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, _two_pow_t
from proveit.trigonometry import Sin

# build up the expression from sub-expressions
sub_expr1 = subtract(_delta_b_floor, frac(l, _two_pow_t))
sub_expr2 = subtract(one, Exp(e, Mult(two, pi, i, subtract(Mult(_two_pow_t, _delta_b_floor), l))))
expr = ExprTuple(Abs(frac(sub_expr2, subtract(one, Exp(e, Mult(two, pi, i, sub_expr1))))), frac(Abs(sub_expr2), Mult(two, Sin(Mult(pi, Abs(sub_expr1))))))

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|\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|, \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: 30 operand: 5
2	Operation	operator: 54 operands: 4
3	ExprTuple	5
4	ExprTuple	6, 7
5	Operation	operator: 54 operands: 8
6	Operation	operator: 30 operand: 12
7	Operation	operator: 48 operands: 10
8	ExprTuple	12, 11
9	ExprTuple	12
10	ExprTuple	63, 13
11	Operation	operator: 42 operands: 14
12	Operation	operator: 42 operands: 15
13	Operation	operator: 16 operand: 21
14	ExprTuple	19, 18
15	ExprTuple	19, 20
16	Literal
17	ExprTuple	21
18	Operation	operator: 50 operand: 25
19	Literal
20	Operation	operator: 50 operand: 26
21	Operation	operator: 48 operands: 24
22	ExprTuple	25
23	ExprTuple	26
24	ExprTuple	38, 27
25	Operation	operator: 61 operands: 28
26	Operation	operator: 61 operands: 29
27	Operation	operator: 30 operand: 37
28	ExprTuple	33, 32
29	ExprTuple	33, 34
30	Literal
31	ExprTuple	37
32	Operation	operator: 48 operands: 35
33	Literal
34	Operation	operator: 48 operands: 36
35	ExprTuple	63, 38, 39, 37
36	ExprTuple	63, 38, 39, 40
37	Operation	operator: 42 operands: 41
38	Literal
39	Literal
40	Operation	operator: 42 operands: 43
41	ExprTuple	53, 44
42	Literal
43	ExprTuple	45, 46
44	Operation	operator: 50 operand: 52
45	Operation	operator: 48 operands: 49
46	Operation	operator: 50 operand: 58
47	ExprTuple	52
48	Literal
49	ExprTuple	59, 53
50	Literal
51	ExprTuple	58
52	Operation	operator: 54 operands: 55
53	Operation	operator: 56 operand: 60
54	Literal
55	ExprTuple	58, 59
56	Literal
57	ExprTuple	60
58	Variable
59	Operation	operator: 61 operands: 62
60	Literal
61	Literal
62	ExprTuple	63, 64
63	Literal
64	Literal