Expression of type Equals

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 Variable, k
from proveit.logic import Equals
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 = Equals(_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(Variable("_a", latex_format = r"{_{-}a}"))))), 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())

\alpha_{b_{\textit{f}} \oplus l} = \left(\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}}} - {_{-}a}\right)})^{k}\right)\right)

stored_expr.style_options()

name	description	default	current value	related methods
operation	'infix' or 'function' style formatting	infix	infix
wrap_positions	position(s) at which wrapping is to occur; '2 n - 1' is after the nth operand, '2 n' is after the nth operation.	()	()	('with_wrapping_at', 'with_wrap_before_operator', 'with_wrap_after_operator', 'without_wrapping', 'wrap_positions')
justification	if any wrap positions are set, justify to the 'left', 'center', or 'right'	center	center	('with_justification',)
direction	Direction of the relation (normal or reversed)	normal	normal	('with_direction_reversed', 'is_reversed')

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Operation	operator: 1 operands: 2
1	Literal
2	ExprTuple	3, 4
3	Operation	operator: 5 operand: 8
4	Operation	operator: 35 operands: 7
5	Literal
6	ExprTuple	8
7	ExprTuple	9, 10
8	Operation	operator: 11 operands: 12
9	Operation	operator: 49 operands: 13
10	Operation	operator: 14 operand: 17
11	Literal
12	ExprTuple	56, 16
13	ExprTuple	48, 55
14	Literal
15	ExprTuple	17
16	Variable
17	Lambda	parameter: 26 body: 19
18	ExprTuple	26
19	Conditional	value: 20 condition: 21
20	Operation	operator: 58 operands: 22
21	Operation	operator: 23 operands: 24
22	ExprTuple	25, 26
23	Literal
24	ExprTuple	26, 27
25	Operation	operator: 58 operands: 28
26	Variable
27	Operation	operator: 29 operands: 30
28	ExprTuple	31, 32
29	Literal
30	ExprTuple	33, 34
31	Literal
32	Operation	operator: 35 operands: 36
33	Literal
34	Operation	operator: 42 operands: 37
35	Literal
36	ExprTuple	60, 38, 39, 40
37	ExprTuple	55, 41
38	Literal
39	Literal
40	Operation	operator: 42 operands: 43
41	Operation	operator: 53 operand: 48
42	Literal
43	ExprTuple	45, 46, 47
44	ExprTuple	48
45	Operation	operator: 49 operands: 50
46	Operation	operator: 51 operand: 56
47	Operation	operator: 53 operand: 57
48	Literal
49	Literal
50	ExprTuple	56, 55
51	Literal
52	ExprTuple	56
53	Literal
54	ExprTuple	57
55	Operation	operator: 58 operands: 59
56	Literal
57	Variable
58	Literal
59	ExprTuple	60, 61
60	Literal
61	Literal