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, l
from proveit.numbers import Add, Exp, Mult, Sum, e, frac, i, one, pi, subtract, two
from proveit.physics.quantum.QPE import SubIndexed, _alpha, _b_floor, _m_domain, _phase, _two_pow_t

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