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 ExprRange, Variable
from proveit.core_expr_types import Len
from proveit.logic import Equals
from proveit.numbers import Exp, Mult, e, frac, i, one, pi, subtract, two
from proveit.physics.quantum.QPE import _delta_b_round, _two_pow_t

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
expr = Equals(Len(operands = [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))))]), Len(operands = [ExprRange(sub_expr1, sub_expr1, one, two)]))

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(\frac{1}{2^{t}}, \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)| = |\left(1, \ldots, 2\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: 6 operands: 5
4	Operation	operator: 6 operands: 7
5	ExprTuple	8, 9
6	Literal
7	ExprTuple	10
8	Operation	operator: 12 operands: 11
9	Operation	operator: 12 operands: 13
10	ExprRange	lambda_map: 14 start_index: 23 end_index: 46
11	ExprTuple	23, 38
12	Literal
13	ExprTuple	15, 16
14	Lambda	parameter: 21 body: 21
15	Operation	operator: 19 operands: 18
16	Operation	operator: 19 operands: 20
17	ExprTuple	21
18	ExprTuple	23, 22
19	Literal
20	ExprTuple	23, 24
21	Variable
22	Operation	operator: 26 operand: 28
23	Literal
24	Operation	operator: 26 operand: 29
25	ExprTuple	28
26	Literal
27	ExprTuple	29
28	Operation	operator: 42 operands: 30
29	Operation	operator: 42 operands: 31
30	ExprTuple	33, 32
31	ExprTuple	33, 34
32	Operation	operator: 36 operands: 35
33	Literal
34	Operation	operator: 36 operands: 37
35	ExprTuple	46, 39, 40, 41, 38
36	Literal
37	ExprTuple	46, 39, 40, 41
38	Operation	operator: 42 operands: 43
39	Literal
40	Literal
41	Operation	operator: 44 operand: 48
42	Literal
43	ExprTuple	46, 47
44	Literal
45	ExprTuple	48
46	Literal
47	Literal
48	Literal