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
expr = ExprTuple(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|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: 18 operand: 5
2	Operation	operator: 35 operands: 4
3	ExprTuple	5
4	ExprTuple	49, 43, 6
5	Operation	operator: 29 operands: 7
6	Operation	operator: 8 operand: 12
7	ExprTuple	10, 11
8	Literal
9	ExprTuple	12
10	Literal
11	Operation	operator: 37 operand: 15
12	Operation	operator: 35 operands: 14
13	ExprTuple	15
14	ExprTuple	25, 16
15	Operation	operator: 46 operands: 17
16	Operation	operator: 18 operand: 22
17	ExprTuple	20, 21
18	Literal
19	ExprTuple	22
20	Literal
21	Operation	operator: 35 operands: 23
22	Operation	operator: 29 operands: 24
23	ExprTuple	49, 25, 26, 27
24	ExprTuple	41, 28
25	Literal
26	Literal
27	Operation	operator: 29 operands: 30
28	Operation	operator: 37 operand: 34
29	Literal
30	ExprTuple	32, 33
31	ExprTuple	34
32	Operation	operator: 35 operands: 36
33	Operation	operator: 37 operand: 42
34	Operation	operator: 39 operands: 40
35	Literal
36	ExprTuple	43, 41
37	Literal
38	ExprTuple	42
39	Literal
40	ExprTuple	42, 43
41	Operation	operator: 44 operand: 48
42	Variable
43	Operation	operator: 46 operands: 47
44	Literal
45	ExprTuple	48
46	Literal
47	ExprTuple	49, 50
48	Literal
49	Literal
50	Literal