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.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_round, _two_pow_t
from proveit.trigonometry import Sin

# build up the expression from sub-expressions
sub_expr1 = Abs(_delta_b_round)
expr = Equals(Abs(frac(subtract(one, Exp(e, Mult(two, pi, i, _delta_b_round, _two_pow_t))), subtract(one, Exp(e, Mult(two, pi, i, _delta_b_round))))), frac(Sin(Mult(_two_pow_t, pi, sub_expr1)), Sin(Mult(pi, sub_expr1))))

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