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

# 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 = -2^{t - 1} + 1}^{-\left(e + 1\right)} \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: 73 operands: 5
4	Operation	operator: 73 operands: 6
5	ExprTuple	8, 7
6	ExprTuple	8, 9
7	Operation	operator: 83 operands: 10
8	Operation	operator: 40 operands: 11
9	Operation	operator: 83 operands: 12
10	ExprTuple	13, 14
11	ExprTuple	91, 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: 63 body: 27
24	Lambda	parameter: 63 body: 28
25	Lambda	parameter: 63 body: 29
26	Lambda	parameter: 63 body: 31
27	Conditional	value: 32 condition: 34
28	Conditional	value: 32 condition: 33
29	Conditional	value: 35 condition: 34
30	ExprTuple	63
31	Conditional	value: 35 condition: 36
32	Operation	operator: 40 operands: 37
33	Operation	operator: 42 operands: 38
34	Operation	operator: 42 operands: 39
35	Operation	operator: 40 operands: 41
36	Operation	operator: 42 operands: 43
37	ExprTuple	91, 44
38	ExprTuple	63, 45
39	ExprTuple	63, 46
40	Literal
41	ExprTuple	91, 47
42	Literal
43	ExprTuple	63, 48
44	Operation	operator: 79 operands: 49
45	Operation	operator: 53 operands: 50
46	Operation	operator: 53 operands: 51
47	Operation	operator: 79 operands: 52
48	Operation	operator: 53 operands: 54
49	ExprTuple	55, 85
50	ExprTuple	66, 71
51	ExprTuple	56, 57
52	ExprTuple	63, 85
53	Literal
54	ExprTuple	72, 58
55	Operation	operator: 83 operands: 59
56	Operation	operator: 83 operands: 60
57	Operation	operator: 89 operand: 66
58	Operation	operator: 83 operands: 62
59	ExprTuple	63, 64
60	ExprTuple	65, 91
61	ExprTuple	66
62	ExprTuple	71, 88
63	Variable
64	Operation	operator: 89 operand: 70
65	Operation	operator: 89 operand: 71
66	Operation	operator: 83 operands: 69
67	ExprTuple	70
68	ExprTuple	71
69	ExprTuple	72, 91
70	Operation	operator: 73 operands: 74
71	Operation	operator: 79 operands: 75
72	Variable
73	Literal
74	ExprTuple	76, 77
75	ExprTuple	85, 78
76	Operation	operator: 79 operands: 80
77	Operation	operator: 81 operand: 86
78	Operation	operator: 83 operands: 84
79	Literal
80	ExprTuple	85, 87
81	Literal
82	ExprTuple	86
83	Literal
84	ExprTuple	87, 88
85	Literal
86	Literal
87	Literal
88	Operation	operator: 89 operand: 91
89	Literal
90	ExprTuple	91
91	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 ¶