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, ExprRange, IndexedVar, Variable, a, c, l
from proveit.logic import InSet
from proveit.numbers import Exp, Mult, frac, one, two, zero
from proveit.physics.quantum.QPE import _diff_l_scaled_delta_floor, _pos_domain

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
expr = Conditional(Mult(IndexedVar(a, one), frac(one, Exp(_diff_l_scaled_delta_floor, two)), ExprRange(sub_expr1, IndexedVar(c, sub_expr1), one, zero)), InSet(l, _pos_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\{a_{1} \cdot \frac{1}{\left(l - \left(2^{t} \cdot \delta_{b_{\textit{f}}}\right)\right)^{2}}\cdot c_{1} \cdot  c_{2} \cdot  \ldots \cdot  c_{0} \textrm{ if } l \in \{e + 1~\ldotp \ldotp~2^{t - 1}\}\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: 41 operands: 3
2	Operation	operator: 4 operands: 5
3	ExprTuple	6, 7, 8
4	Literal
5	ExprTuple	33, 9
6	IndexedVar	variable: 10 index: 40
7	Operation	operator: 11 operands: 12
8	ExprRange	lambda_map: 13 start_index: 40 end_index: 14
9	Operation	operator: 15 operands: 16
10	Variable
11	Literal
12	ExprTuple	40, 17
13	Lambda	parameter: 27 body: 18
14	Literal
15	Literal
16	ExprTuple	19, 20
17	Operation	operator: 45 operands: 21
18	IndexedVar	variable: 22 index: 27
19	Operation	operator: 31 operands: 24
20	Operation	operator: 45 operands: 25
21	ExprTuple	26, 49
22	Variable
23	ExprTuple	27
24	ExprTuple	28, 40
25	ExprTuple	49, 29
26	Operation	operator: 31 operands: 30
27	Variable
28	Variable
29	Operation	operator: 31 operands: 32
30	ExprTuple	33, 34
31	Literal
32	ExprTuple	50, 35
33	Variable
34	Operation	operator: 37 operand: 39
35	Operation	operator: 37 operand: 40
36	ExprTuple	39
37	Literal
38	ExprTuple	40
39	Operation	operator: 41 operands: 42
40	Literal
41	Literal
42	ExprTuple	43, 44
43	Operation	operator: 45 operands: 46
44	Operation	operator: 47 operand: 51
45	Literal
46	ExprTuple	49, 50
47	Literal
48	ExprTuple	51
49	Literal
50	Literal
51	Literal