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

# build up the expression from sub-expressions
expr = ExprTuple(Abs(_rel_indexed_alpha), Mult(frac(one, _two_pow_t), frac(Abs(subtract(one, Exp(e, Mult(two, pi, i, subtract(Mult(_two_pow_t, _delta_b_floor), l))))), Mult(two, Sin(Mult(pi, Abs(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(\left|\alpha_{b_{\textit{f}} \oplus l}\right|, \frac{1}{2^{t}} \cdot \frac{\left|1 - \mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot \left(\left(2^{t} \cdot \delta_{b_{\textit{f}}}\right) - l\right)}\right|}{2 \cdot \sin{\left(\pi \cdot \left|\delta_{b_{\textit{f}}} - \frac{l}{2^{t}}\right|\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: 32 operand: 5
2	Operation	operator: 49 operands: 4
3	ExprTuple	5
4	ExprTuple	6, 7
5	Operation	operator: 8 operand: 12
6	Operation	operator: 53 operands: 10
7	Operation	operator: 53 operands: 11
8	Literal
9	ExprTuple	12
10	ExprTuple	24, 57
11	ExprTuple	13, 14
12	Operation	operator: 15 operands: 16
13	Operation	operator: 32 operand: 19
14	Operation	operator: 49 operands: 18
15	Literal
16	ExprTuple	62, 56
17	ExprTuple	19
18	ExprTuple	63, 20
19	Operation	operator: 43 operands: 21
20	Operation	operator: 22 operand: 26
21	ExprTuple	24, 25
22	Literal
23	ExprTuple	26
24	Literal
25	Operation	operator: 51 operand: 29
26	Operation	operator: 49 operands: 28
27	ExprTuple	29
28	ExprTuple	39, 30
29	Operation	operator: 60 operands: 31
30	Operation	operator: 32 operand: 36
31	ExprTuple	34, 35
32	Literal
33	ExprTuple	36
34	Literal
35	Operation	operator: 49 operands: 37
36	Operation	operator: 43 operands: 38
37	ExprTuple	63, 39, 40, 41
38	ExprTuple	55, 42
39	Literal
40	Literal
41	Operation	operator: 43 operands: 44
42	Operation	operator: 51 operand: 48
43	Literal
44	ExprTuple	46, 47
45	ExprTuple	48
46	Operation	operator: 49 operands: 50
47	Operation	operator: 51 operand: 56
48	Operation	operator: 53 operands: 54
49	Literal
50	ExprTuple	57, 55
51	Literal
52	ExprTuple	56
53	Literal
54	ExprTuple	56, 57
55	Operation	operator: 58 operand: 62
56	Variable
57	Operation	operator: 60 operands: 61
58	Literal
59	ExprTuple	62
60	Literal
61	ExprTuple	63, 64
62	Literal
63	Literal
64	Literal