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(frac(one, _two_pow_t), frac(Abs(subtract(one, Exp(e, Mult(two, pi, i, subtract(Mult(_two_pow_t, _delta_b_floor), l))))), Mult(two, 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(\frac{1}{2^{t}}, \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: 43 operands: 3
2	Operation	operator: 43 operands: 4
3	ExprTuple	14, 47
4	ExprTuple	5, 6
5	Operation	operator: 22 operand: 9
6	Operation	operator: 39 operands: 8
7	ExprTuple	9
8	ExprTuple	53, 10
9	Operation	operator: 33 operands: 11
10	Operation	operator: 12 operand: 16
11	ExprTuple	14, 15
12	Literal
13	ExprTuple	16
14	Literal
15	Operation	operator: 41 operand: 19
16	Operation	operator: 39 operands: 18
17	ExprTuple	19
18	ExprTuple	29, 20
19	Operation	operator: 50 operands: 21
20	Operation	operator: 22 operand: 26
21	ExprTuple	24, 25
22	Literal
23	ExprTuple	26
24	Literal
25	Operation	operator: 39 operands: 27
26	Operation	operator: 33 operands: 28
27	ExprTuple	53, 29, 30, 31
28	ExprTuple	45, 32
29	Literal
30	Literal
31	Operation	operator: 33 operands: 34
32	Operation	operator: 41 operand: 38
33	Literal
34	ExprTuple	36, 37
35	ExprTuple	38
36	Operation	operator: 39 operands: 40
37	Operation	operator: 41 operand: 46
38	Operation	operator: 43 operands: 44
39	Literal
40	ExprTuple	47, 45
41	Literal
42	ExprTuple	46
43	Literal
44	ExprTuple	46, 47
45	Operation	operator: 48 operand: 52
46	Variable
47	Operation	operator: 50 operands: 51
48	Literal
49	ExprTuple	52
50	Literal
51	ExprTuple	53, 54
52	Literal
53	Literal
54	Literal