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

# build up the expression from sub-expressions
expr = ExprTuple(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(\frac{1}{2^{t}}, \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)

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