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, l
from proveit.numbers import Add, Exp, Mult, Neg, Sum, e, frac, i, one, pi, two
from proveit.physics.quantum.QPE import _b_floor, _delta_b_floor, _m_domain, _rel_indexed_alpha, _two_pow_t

# build up the expression from sub-expressions
expr = ExprTuple(_rel_indexed_alpha, Mult(frac(one, _two_pow_t), Sum(index_or_indices = [k], summand = Exp(Exp(e, Mult(two, pi, i, Add(frac(_b_floor, _two_pow_t), _delta_b_floor, Neg(frac(Add(_b_floor, l), _two_pow_t))))), k), domain = _m_domain)))

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(\alpha_{b_{\textit{f}} \oplus l}, \frac{1}{2^{t}} \cdot \left(\sum_{k = 0}^{2^{t} - 1} (\mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot \left(\frac{b_{\textit{f}}}{2^{t}} + \delta_{b_{\textit{f}}} - \frac{b_{\textit{f}} + l}{2^{t}}\right)})^{k}\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: 3 operand: 6
2	Operation	operator: 31 operands: 5
3	Literal
4	ExprTuple	6
5	ExprTuple	7, 8
6	Operation	operator: 9 operands: 55
7	Operation	operator: 50 operands: 10
8	Operation	operator: 11 operand: 13
9	Literal
10	ExprTuple	43, 53
11	Literal
12	ExprTuple	13
13	Lambda	parameter: 22 body: 15
14	ExprTuple	22
15	Conditional	value: 16 condition: 17
16	Operation	operator: 56 operands: 18
17	Operation	operator: 19 operands: 20
18	ExprTuple	21, 22
19	Literal
20	ExprTuple	22, 23
21	Operation	operator: 56 operands: 24
22	Variable
23	Operation	operator: 25 operands: 26
24	ExprTuple	27, 28
25	Literal
26	ExprTuple	29, 30
27	Literal
28	Operation	operator: 31 operands: 32
29	Literal
30	Operation	operator: 54 operands: 33
31	Literal
32	ExprTuple	60, 34, 35, 36
33	ExprTuple	53, 37
34	Literal
35	Literal
36	Operation	operator: 54 operands: 38
37	Operation	operator: 47 operand: 43
38	ExprTuple	40, 41, 42
39	ExprTuple	43
40	Operation	operator: 50 operands: 44
41	Operation	operator: 45 operand: 58
42	Operation	operator: 47 operand: 49
43	Literal
44	ExprTuple	58, 53
45	Literal
46	ExprTuple	58
47	Literal
48	ExprTuple	49
49	Operation	operator: 50 operands: 51
50	Literal
51	ExprTuple	52, 53
52	Operation	operator: 54 operands: 55
53	Operation	operator: 56 operands: 57
54	Literal
55	ExprTuple	58, 59
56	Literal
57	ExprTuple	60, 61
58	Literal
59	Variable
60	Literal
61	Literal