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, Mult, frac, pi, 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)
sub_expr2 = Sin(Mult(_two_pow_t, pi, sub_expr1))
sub_expr3 = Sin(Mult(pi, sub_expr1))
expr = ExprTuple(frac(Mult(two, sub_expr2), Mult(two, sub_expr3)), frac(sub_expr2, sub_expr3))

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{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)}}, \frac{\sin{\left(2^{t} \cdot \pi \cdot \left|\delta_{b_{\textit{r}}}\right|\right)}}{\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	10, 11
6	Operation	operator: 18 operands: 8
7	Operation	operator: 18 operands: 9
8	ExprTuple	27, 10
9	ExprTuple	27, 11
10	Operation	operator: 13 operand: 15
11	Operation	operator: 13 operand: 16
12	ExprTuple	15
13	Literal
14	ExprTuple	16
15	Operation	operator: 18 operands: 17
16	Operation	operator: 18 operands: 19
17	ExprTuple	20, 21, 22
18	Literal
19	ExprTuple	21, 22
20	Operation	operator: 23 operands: 24
21	Literal
22	Operation	operator: 25 operand: 29
23	Literal
24	ExprTuple	27, 28
25	Literal
26	ExprTuple	29
27	Literal
28	Literal
29	Operation	operator: 30 operand: 32
30	Literal
31	ExprTuple	32
32	Literal