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 Exp, Mult, e, frac, i, one, pi, subtract, two
from proveit.physics.quantum.QPE import _delta_b_floor, _rel_indexed_alpha, _two_pow_t

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

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