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(Mult(two, Sin(Mult(_two_pow_t, pi, sub_expr1))), Mult(two, Sin(Mult(pi, sub_expr1))))).with_wrapping_at(2)

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())

\begin{array}{c} \begin{array}{l} \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{2 \cdot \sin{\left(2^{t} \cdot \pi \cdot \left|\delta_{b_{\textit{r}}}\right|\right)}}{2 \cdot \sin{\left(\pi \cdot \left|\delta_{b_{\textit{r}}}\right|\right)}} \end{array} \end{array}

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.	()	(2)	('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: 41 operand: 16
9	Operation	operator: 41 operand: 17
10	Operation	operator: 47 operands: 14
11	Operation	operator: 47 operands: 15
12	ExprTuple	16
13	ExprTuple	17
14	ExprTuple	57, 18
15	ExprTuple	57, 19
16	Operation	operator: 21 operands: 20
17	Operation	operator: 21 operands: 22
18	Operation	operator: 24 operand: 29
19	Operation	operator: 24 operand: 30
20	ExprTuple	27, 26
21	Literal
22	ExprTuple	27, 28
23	ExprTuple	29
24	Literal
25	ExprTuple	30
26	Operation	operator: 32 operand: 36
27	Literal
28	Operation	operator: 32 operand: 37
29	Operation	operator: 47 operands: 34
30	Operation	operator: 47 operands: 35
31	ExprTuple	36
32	Literal
33	ExprTuple	37
34	ExprTuple	49, 50, 38
35	ExprTuple	50, 38
36	Operation	operator: 53 operands: 39
37	Operation	operator: 53 operands: 40
38	Operation	operator: 41 operand: 52
39	ExprTuple	44, 43
40	ExprTuple	44, 45
41	Literal
42	ExprTuple	52
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