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), frac(Abs(subtract(one, Exp(e, Mult(two, pi, i, subtract(Mult(_two_pow_t, _delta_b_floor), l))))), Mult(two, _two_pow_t, 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{\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 2^{t} \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: 28 operand: 5
2	Operation	operator: 49 operands: 4
3	ExprTuple	5
4	ExprTuple	6, 7
5	Operation	operator: 8 operand: 12
6	Operation	operator: 28 operand: 13
7	Operation	operator: 45 operands: 11
8	Literal
9	ExprTuple	12
10	ExprTuple	13
11	ExprTuple	59, 53, 14
12	Operation	operator: 15 operands: 16
13	Operation	operator: 39 operands: 17
14	Operation	operator: 18 operand: 22
15	Literal
16	ExprTuple	58, 52
17	ExprTuple	20, 21
18	Literal
19	ExprTuple	22
20	Literal
21	Operation	operator: 47 operand: 25
22	Operation	operator: 45 operands: 24
23	ExprTuple	25
24	ExprTuple	35, 26
25	Operation	operator: 56 operands: 27
26	Operation	operator: 28 operand: 32
27	ExprTuple	30, 31
28	Literal
29	ExprTuple	32
30	Literal
31	Operation	operator: 45 operands: 33
32	Operation	operator: 39 operands: 34
33	ExprTuple	59, 35, 36, 37
34	ExprTuple	51, 38
35	Literal
36	Literal
37	Operation	operator: 39 operands: 40
38	Operation	operator: 47 operand: 44
39	Literal
40	ExprTuple	42, 43
41	ExprTuple	44
42	Operation	operator: 45 operands: 46
43	Operation	operator: 47 operand: 52
44	Operation	operator: 49 operands: 50
45	Literal
46	ExprTuple	53, 51
47	Literal
48	ExprTuple	52
49	Literal
50	ExprTuple	52, 53
51	Operation	operator: 54 operand: 58
52	Variable
53	Operation	operator: 56 operands: 57
54	Literal
55	ExprTuple	58
56	Literal
57	ExprTuple	59, 60
58	Literal
59	Literal
60	Literal