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 l
from proveit.logic import Equals
from proveit.numbers import Abs, Exp, Mult, e, frac, i, one, pi, subtract, two
from proveit.physics.quantum.QPE import _delta_b_floor, _rel_indexed_alpha, _two_pow_t
from proveit.trigonometry import Sin

# build up the expression from sub-expressions
expr = Equals(Abs(_rel_indexed_alpha), Mult(frac(one, _two_pow_t), frac(Abs(subtract(one, Exp(e, Mult(two, pi, i, subtract(Mult(_two_pow_t, _delta_b_floor), l))))), Mult(two, Sin(Mult(pi, Abs(subtract(_delta_b_floor, frac(l, _two_pow_t)))))))))

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}\right| = \left(\frac{1}{2^{t}} \cdot \frac{\left|1 - \mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot \left(\left(2^{t} \cdot \delta_{b_{\textit{f}}}\right) - l\right)}\right|}{2 \cdot \sin{\left(\pi \cdot \left|\delta_{b_{\textit{f}}} - \frac{l}{2^{t}}\right|\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: 34 operand: 7
4	Operation	operator: 51 operands: 6
5	ExprTuple	7
6	ExprTuple	8, 9
7	Operation	operator: 10 operand: 14
8	Operation	operator: 55 operands: 12
9	Operation	operator: 55 operands: 13
10	Literal
11	ExprTuple	14
12	ExprTuple	26, 59
13	ExprTuple	15, 16
14	Operation	operator: 17 operands: 18
15	Operation	operator: 34 operand: 21
16	Operation	operator: 51 operands: 20
17	Literal
18	ExprTuple	64, 58
19	ExprTuple	21
20	ExprTuple	65, 22
21	Operation	operator: 45 operands: 23
22	Operation	operator: 24 operand: 28
23	ExprTuple	26, 27
24	Literal
25	ExprTuple	28
26	Literal
27	Operation	operator: 53 operand: 31
28	Operation	operator: 51 operands: 30
29	ExprTuple	31
30	ExprTuple	41, 32
31	Operation	operator: 62 operands: 33
32	Operation	operator: 34 operand: 38
33	ExprTuple	36, 37
34	Literal
35	ExprTuple	38
36	Literal
37	Operation	operator: 51 operands: 39
38	Operation	operator: 45 operands: 40
39	ExprTuple	65, 41, 42, 43
40	ExprTuple	57, 44
41	Literal
42	Literal
43	Operation	operator: 45 operands: 46
44	Operation	operator: 53 operand: 50
45	Literal
46	ExprTuple	48, 49
47	ExprTuple	50
48	Operation	operator: 51 operands: 52
49	Operation	operator: 53 operand: 58
50	Operation	operator: 55 operands: 56
51	Literal
52	ExprTuple	59, 57
53	Literal
54	ExprTuple	58
55	Literal
56	ExprTuple	58, 59
57	Operation	operator: 60 operand: 64
58	Variable
59	Operation	operator: 62 operands: 63
60	Literal
61	ExprTuple	64
62	Literal
63	ExprTuple	65, 66
64	Literal
65	Literal
66	Literal