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, e, 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(Exp(e, Mult(two, pi, i, subtract(_delta_b_floor, frac(l, _two_pow_t)))), Exp(e, Mult(two, pi, i, Add(Mult(sub_expr1, l, Exp(two, Mult(sub_expr1, _t))), _delta_b_floor))))

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())

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