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(l, two))
sub_expr4 = subtract(_two_pow__t_minus_one, one)
sub_expr5 = frac(one, Exp(_diff_l_scaled_delta_floor, two))
expr = LessEq(Mult(sub_expr2, Add(Sum(index_or_indices = sub_expr1, summand = sub_expr5, domain = _neg_domain), Sum(index_or_indices = sub_expr1, summand = sub_expr5, domain = _pos_domain))), Mult(sub_expr2, Add(Sum(index_or_indices = sub_expr1, summand = sub_expr3, domain = Interval(Add(e, one), sub_expr4)), Sum(index_or_indices = sub_expr1, summand = sub_expr3, domain = Interval(e, sub_expr4)))))

# 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(\frac{1}{4} \cdot \left(\left(\sum_{l = e + 1}^{2^{t - 1} - 1} \frac{1}{l^{2}}\right) + \left(\sum_{l = e}^{2^{t - 1} - 1} \frac{1}{l^{2}}\right)\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: 78 operands: 6
5	ExprTuple	8, 7
6	ExprTuple	8, 9
7	Operation	operator: 83 operands: 10
8	Operation	operator: 42 operands: 11
9	Operation	operator: 83 operands: 12
10	ExprTuple	13, 14
11	ExprTuple	95, 15
12	ExprTuple	16, 17
13	Operation	operator: 21 operand: 23
14	Operation	operator: 21 operand: 24
15	Literal
16	Operation	operator: 21 operand: 25
17	Operation	operator: 21 operand: 26
18	ExprTuple	23
19	ExprTuple	24
20	ExprTuple	25
21	Literal
22	ExprTuple	26
23	Lambda	parameter: 69 body: 27
24	Lambda	parameter: 69 body: 28
25	Lambda	parameter: 69 body: 29
26	Lambda	parameter: 69 body: 31
27	Conditional	value: 33 condition: 32
28	Conditional	value: 33 condition: 34
29	Conditional	value: 36 condition: 35
30	ExprTuple	69
31	Conditional	value: 36 condition: 37
32	Operation	operator: 44 operands: 38
33	Operation	operator: 42 operands: 39
34	Operation	operator: 44 operands: 40
35	Operation	operator: 44 operands: 41
36	Operation	operator: 42 operands: 43
37	Operation	operator: 44 operands: 45
38	ExprTuple	69, 46
39	ExprTuple	95, 47
40	ExprTuple	69, 48
41	ExprTuple	69, 49
42	Literal
43	ExprTuple	95, 50
44	Literal
45	ExprTuple	69, 51
46	Operation	operator: 57 operands: 52
47	Operation	operator: 85 operands: 53
48	Operation	operator: 57 operands: 54
49	Operation	operator: 57 operands: 55
50	Operation	operator: 85 operands: 56
51	Operation	operator: 57 operands: 58
52	ExprTuple	59, 60
53	ExprTuple	61, 90
54	ExprTuple	68, 74
55	ExprTuple	68, 62
56	ExprTuple	69, 90
57	Literal
58	ExprTuple	75, 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 ¶