Expression of type ExprTuple

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 ExprTuple
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 = ExprTuple(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, \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
wrap_positions	position(s) at which wrapping is to occur; 'n' is after the nth comma.	()	()	('with_wrapping_at',)
justification	if any wrap positions are set, justify to the 'left', 'center', or 'right'	left	left	('with_justification',)

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	ExprTuple	1, 2
1	Operation	operator: 25 operands: 3
2	Operation	operator: 25 operands: 4
3	ExprTuple	5, 7
4	ExprTuple	6, 7
5	Operation	operator: 25 operands: 8
6	Operation	operator: 25 operands: 9
7	Operation	operator: 43 operand: 13
8	ExprTuple	13, 11
9	ExprTuple	13, 12
10	ExprTuple	13
11	Operation	operator: 15 operand: 17
12	Operation	operator: 15 operand: 18
13	Literal
14	ExprTuple	17
15	Literal
16	ExprTuple	18
17	Operation	operator: 20 operands: 19
18	Operation	operator: 20 operands: 21
19	ExprTuple	40, 22
20	Literal
21	ExprTuple	40, 23
22	Operation	operator: 25 operands: 24
23	Operation	operator: 25 operands: 26
24	ExprTuple	40, 27
25	Literal
26	ExprTuple	40, 28
27	Operation	operator: 36 operands: 29
28	Operation	operator: 34 operands: 30
29	ExprTuple	45, 31
30	ExprTuple	32, 33
31	Operation	operator: 34 operands: 35
32	Operation	operator: 36 operands: 37
33	Operation	operator: 38 operands: 39
34	Literal
35	ExprTuple	40, 41
36	Literal
37	ExprTuple	45, 40
38	Literal
39	ExprTuple	41, 42
40	Literal
41	Literal
42	Operation	operator: 43 operand: 45
43	Literal
44	ExprTuple	45
45	Literal