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, e, l
from proveit.numbers import Exp, Interval, Sum, frac, one, subtract, two
from proveit.physics.quantum.QPE import _neg_domain, _two_pow__t_minus_one

# build up the expression from sub-expressions
sub_expr1 = [l]
sub_expr2 = frac(one, Exp(l, two))
expr = ExprTuple(Sum(index_or_indices = sub_expr1, summand = sub_expr2, domain = _neg_domain), Sum(index_or_indices = sub_expr1, summand = sub_expr2, domain = Interval(e, subtract(_two_pow__t_minus_one, one))))

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 = -2^{t - 1} + 1}^{-\left(e + 1\right)} \frac{1}{l^{2}}, \sum_{l = e}^{2^{t - 1} - 1} \frac{1}{l^{2}}\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: 4 operand: 6
2	Operation	operator: 4 operand: 7
3	ExprTuple	6
4	Literal
5	ExprTuple	7
6	Lambda	parameter: 28 body: 8
7	Lambda	parameter: 28 body: 10
8	Conditional	value: 12 condition: 11
9	ExprTuple	28
10	Conditional	value: 12 condition: 13
11	Operation	operator: 17 operands: 14
12	Operation	operator: 15 operands: 16
13	Operation	operator: 17 operands: 18
14	ExprTuple	28, 19
15	Literal
16	ExprTuple	49, 20
17	Literal
18	ExprTuple	28, 21
19	Operation	operator: 24 operands: 22
20	Operation	operator: 39 operands: 23
21	Operation	operator: 24 operands: 25
22	ExprTuple	26, 27
23	ExprTuple	28, 41
24	Literal
25	ExprTuple	38, 29
26	Operation	operator: 43 operands: 30
27	Operation	operator: 47 operand: 34
28	Variable
29	Operation	operator: 43 operands: 32
30	ExprTuple	33, 49
31	ExprTuple	34
32	ExprTuple	37, 46
33	Operation	operator: 47 operand: 37
34	Operation	operator: 43 operands: 36
35	ExprTuple	37
36	ExprTuple	38, 49
37	Operation	operator: 39 operands: 40
38	Variable
39	Literal
40	ExprTuple	41, 42
41	Literal
42	Operation	operator: 43 operands: 44
43	Literal
44	ExprTuple	45, 46
45	Literal
46	Operation	operator: 47 operand: 49
47	Literal
48	ExprTuple	49
49	Literal