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, VecAdd, VecSum
from proveit.numbers import Add, Exp, Interval, Mult, e, i, one, pi, subtract, two, zero
from proveit.physics.quantum import NumKet
from proveit.physics.quantum.QPE import _phase, two_pow_t

# build up the expression from sub-expressions
sub_expr1 = [k]
sub_expr2 = ScalarMult(Exp(e, Mult(two, pi, i, _phase, k)), NumKet(k, Add(t, one)))
sub_expr3 = subtract(Mult(two, two_pow_t), one)
expr = ExprTuple(VecSum(index_or_indices = sub_expr1, summand = sub_expr2, domain = Interval(zero, sub_expr3)), VecAdd(VecSum(index_or_indices = sub_expr1, summand = sub_expr2, domain = Interval(zero, subtract(two_pow_t, one))), VecSum(index_or_indices = sub_expr1, summand = sub_expr2, domain = Interval(two_pow_t, 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(\sum_{k=0}^{2^{t} - 1} \left(\mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot \varphi \cdot k} \cdot \lvert k \rangle_{t + 1}\right)\right) + \left(\sum_{k=2^{t}}^{\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)\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: 11 operand: 6
2	Operation	operator: 4 operands: 5
3	ExprTuple	6
4	Literal
5	ExprTuple	7, 8
6	Lambda	parameter: 54 body: 9
7	Operation	operator: 11 operand: 14
8	Operation	operator: 11 operand: 15
9	Conditional	value: 22 condition: 13
10	ExprTuple	14
11	Literal
12	ExprTuple	15
13	Operation	operator: 28 operands: 16
14	Lambda	parameter: 54 body: 17
15	Lambda	parameter: 54 body: 19
16	ExprTuple	54, 20
17	Conditional	value: 22 condition: 21
18	ExprTuple	54
19	Conditional	value: 22 condition: 23
20	Operation	operator: 38 operands: 24
21	Operation	operator: 28 operands: 25
22	Operation	operator: 26 operands: 27
23	Operation	operator: 28 operands: 29
24	ExprTuple	40, 45
25	ExprTuple	54, 30
26	Literal
27	ExprTuple	31, 32
28	Literal
29	ExprTuple	54, 33
30	Operation	operator: 38 operands: 34
31	Operation	operator: 63 operands: 35
32	Operation	operator: 36 operands: 37
33	Operation	operator: 38 operands: 39
34	ExprTuple	40, 41
35	ExprTuple	42, 43
36	Literal
37	ExprTuple	54, 44
38	Literal
39	ExprTuple	61, 45
40	Literal
41	Operation	operator: 49 operands: 46
42	Literal
43	Operation	operator: 57 operands: 47
44	Operation	operator: 49 operands: 48
45	Operation	operator: 49 operands: 50
46	ExprTuple	61, 56
47	ExprTuple	65, 51, 52, 53, 54
48	ExprTuple	66, 62
49	Literal
50	ExprTuple	55, 56
51	Literal
52	Literal
53	Literal
54	Variable
55	Operation	operator: 57 operands: 58
56	Operation	operator: 59 operand: 62
57	Literal
58	ExprTuple	65, 61
59	Literal
60	ExprTuple	62
61	Operation	operator: 63 operands: 64
62	Literal
63	Literal
64	ExprTuple	65, 66
65	Literal
66	Variable