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, _two_pow_t

# build up the expression from sub-expressions
sub_expr1 = subtract(one, Exp(e, Mult(two, pi, i, subtract(_delta_b_floor, frac(l, _two_pow_t)))))
expr = Equals(frac(subtract(one, Exp(e, Mult(two, pi, i, subtract(Mult(_delta_b_floor, _two_pow_t), l)))), sub_expr1), frac(subtract(one, Exp(e, Mult(two, pi, i, subtract(Mult(_two_pow_t, _delta_b_floor), l)))), 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{1 - \mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot \left(\left(\delta_{b_{\textit{f}}} \cdot 2^{t}\right) - l\right)}}{1 - \mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot \left(\delta_{b_{\textit{f}}} - \frac{l}{2^{t}}\right)}} = \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)}}

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: 56 operands: 5
4	Operation	operator: 56 operands: 6
5	ExprTuple	7, 9
6	ExprTuple	8, 9
7	Operation	operator: 40 operands: 10
8	Operation	operator: 40 operands: 11
9	Operation	operator: 40 operands: 12
10	ExprTuple	15, 13
11	ExprTuple	15, 14
12	ExprTuple	15, 16
13	Operation	operator: 50 operand: 20
14	Operation	operator: 50 operand: 21
15	Literal
16	Operation	operator: 50 operand: 22
17	ExprTuple	20
18	ExprTuple	21
19	ExprTuple	22
20	Operation	operator: 61 operands: 23
21	Operation	operator: 61 operands: 24
22	Operation	operator: 61 operands: 25
23	ExprTuple	28, 26
24	ExprTuple	28, 27
25	ExprTuple	28, 29
26	Operation	operator: 47 operands: 30
27	Operation	operator: 47 operands: 31
28	Literal
29	Operation	operator: 47 operands: 32
30	ExprTuple	63, 35, 36, 33
31	ExprTuple	63, 35, 36, 34
32	ExprTuple	63, 35, 36, 37
33	Operation	operator: 40 operands: 38
34	Operation	operator: 40 operands: 39
35	Literal
36	Literal
37	Operation	operator: 40 operands: 41
38	ExprTuple	42, 44
39	ExprTuple	43, 44
40	Literal
41	ExprTuple	52, 45
42	Operation	operator: 47 operands: 46
43	Operation	operator: 47 operands: 48
44	Operation	operator: 50 operand: 59
45	Operation	operator: 50 operand: 53
46	ExprTuple	52, 60
47	Literal
48	ExprTuple	60, 52
49	ExprTuple	59
50	Literal
51	ExprTuple	53
52	Operation	operator: 54 operand: 58
53	Operation	operator: 56 operands: 57
54	Literal
55	ExprTuple	58
56	Literal
57	ExprTuple	59, 60
58	Literal
59	Variable
60	Operation	operator: 61 operands: 62
61	Literal
62	ExprTuple	63, 64
63	Literal
64	Literal