Expression of type ExprTuple ¶

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 ExprRange, ExprTuple, IndexedVar, Variable, a, c, l
from proveit.logic import Equals, Forall, InSet
from proveit.numbers import Complex, Exp, Mult, Sum, frac, one, two, zero
from proveit.physics.quantum.QPE import _diff_l_scaled_delta_floor, _neg_domain

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
sub_expr2 = [l]
sub_expr3 = IndexedVar(a, one)
sub_expr4 = ExprRange(sub_expr1, IndexedVar(c, sub_expr1), one, zero)
sub_expr5 = frac(one, Exp(_diff_l_scaled_delta_floor, two))
expr = ExprTuple(Forall(instance_param_or_params = sub_expr2, instance_expr = InSet(sub_expr5, Complex), domain = _neg_domain), Forall(instance_param_or_params = [sub_expr3, sub_expr4], instance_expr = Equals(Mult(sub_expr3, Sum(index_or_indices = sub_expr2, summand = sub_expr5, domain = _neg_domain), sub_expr4), Sum(index_or_indices = sub_expr2, summand = Mult(sub_expr3, sub_expr5, sub_expr4), domain = _neg_domain)).with_wrapping_at(2), domain = Complex).with_wrapping())

# 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(\forall_{l \in \{-2^{t - 1} + 1~\ldotp \ldotp~-\left(e + 1\right)\}}~\left(\frac{1}{\left(l - \left(2^{t} \cdot \delta_{b_{\textit{f}}}\right)\right)^{2}} \in \mathbb{C}\right), \begin{array}{l}\forall_{a_{1}, c_{1}, c_{2}, \ldots, c_{0} \in \mathbb{C}}~\\
\left(\begin{array}{c} \begin{array}{l} \left(a_{1} \cdot \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)\cdot c_{1} \cdot  c_{2} \cdot  \ldots \cdot  c_{0}\right) =  \\ \left(\sum_{l = -2^{t - 1} + 1}^{-\left(e + 1\right)} \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}\right)\right) \end{array} \end{array}\right)\end{array}\right)

stored_expr.style_options()

# display the expression information
stored_expr.expr_info()

name	description	default	current value	related methods
wrap_positions	position(s) at which wrapping is to occur; 'n' is after the nth comma.	()	()	('with_wrapping_at',)
justification	if any wrap positions are set, justify to the 'left', 'center', or 'right'	left	left	('with_justification',)

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

Expression of type ExprTuple¶

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

Expression of type ExprTuple ¶

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