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 And, InSet, NotEquals
from proveit.numbers import Abs, Exp, LessEq, Mult, four, frac, one, two, zero
from proveit.physics.quantum.QPE import _diff_l_scaled_delta_floor, _full_domain, _rel_indexed_alpha

# build up the expression from sub-expressions
expr = Conditional(LessEq(Exp(Abs(_rel_indexed_alpha), two), frac(one, Mult(four, Exp(_diff_l_scaled_delta_floor, two)))), And(InSet(l, _full_domain), NotEquals(l, zero)))

# 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|\alpha_{b_{\textit{f}} \oplus l}\right|^{2} \leq \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~2^{t - 1}\} ,  l \neq 0\right..

stored_expr.style_options()

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions
0	Conditional	value: 1 condition: 2
1	Operation	operator: 3 operands: 4
2	Operation	operator: 5 operands: 6
3	Literal
4	ExprTuple	7, 8
5	Literal
6	ExprTuple	9, 10
7	Operation	operator: 56 operands: 11
8	Operation	operator: 12 operands: 13
9	Operation	operator: 14 operands: 15
10	Operation	operator: 16 operands: 17
11	ExprTuple	18, 62
12	Literal
13	ExprTuple	65, 19
14	Literal
15	ExprTuple	42, 20
16	Literal
17	ExprTuple	42, 21
18	Operation	operator: 22 operand: 27
19	Operation	operator: 49 operands: 24
20	Operation	operator: 25 operands: 26
21	Literal
22	Literal
23	ExprTuple	27
24	ExprTuple	28, 29
25	Literal
26	ExprTuple	30, 44
27	Operation	operator: 31 operand: 35
28	Literal
29	Operation	operator: 56 operands: 33
30	Operation	operator: 51 operands: 34
31	Literal
32	ExprTuple	35
33	ExprTuple	36, 62
34	ExprTuple	37, 65
35	Operation	operator: 38 operands: 39
36	Operation	operator: 51 operands: 40
37	Operation	operator: 60 operand: 44
38	Literal
39	ExprTuple	64, 42
40	ExprTuple	42, 43
41	ExprTuple	44
42	Variable
43	Operation	operator: 60 operand: 47
44	Operation	operator: 56 operands: 46
45	ExprTuple	47
46	ExprTuple	62, 48
47	Operation	operator: 49 operands: 50
48	Operation	operator: 51 operands: 52
49	Literal
50	ExprTuple	53, 54
51	Literal
52	ExprTuple	63, 55
53	Operation	operator: 56 operands: 57
54	Operation	operator: 58 operand: 64
55	Operation	operator: 60 operand: 65
56	Literal
57	ExprTuple	62, 63
58	Literal
59	ExprTuple	64
60	Literal
61	ExprTuple	65
62	Literal
63	Literal
64	Literal
65	Literal

Expression of type Conditional¶

from the theory of proveit.physics.quantum.QPE¶

Expression of type Conditional ¶

from the theory of proveit.physics.quantum.QPE ¶