Expression of type LessEq ¶

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 e, l
from proveit.numbers import Add, Exp, Interval, LessEq, Mult, Sum, four, frac, one, subtract, two
from proveit.physics.quantum.QPE import _diff_l_scaled_delta_floor, _neg_domain, _pos_domain, _two_pow__t_minus_one

# build up the expression from sub-expressions
sub_expr1 = [l]
sub_expr2 = frac(one, four)
sub_expr3 = frac(one, Exp(_diff_l_scaled_delta_floor, two))
expr = LessEq(Mult(sub_expr2, Add(Sum(index_or_indices = sub_expr1, summand = sub_expr3, domain = _neg_domain), Sum(index_or_indices = sub_expr1, summand = sub_expr3, domain = _pos_domain))), Add(Mult(frac(one, two), Sum(index_or_indices = sub_expr1, summand = frac(one, Exp(l, two)), domain = Interval(Add(e, one), subtract(_two_pow__t_minus_one, one)))), Mult(sub_expr2, frac(one, Exp(e, two)))))

# 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(\left(\sum_{l = -2^{t - 1} + 1}^{-\left(e + 1\right)} \frac{1}{\left(l - \left(2^{t} \cdot \delta_{b_{\textit{f}}}\right)\right)^{2}}\right) + \left(\sum_{l = e + 1}^{2^{t - 1}} \frac{1}{\left(l - \left(2^{t} \cdot \delta_{b_{\textit{f}}}\right)\right)^{2}}\right)\right)\right) \leq \left(\left(\frac{1}{2} \cdot \left(\sum_{l = e + 1}^{2^{t - 1} - 1} \frac{1}{l^{2}}\right)\right) + \left(\frac{1}{4} \cdot \frac{1}{e^{2}}\right)\right)

stored_expr.style_options()

# display the expression information
stored_expr.expr_info()

name	description	default	current value	related methods
operation	'infix' or 'function' style formatting	infix	infix
wrap_positions	position(s) at which wrapping is to occur; '2 n - 1' is after the nth operand, '2 n' is after the nth operation.	()	()	('with_wrapping_at', 'with_wrap_before_operator', 'with_wrap_after_operator', 'without_wrapping', 'wrap_positions')
justification	if any wrap positions are set, justify to the 'left', 'center', or 'right'	center	center	('with_justification',)
direction	Direction of the relation (normal or reversed)	normal	normal	('with_direction_reversed', 'is_reversed')

	core type	sub-expressions
0	Operation	operator: 1 operands: 2
1	Literal
2	ExprTuple	3, 4
3	Operation	operator: 78 operands: 5
4	Operation	operator: 83 operands: 6
5	ExprTuple	17, 7
6	ExprTuple	8, 9
7	Operation	operator: 83 operands: 10
8	Operation	operator: 78 operands: 11
9	Operation	operator: 78 operands: 12
10	ExprTuple	13, 14
11	ExprTuple	15, 16
12	ExprTuple	17, 18
13	Operation	operator: 22 operand: 26
14	Operation	operator: 22 operand: 27
15	Operation	operator: 44 operands: 21
16	Operation	operator: 22 operand: 28
17	Operation	operator: 44 operands: 24
18	Operation	operator: 44 operands: 25
19	ExprTuple	26
20	ExprTuple	27
21	ExprTuple	95, 90
22	Literal
23	ExprTuple	28
24	ExprTuple	95, 29
25	ExprTuple	95, 30
26	Lambda	parameter: 69 body: 31
27	Lambda	parameter: 69 body: 32
28	Lambda	parameter: 69 body: 34
29	Literal
30	Operation	operator: 85 operands: 35
31	Conditional	value: 37 condition: 36
32	Conditional	value: 37 condition: 38
33	ExprTuple	69
34	Conditional	value: 39 condition: 40
35	ExprTuple	75, 90
36	Operation	operator: 46 operands: 41
37	Operation	operator: 44 operands: 42
38	Operation	operator: 46 operands: 43
39	Operation	operator: 44 operands: 45
40	Operation	operator: 46 operands: 47
41	ExprTuple	69, 48
42	ExprTuple	95, 49
43	ExprTuple	69, 50
44	Literal
45	ExprTuple	95, 51
46	Literal
47	ExprTuple	69, 52
48	Operation	operator: 57 operands: 53
49	Operation	operator: 85 operands: 54
50	Operation	operator: 57 operands: 55
51	Operation	operator: 85 operands: 56
52	Operation	operator: 57 operands: 58
53	ExprTuple	59, 60
54	ExprTuple	61, 90
55	ExprTuple	68, 74
56	ExprTuple	69, 90
57	Literal
58	ExprTuple	68, 62
59	Operation	operator: 83 operands: 63
60	Operation	operator: 93 operand: 68
61	Operation	operator: 83 operands: 65
62	Operation	operator: 83 operands: 66
63	ExprTuple	67, 95
64	ExprTuple	68
65	ExprTuple	69, 70
66	ExprTuple	74, 89
67	Operation	operator: 93 operand: 74
68	Operation	operator: 83 operands: 72
69	Variable
70	Operation	operator: 93 operand: 76
71	ExprTuple	74
72	ExprTuple	75, 95
73	ExprTuple	76
74	Operation	operator: 85 operands: 77
75	Variable
76	Operation	operator: 78 operands: 79
77	ExprTuple	90, 80
78	Literal
79	ExprTuple	81, 82
80	Operation	operator: 83 operands: 84
81	Operation	operator: 85 operands: 86
82	Operation	operator: 87 operand: 92
83	Literal
84	ExprTuple	91, 89
85	Literal
86	ExprTuple	90, 91
87	Literal
88	ExprTuple	92
89	Operation	operator: 93 operand: 95
90	Literal
91	Literal
92	Literal
93	Literal
94	ExprTuple	95
95	Literal

Expression of type LessEq¶

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

Expression of type LessEq ¶

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