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 Add, Exp, Interval, Sum, four, 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(frac(one, four), Add(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(\frac{1}{4}, \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)

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