Expression of type Equals

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, IndexedVar, Variable, a, c, l
from proveit.logic import Equals
from proveit.numbers import 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 = 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)

expr:

# 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())

\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}

stored_expr.style_options()

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.	()	(2)	('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')

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Operation	operator: 1 operands: 2
1	Literal
2	ExprTuple	3, 4
3	Operation	operator: 54 operands: 5
4	Operation	operator: 9 operand: 8
5	ExprTuple	18, 7, 20
6	ExprTuple	8
7	Operation	operator: 9 operand: 12
8	Lambda	parameter: 45 body: 11
9	Literal
10	ExprTuple	12
11	Conditional	value: 13 condition: 17
12	Lambda	parameter: 45 body: 15
13	Operation	operator: 54 operands: 16
14	ExprTuple	45
15	Conditional	value: 19 condition: 17
16	ExprTuple	18, 19, 20
17	Operation	operator: 21 operands: 22
18	IndexedVar	variable: 23 index: 71
19	Operation	operator: 24 operands: 25
20	ExprRange	lambda_map: 26 start_index: 71 end_index: 27
21	Literal
22	ExprTuple	45, 28
23	Variable
24	Literal
25	ExprTuple	71, 29
26	Lambda	parameter: 39 body: 30
27	Literal
28	Operation	operator: 31 operands: 32
29	Operation	operator: 61 operands: 33
30	IndexedVar	variable: 34 index: 39
31	Literal
32	ExprTuple	36, 37
33	ExprTuple	38, 66
34	Variable
35	ExprTuple	39
36	Operation	operator: 59 operands: 40
37	Operation	operator: 69 operand: 44
38	Operation	operator: 59 operands: 42
39	Variable
40	ExprTuple	43, 71
41	ExprTuple	44
42	ExprTuple	45, 46
43	Operation	operator: 69 operand: 50
44	Operation	operator: 59 operands: 48
45	Variable
46	Operation	operator: 69 operand: 52
47	ExprTuple	50
48	ExprTuple	51, 71
49	ExprTuple	52
50	Operation	operator: 61 operands: 53
51	Variable
52	Operation	operator: 54 operands: 55
53	ExprTuple	66, 56
54	Literal
55	ExprTuple	57, 58
56	Operation	operator: 59 operands: 60
57	Operation	operator: 61 operands: 62
58	Operation	operator: 63 operand: 68
59	Literal
60	ExprTuple	67, 65
61	Literal
62	ExprTuple	66, 67
63	Literal
64	ExprTuple	68
65	Operation	operator: 69 operand: 71
66	Literal
67	Literal
68	Literal
69	Literal
70	ExprTuple	71
71	Literal