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))
expr = ExprTuple(Abs(subtract(one, Exp(e, Mult(two, pi, i, sub_expr1)))), 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|1 - \mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot \left(\delta_{b_{\textit{f}}} - \frac{l}{2^{t}}\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: 18 operand: 5
2	Operation	operator: 22 operands: 4
3	ExprTuple	5
4	ExprTuple	43, 6
5	Operation	operator: 27 operands: 7
6	Operation	operator: 8 operand: 12
7	ExprTuple	10, 11
8	Literal
9	ExprTuple	12
10	Literal
11	Operation	operator: 33 operand: 15
12	Operation	operator: 22 operands: 14
13	ExprTuple	15
14	ExprTuple	24, 16
15	Operation	operator: 41 operands: 17
16	Operation	operator: 18 operand: 26
17	ExprTuple	20, 21
18	Literal
19	ExprTuple	26
20	Literal
21	Operation	operator: 22 operands: 23
22	Literal
23	ExprTuple	43, 24, 25, 26
24	Literal
25	Literal
26	Operation	operator: 27 operands: 28
27	Literal
28	ExprTuple	29, 30
29	Operation	operator: 31 operand: 35
30	Operation	operator: 33 operand: 36
31	Literal
32	ExprTuple	35
33	Literal
34	ExprTuple	36
35	Literal
36	Operation	operator: 37 operands: 38
37	Literal
38	ExprTuple	39, 40
39	Variable
40	Operation	operator: 41 operands: 42
41	Literal
42	ExprTuple	43, 44
43	Literal
44	Literal