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

# build up the expression from sub-expressions
expr = ExprTuple(_rel_indexed_alpha, Mult(frac(one, _two_pow_t), frac(subtract(one, Exp(e, Mult(two, pi, i, subtract(Mult(_two_pow_t, _delta_b_floor), l)))), subtract(one, Exp(e, Mult(two, pi, i, subtract(_delta_b_floor, frac(l, _two_pow_t))))))))

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