Expression of type Conditional

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 Conditional, l
from proveit.logic import InSet
from proveit.numbers import Exp, Mult, four, frac, one, two
from proveit.physics.quantum.QPE import _diff_l_scaled_delta_floor, _neg_domain

# build up the expression from sub-expressions
expr = Conditional(Mult(frac(one, four), frac(one, Exp(_diff_l_scaled_delta_floor, two))), InSet(l, _neg_domain))

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}{4} \cdot \frac{1}{\left(l - \left(2^{t} \cdot \delta_{b_{\textit{f}}}\right)\right)^{2}} \textrm{ if } l \in \{-2^{t - 1} + 1~\ldotp \ldotp~-\left(e + 1\right)\}\right..

stored_expr.style_options()

name	description	default	current value	related methods
condition_delimiter	'comma' or 'and'	comma	comma	('with_comma_delimiter', 'with_conjunction_delimiter')

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Conditional	value: 1 condition: 2
1	Operation	operator: 35 operands: 3
2	Operation	operator: 4 operands: 5
3	ExprTuple	6, 7
4	Literal
5	ExprTuple	27, 8
6	Operation	operator: 10 operands: 9
7	Operation	operator: 10 operands: 11
8	Operation	operator: 12 operands: 13
9	ExprTuple	51, 14
10	Literal
11	ExprTuple	51, 15
12	Literal
13	ExprTuple	16, 17
14	Literal
15	Operation	operator: 42 operands: 18
16	Operation	operator: 37 operands: 19
17	Operation	operator: 46 operand: 23
18	ExprTuple	21, 48
19	ExprTuple	22, 51
20	ExprTuple	23
21	Operation	operator: 37 operands: 24
22	Operation	operator: 46 operand: 29
23	Operation	operator: 37 operands: 26
24	ExprTuple	27, 28
25	ExprTuple	29
26	ExprTuple	30, 51
27	Variable
28	Operation	operator: 46 operand: 33
29	Operation	operator: 42 operands: 32
30	Variable
31	ExprTuple	33
32	ExprTuple	48, 34
33	Operation	operator: 35 operands: 36
34	Operation	operator: 37 operands: 38
35	Literal
36	ExprTuple	39, 40
37	Literal
38	ExprTuple	49, 41
39	Operation	operator: 42 operands: 43
40	Operation	operator: 44 operand: 50
41	Operation	operator: 46 operand: 51
42	Literal
43	ExprTuple	48, 49
44	Literal
45	ExprTuple	50
46	Literal
47	ExprTuple	51
48	Literal
49	Literal
50	Literal
51	Literal