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, Variable, k
from proveit.numbers import Add, Exp, Mult, Neg, Sum, e, frac, i, one, pi, two
from proveit.physics.quantum.QPE import _b_floor, _delta_b_floor, _m_domain, _rel_indexed_alpha, _two_pow_t

# build up the expression from sub-expressions
expr = ExprTuple(_rel_indexed_alpha, Mult(frac(one, _two_pow_t), Sum(index_or_indices = [k], summand = Exp(Exp(e, Mult(two, pi, i, Add(frac(_b_floor, _two_pow_t), _delta_b_floor, Neg(Variable("_a", latex_format = r"{_{-}a}"))))), k), domain = _m_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(\alpha_{b_{\textit{f}} \oplus l}, \frac{1}{2^{t}} \cdot \left(\sum_{k = 0}^{2^{t} - 1} (\mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot \left(\frac{b_{\textit{f}}}{2^{t}} + \delta_{b_{\textit{f}}} - {_{-}a}\right)})^{k}\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: 33 operands: 5
3	Literal
4	ExprTuple	6
5	ExprTuple	7, 8
6	Operation	operator: 9 operands: 10
7	Operation	operator: 47 operands: 11
8	Operation	operator: 12 operand: 15
9	Literal
10	ExprTuple	54, 14
11	ExprTuple	46, 53
12	Literal
13	ExprTuple	15
14	Variable
15	Lambda	parameter: 24 body: 17
16	ExprTuple	24
17	Conditional	value: 18 condition: 19
18	Operation	operator: 56 operands: 20
19	Operation	operator: 21 operands: 22
20	ExprTuple	23, 24
21	Literal
22	ExprTuple	24, 25
23	Operation	operator: 56 operands: 26
24	Variable
25	Operation	operator: 27 operands: 28
26	ExprTuple	29, 30
27	Literal
28	ExprTuple	31, 32
29	Literal
30	Operation	operator: 33 operands: 34
31	Literal
32	Operation	operator: 40 operands: 35
33	Literal
34	ExprTuple	58, 36, 37, 38
35	ExprTuple	53, 39
36	Literal
37	Literal
38	Operation	operator: 40 operands: 41
39	Operation	operator: 51 operand: 46
40	Literal
41	ExprTuple	43, 44, 45
42	ExprTuple	46
43	Operation	operator: 47 operands: 48
44	Operation	operator: 49 operand: 54
45	Operation	operator: 51 operand: 55
46	Literal
47	Literal
48	ExprTuple	54, 53
49	Literal
50	ExprTuple	54
51	Literal
52	ExprTuple	55
53	Operation	operator: 56 operands: 57
54	Literal
55	Variable
56	Literal
57	ExprTuple	58, 59
58	Literal
59	Literal