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 Add, Exp, Mult, e, i, one, pi, two
from proveit.physics.quantum.QPE import _delta_b_round, _two_pow_t, _two_pow_t__minus_one

# build up the expression from sub-expressions
expr = Equals(Exp(Exp(e, Mult(two, pi, i, _delta_b_round)), Add(_two_pow_t__minus_one, one)), Exp(e, Mult(two, pi, i, _delta_b_round, _two_pow_t)))

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 \delta_{b_{\textit{r}}}})^{\left(2^{t} - 1\right) + 1} = \mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot \delta_{b_{\textit{r}}} \cdot 2^{t}}

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: 27 operands: 5
4	Operation	operator: 27 operands: 6
5	ExprTuple	7, 8
6	ExprTuple	13, 9
7	Operation	operator: 27 operands: 10
8	Operation	operator: 18 operands: 11
9	Operation	operator: 16 operands: 12
10	ExprTuple	13, 14
11	ExprTuple	15, 34
12	ExprTuple	32, 20, 21, 22, 23
13	Literal
14	Operation	operator: 16 operands: 17
15	Operation	operator: 18 operands: 19
16	Literal
17	ExprTuple	32, 20, 21, 22
18	Literal
19	ExprTuple	23, 24
20	Literal
21	Literal
22	Operation	operator: 25 operand: 31
23	Operation	operator: 27 operands: 28
24	Operation	operator: 29 operand: 34
25	Literal
26	ExprTuple	31
27	Literal
28	ExprTuple	32, 33
29	Literal
30	ExprTuple	34
31	Literal
32	Literal
33	Literal
34	Literal