTuple	75, 65, 66, 67, 69
31	Literal
32	Literal
33	ExprTuple	36
34	Operation	operator: 63 operands: 37
35	Operation	operator: 63 operands: 38
36	Lambda	parameter: 68 body: 40
37	ExprTuple	76, 77
38	ExprTuple	41, 70
39	ExprTuple	68
40	Conditional	value: 42 condition: 43
41	Operation	operator: 61 operands: 44
42	Operation	operator: 45 operands: 46
43	Operation	operator: 47 operands: 48
44	ExprTuple	75, 69
45	Literal
46	ExprTuple	49, 50
47	Literal
48	ExprTuple	68, 51
49	Operation	operator: 71 operands: 52
50	Operation	operator: 53 operands: 54
51	Operation	operator: 55 operands: 56
52	ExprTuple	57, 58
53	Literal
54	ExprTuple	68, 76
55	Literal
56	ExprTuple	59, 60
57	Literal
58	Operation	operator: 61 operands: 62
59	Literal
60	Operation	operator: 63 operands: 64
61	Literal
62	ExprTuple	75, 65, 66, 67, 68
63	Literal
64	ExprTuple	69, 70
65	Literal
66	Literal
67	Literal
68	Variable
69	Operation	operator: 71 operands: 72
70	Operation	operator: 73 operand: 77
71	Literal
72	ExprTuple	75, 76
73	Literal
74	ExprTuple	77
75	Literal
76	Variable
77	Literal