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, Mult, Sum, four, frac, one, subtract, two
from proveit.physics.quantum.QPE import Pfail, _two_pow__t_minus_one

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

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(\left[P_{\rm fail}\right]\left(e\right), \left(\frac{1}{2} \cdot \left(\sum_{l = e + 1}^{2^{t - 1} - 1} \frac{1}{l^{2}}\right)\right) + \left(\frac{1}{4} \cdot \frac{1}{e^{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: 3 operand: 42
2	Operation	operator: 48 operands: 5
3	Literal
4	ExprTuple	42
5	ExprTuple	6, 7
6	Operation	operator: 9 operands: 8
7	Operation	operator: 9 operands: 10
8	ExprTuple	11, 12
9	Literal
10	ExprTuple	13, 14
11	Operation	operator: 28 operands: 15
12	Operation	operator: 16 operand: 20
13	Operation	operator: 28 operands: 18
14	Operation	operator: 28 operands: 19
15	ExprTuple	54, 46
16	Literal
17	ExprTuple	20
18	ExprTuple	54, 21
19	ExprTuple	54, 22
20	Lambda	parameter: 37 body: 24
21	Literal
22	Operation	operator: 44 operands: 25
23	ExprTuple	37
24	Conditional	value: 26 condition: 27
25	ExprTuple	42, 46
26	Operation	operator: 28 operands: 29
27	Operation	operator: 30 operands: 31
28	Literal
29	ExprTuple	54, 32
30	Literal
31	ExprTuple	37, 33
32	Operation	operator: 44 operands: 34
33	Operation	operator: 35 operands: 36
34	ExprTuple	37, 46
35	Literal
36	ExprTuple	38, 39
37	Variable
38	Operation	operator: 48 operands: 40
39	Operation	operator: 48 operands: 41
40	ExprTuple	42, 54
41	ExprTuple	43, 51
42	Variable
43	Operation	operator: 44 operands: 45
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