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(frac(one, Mult(four, 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 \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: 3 operands: 4
2	Operation	operator: 5 operands: 6
3	Literal
4	ExprTuple	49, 7
5	Literal
6	ExprTuple	25, 8
7	Operation	operator: 33 operands: 9
8	Operation	operator: 10 operands: 11
9	ExprTuple	12, 13
10	Literal
11	ExprTuple	14, 15
12	Literal
13	Operation	operator: 40 operands: 16
14	Operation	operator: 35 operands: 17
15	Operation	operator: 44 operand: 21
16	ExprTuple	19, 46
17	ExprTuple	20, 49
18	ExprTuple	21
19	Operation	operator: 35 operands: 22
20	Operation	operator: 44 operand: 27
21	Operation	operator: 35 operands: 24
22	ExprTuple	25, 26
23	ExprTuple	27
24	ExprTuple	28, 49
25	Variable
26	Operation	operator: 44 operand: 31
27	Operation	operator: 40 operands: 30
28	Variable
29	ExprTuple	31
30	ExprTuple	46, 32
31	Operation	operator: 33 operands: 34
32	Operation	operator: 35 operands: 36
33	Literal
34	ExprTuple	37, 38
35	Literal
36	ExprTuple	47, 39
37	Operation	operator: 40 operands: 41
38	Operation	operator: 42 operand: 48
39	Operation	operator: 44 operand: 49
40	Literal
41	ExprTuple	46, 47
42	Literal
43	ExprTuple	48
44	Literal
45	ExprTuple	49
46	Literal
47	Literal
48	Literal
49	Literal