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 Exp, Mod, Mult, e, frac, i, one, pi, subtract, two
from proveit.physics.quantum.QPE import SubIndexed, _alpha, _b_round, _delta_b_round, _two_pow_t

# build up the expression from sub-expressions
expr = Equals(SubIndexed(_alpha, [Mod(_b_round, _two_pow_t)]), Mult(frac(one, _two_pow_t), frac(subtract(one, Exp(e, Mult(two, pi, i, _delta_b_round, _two_pow_t))), subtract(one, Exp(e, Mult(two, pi, i, _delta_b_round))))))

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())

\alpha_{b_{\textit{r}} ~\textup{mod}~ 2^{t}} = \left(\frac{1}{2^{t}} \cdot \frac{1 - \mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot \delta_{b_{\textit{r}}} \cdot 2^{t}}}{1 - \mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot \delta_{b_{\textit{r}}}}}\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: 5 operand: 8
4	Operation	operator: 35 operands: 7
5	Literal
6	ExprTuple	8
7	ExprTuple	9, 10
8	Operation	operator: 11 operands: 12
9	Operation	operator: 14 operands: 13
10	Operation	operator: 14 operands: 15
11	Literal
12	ExprTuple	47, 37
13	ExprTuple	22, 37
14	Literal
15	ExprTuple	16, 17
16	Operation	operator: 19 operands: 18
17	Operation	operator: 19 operands: 20
18	ExprTuple	22, 21
19	Literal
20	ExprTuple	22, 23
21	Operation	operator: 25 operand: 27
22	Literal
23	Operation	operator: 25 operand: 28
24	ExprTuple	27
25	Literal
26	ExprTuple	28
27	Operation	operator: 41 operands: 29
28	Operation	operator: 41 operands: 30
29	ExprTuple	32, 31
30	ExprTuple	32, 33
31	Operation	operator: 35 operands: 34
32	Literal
33	Operation	operator: 35 operands: 36
34	ExprTuple	45, 38, 39, 40, 37
35	Literal
36	ExprTuple	45, 38, 39, 40
37	Operation	operator: 41 operands: 42
38	Literal
39	Literal
40	Operation	operator: 43 operand: 47
41	Literal
42	ExprTuple	45, 46
43	Literal
44	ExprTuple	47
45	Literal
46	Literal
47	Literal