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 Add, Ceil, Exp, Log, Mult, Neg, frac, one, subtract, two
from proveit.physics.quantum.QPE import _eps, _n

# build up the expression from sub-expressions
expr = Equals(subtract(Add(_n, Ceil(Log(two, Add(two, frac(one, Mult(two, _eps)))))), _n), subtract(Add(_n, Ceil(Log(two, Add(two, Mult(frac(one, two), Exp(_eps, Neg(one))))))), _n))

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(\left(n + \left\lceil \textrm{log}_2\left(2 + \frac{1}{2 \cdot \epsilon}\right)\right\rceil\right) - n\right) = \left(\left(n + \left\lceil \textrm{log}_2\left(2 + \left(\frac{1}{2} \cdot \epsilon^{-1}\right)\right)\right\rceil\right) - n\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: 27 operands: 5
4	Operation	operator: 27 operands: 6
5	ExprTuple	7, 9
6	ExprTuple	8, 9
7	Operation	operator: 27 operands: 10
8	Operation	operator: 27 operands: 11
9	Operation	operator: 45 operand: 15
10	ExprTuple	15, 13
11	ExprTuple	15, 14
12	ExprTuple	15
13	Operation	operator: 17 operand: 19
14	Operation	operator: 17 operand: 20
15	Literal
16	ExprTuple	19
17	Literal
18	ExprTuple	20
19	Operation	operator: 22 operands: 21
20	Operation	operator: 22 operands: 23
21	ExprTuple	42, 24
22	Literal
23	ExprTuple	42, 25
24	Operation	operator: 27 operands: 26
25	Operation	operator: 27 operands: 28
26	ExprTuple	42, 29
27	Literal
28	ExprTuple	42, 30
29	Operation	operator: 38 operands: 31
30	Operation	operator: 36 operands: 32
31	ExprTuple	47, 33
32	ExprTuple	34, 35
33	Operation	operator: 36 operands: 37
34	Operation	operator: 38 operands: 39
35	Operation	operator: 40 operands: 41
36	Literal
37	ExprTuple	42, 43
38	Literal
39	ExprTuple	47, 42
40	Literal
41	ExprTuple	43, 44
42	Literal
43	Literal
44	Operation	operator: 45 operand: 47
45	Literal
46	ExprTuple	47
47	Literal