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 = frac(one, _two_pow_t)
sub_expr2 = Abs(_delta_b_round)
expr = Equals(Abs(Mult(sub_expr1, 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)))))), Mult(sub_expr1, frac(Sin(Mult(_two_pow_t, pi, sub_expr2)), Sin(Mult(pi, sub_expr2)))))

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