Expression of type Equals

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.logic import Equals
from proveit.numbers import Abs, Mod, Mult, frac, one, pi
from proveit.physics.quantum.QPE import SubIndexed, _alpha, _b_round, _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 = Equals(Abs(SubIndexed(_alpha, [Mod(_b_round, _two_pow_t)])), Mult(frac(one, _two_pow_t), frac(Sin(Mult(_two_pow_t, pi, sub_expr1)), 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|\alpha_{b_{\textit{r}} ~\textup{mod}~ 2^{t}}\right| = \left(\frac{1}{2^{t}} \cdot \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
operation	'infix' or 'function' style formatting	infix	infix
wrap_positions	position(s) at which wrapping is to occur; '2 n - 1' is after the nth operand, '2 n' is after the nth operation.	()	()	('with_wrapping_at', 'with_wrap_before_operator', 'with_wrap_after_operator', 'without_wrapping', 'wrap_positions')
justification	if any wrap positions are set, justify to the 'left', 'center', or 'right'	center	center	('with_justification',)
direction	Direction of the relation (normal or reversed)	normal	normal	('with_direction_reversed', 'is_reversed')

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Operation	operator: 1 operands: 2
1	Literal
2	ExprTuple	3, 4
3	Operation	operator: 34 operand: 7
4	Operation	operator: 27 operands: 6
5	ExprTuple	7
6	ExprTuple	8, 9
7	Operation	operator: 10 operand: 15
8	Operation	operator: 13 operands: 12
9	Operation	operator: 13 operands: 14
10	Literal
11	ExprTuple	15
12	ExprTuple	16, 29
13	Literal
14	ExprTuple	17, 18
15	Operation	operator: 19 operands: 20
16	Literal
17	Operation	operator: 22 operand: 24
18	Operation	operator: 22 operand: 25
19	Literal
20	ExprTuple	41, 29
21	ExprTuple	24
22	Literal
23	ExprTuple	25
24	Operation	operator: 27 operands: 26
25	Operation	operator: 27 operands: 28
26	ExprTuple	29, 30, 31
27	Literal
28	ExprTuple	30, 31
29	Operation	operator: 32 operands: 33
30	Literal
31	Operation	operator: 34 operand: 38
32	Literal
33	ExprTuple	36, 37
34	Literal
35	ExprTuple	38
36	Literal
37	Literal
38	Operation	operator: 39 operand: 41
39	Literal
40	ExprTuple	41
41	Literal