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(frac(Abs(subtract(one, Exp(e, Mult(two, pi, i, _delta_b_round, _two_pow_t)))), Abs(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())

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