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, l
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_floor, _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, subtract(Mult(_two_pow_t, _delta_b_floor), l)))), subtract(one, Exp(e, Mult(two, pi, i, subtract(_delta_b_floor, frac(l, _two_pow_t))))))]), 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 \left(\left(2^{t} \cdot \delta_{b_{\textit{f}}}\right) - l\right)}}{1 - \mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot \left(\delta_{b_{\textit{f}}} - \frac{l}{2^{t}}\right)}}\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: 53 operands: 11
9	Operation	operator: 53 operands: 12
10	ExprRange	lambda_map: 13 start_index: 21 end_index: 60
11	ExprTuple	21, 57
12	ExprTuple	14, 15
13	Lambda	parameter: 19 body: 19
14	Operation	operator: 39 operands: 17
15	Operation	operator: 39 operands: 18
16	ExprTuple	19
17	ExprTuple	21, 20
18	ExprTuple	21, 22
19	Variable
20	Operation	operator: 47 operand: 25
21	Literal
22	Operation	operator: 47 operand: 26
23	ExprTuple	25
24	ExprTuple	26
25	Operation	operator: 58 operands: 27
26	Operation	operator: 58 operands: 28
27	ExprTuple	30, 29
28	ExprTuple	30, 31
29	Operation	operator: 44 operands: 32
30	Literal
31	Operation	operator: 44 operands: 33
32	ExprTuple	60, 35, 36, 34
33	ExprTuple	60, 35, 36, 37
34	Operation	operator: 39 operands: 38
35	Literal
36	Literal
37	Operation	operator: 39 operands: 40
38	ExprTuple	41, 42
39	Literal
40	ExprTuple	49, 43
41	Operation	operator: 44 operands: 45
42	Operation	operator: 47 operand: 56
43	Operation	operator: 47 operand: 50
44	Literal
45	ExprTuple	57, 49
46	ExprTuple	56
47	Literal
48	ExprTuple	50
49	Operation	operator: 51 operand: 55
50	Operation	operator: 53 operands: 54
51	Literal
52	ExprTuple	55
53	Literal
54	ExprTuple	56, 57
55	Literal
56	Variable
57	Operation	operator: 58 operands: 59
58	Literal
59	ExprTuple	60, 61
60	Literal
61	Literal