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 import l
from proveit.logic import Equals
from proveit.numbers import Add, Exp, Mult, Neg, frac, i, one, pi, subtract, two
from proveit.physics.quantum.QPE import _delta_b_floor, _t, _two_pow_t

# build up the expression from sub-expressions
sub_expr1 = Neg(one)
expr = Equals(Mult(two, pi, subtract(_delta_b_floor, frac(l, _two_pow_t)), i), Mult(two, pi, Add(_delta_b_floor, Mult(sub_expr1, l, Exp(two, Mult(sub_expr1, _t)))), i))

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(2 \cdot \pi \cdot \left(\delta_{b_{\textit{f}}} - \frac{l}{2^{t}}\right) \cdot \mathsf{i}\right) = \left(2 \cdot \pi \cdot \left(\delta_{b_{\textit{f}}} + \left(\left(-1\right) \cdot l \cdot 2^{\left(-1\right) \cdot t}\right)\right) \cdot \mathsf{i}\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: 32 operands: 5
4	Operation	operator: 32 operands: 6
5	ExprTuple	34, 8, 7, 10
6	ExprTuple	34, 8, 9, 10
7	Operation	operator: 12 operands: 11
8	Literal
9	Operation	operator: 12 operands: 13
10	Literal
11	ExprTuple	15, 14
12	Literal
13	ExprTuple	15, 16
14	Operation	operator: 37 operand: 21
15	Operation	operator: 18 operand: 22
16	Operation	operator: 32 operands: 20
17	ExprTuple	21
18	Literal
19	ExprTuple	22
20	ExprTuple	35, 27, 23
21	Operation	operator: 24 operands: 25
22	Literal
23	Operation	operator: 30 operands: 26
24	Literal
25	ExprTuple	27, 28
26	ExprTuple	34, 29
27	Variable
28	Operation	operator: 30 operands: 31
29	Operation	operator: 32 operands: 33
30	Literal
31	ExprTuple	34, 36
32	Literal
33	ExprTuple	35, 36
34	Literal
35	Operation	operator: 37 operand: 39
36	Literal
37	Literal
38	ExprTuple	39
39	Literal