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 ExprTuple, l
from proveit.numbers import Exp, Mult, Sum, four, frac, one, two
from proveit.physics.quantum.QPE import _diff_l_scaled_delta_floor, _pos_domain

# build up the expression from sub-expressions
sub_expr1 = [l]
sub_expr2 = Exp(_diff_l_scaled_delta_floor, two)
expr = ExprTuple(Sum(index_or_indices = sub_expr1, summand = frac(one, Mult(four, sub_expr2)), domain = _pos_domain), Mult(frac(one, four), Sum(index_or_indices = sub_expr1, summand = frac(one, sub_expr2), domain = _pos_domain)))

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())

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

stored_expr.style_options()

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',)

# display the expression information
stored_expr.expr_info()

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