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, k, l
from proveit.numbers import Exp, Mult, Sum, e, frac, i, one, pi, subtract, two
from proveit.physics.quantum.QPE import _delta_b_floor, _m_domain, _two_pow_t

# build up the expression from sub-expressions
sub_expr1 = subtract(_delta_b_floor, frac(l, _two_pow_t))
sub_expr2 = Exp(e, Mult(two, pi, i, sub_expr1))
expr = ExprTuple(Sum(index_or_indices = [k], summand = Exp(sub_expr2, k), domain = _m_domain), frac(subtract(one, Exp(e, Mult(two, pi, i, sub_expr1, _two_pow_t))), subtract(one, sub_expr2)))

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_{k = 0}^{2^{t} - 1} (\mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot \left(\delta_{b_{\textit{f}}} - \frac{l}{2^{t}}\right)})^{k}, \frac{1 - \mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot \left(\delta_{b_{\textit{f}}} - \frac{l}{2^{t}}\right) \cdot 2^{t}}}{1 - \mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot \left(\delta_{b_{\textit{f}}} - \frac{l}{2^{t}}\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: 6
2	Operation	operator: 55 operands: 5
3	Literal
4	ExprTuple	6
5	ExprTuple	7, 8
6	Lambda	parameter: 22 body: 10
7	Operation	operator: 44 operands: 11
8	Operation	operator: 44 operands: 12
9	ExprTuple	22
10	Conditional	value: 13 condition: 14
11	ExprTuple	46, 15
12	ExprTuple	46, 16
13	Operation	operator: 59 operands: 17
14	Operation	operator: 18 operands: 19
15	Operation	operator: 51 operand: 24
16	Operation	operator: 51 operand: 25
17	ExprTuple	25, 22
18	Literal
19	ExprTuple	22, 23
20	ExprTuple	24
21	ExprTuple	25
22	Variable
23	Operation	operator: 26 operands: 27
24	Operation	operator: 59 operands: 28
25	Operation	operator: 59 operands: 29
26	Literal
27	ExprTuple	30, 31
28	ExprTuple	33, 32
29	ExprTuple	33, 34
30	Literal
31	Operation	operator: 44 operands: 35
32	Operation	operator: 37 operands: 36
33	Literal
34	Operation	operator: 37 operands: 38
35	ExprTuple	58, 39
36	ExprTuple	61, 40, 41, 42, 58
37	Literal
38	ExprTuple	61, 40, 41, 42
39	Operation	operator: 51 operand: 46
40	Literal
41	Literal
42	Operation	operator: 44 operands: 45
43	ExprTuple	46
44	Literal
45	ExprTuple	47, 48
46	Literal
47	Operation	operator: 49 operand: 53
48	Operation	operator: 51 operand: 54
49	Literal
50	ExprTuple	53
51	Literal
52	ExprTuple	54
53	Literal
54	Operation	operator: 55 operands: 56
55	Literal
56	ExprTuple	57, 58
57	Variable
58	Operation	operator: 59 operands: 60
59	Literal
60	ExprTuple	61, 62
61	Literal
62	Literal