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

# build up the expression from sub-expressions
sub_expr1 = Abs(_delta_b_round)
expr = ExprTuple(frac(Abs(subtract(one, Exp(e, Mult(two, pi, i, _delta_b_round, _two_pow_t)))), Abs(subtract(one, Exp(e, Mult(two, pi, i, _delta_b_round))))), frac(Mult(two, Sin(Mult(_two_pow_t, pi, sub_expr1))), Mult(two, Sin(Mult(pi, 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(\frac{\left|1 - \mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot \delta_{b_{\textit{r}}} \cdot 2^{t}}\right|}{\left|1 - \mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot \delta_{b_{\textit{r}}}}\right|}, \frac{2 \cdot \sin{\left(2^{t} \cdot \pi \cdot \left|\delta_{b_{\textit{r}}}\right|\right)}}{2 \cdot \sin{\left(\pi \cdot \left|\delta_{b_{\textit{r}}}\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: 4 operands: 3
2	Operation	operator: 4 operands: 5
3	ExprTuple	6, 7
4	Literal
5	ExprTuple	8, 9
6	Operation	operator: 39 operand: 14
7	Operation	operator: 39 operand: 15
8	Operation	operator: 45 operands: 12
9	Operation	operator: 45 operands: 13
10	ExprTuple	14
11	ExprTuple	15
12	ExprTuple	55, 16
13	ExprTuple	55, 17
14	Operation	operator: 19 operands: 18
15	Operation	operator: 19 operands: 20
16	Operation	operator: 22 operand: 27
17	Operation	operator: 22 operand: 28
18	ExprTuple	25, 24
19	Literal
20	ExprTuple	25, 26
21	ExprTuple	27
22	Literal
23	ExprTuple	28
24	Operation	operator: 30 operand: 34
25	Literal
26	Operation	operator: 30 operand: 35
27	Operation	operator: 45 operands: 32
28	Operation	operator: 45 operands: 33
29	ExprTuple	34
30	Literal
31	ExprTuple	35
32	ExprTuple	47, 48, 36
33	ExprTuple	48, 36
34	Operation	operator: 51 operands: 37
35	Operation	operator: 51 operands: 38
36	Operation	operator: 39 operand: 50
37	ExprTuple	42, 41
38	ExprTuple	42, 43
39	Literal
40	ExprTuple	50
41	Operation	operator: 45 operands: 44
42	Literal
43	Operation	operator: 45 operands: 46
44	ExprTuple	55, 48, 49, 50, 47
45	Literal
46	ExprTuple	55, 48, 49, 50
47	Operation	operator: 51 operands: 52
48	Literal
49	Literal
50	Operation	operator: 53 operand: 57
51	Literal
52	ExprTuple	55, 56
53	Literal
54	ExprTuple	57
55	Literal
56	Literal
57	Literal