Expression of type InSet

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 InSet
from proveit.numbers import Complex, 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
expr = InSet(Mult(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))))))), Complex)

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}} \cdot \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) \in \mathbb{C}

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: 38 operands: 5
4	Literal
5	ExprTuple	6, 7
6	Operation	operator: 47 operands: 8
7	Operation	operator: 47 operands: 9
8	ExprTuple	15, 51
9	ExprTuple	10, 11
10	Operation	operator: 33 operands: 12
11	Operation	operator: 33 operands: 13
12	ExprTuple	15, 14
13	ExprTuple	15, 16
14	Operation	operator: 41 operand: 19
15	Literal
16	Operation	operator: 41 operand: 20
17	ExprTuple	19
18	ExprTuple	20
19	Operation	operator: 52 operands: 21
20	Operation	operator: 52 operands: 22
21	ExprTuple	24, 23
22	ExprTuple	24, 25
23	Operation	operator: 38 operands: 26
24	Literal
25	Operation	operator: 38 operands: 27
26	ExprTuple	54, 29, 30, 28
27	ExprTuple	54, 29, 30, 31
28	Operation	operator: 33 operands: 32
29	Literal
30	Literal
31	Operation	operator: 33 operands: 34
32	ExprTuple	35, 36
33	Literal
34	ExprTuple	43, 37
35	Operation	operator: 38 operands: 39
36	Operation	operator: 41 operand: 50
37	Operation	operator: 41 operand: 44
38	Literal
39	ExprTuple	51, 43
40	ExprTuple	50
41	Literal
42	ExprTuple	44
43	Operation	operator: 45 operand: 49
44	Operation	operator: 47 operands: 48
45	Literal
46	ExprTuple	49
47	Literal
48	ExprTuple	50, 51
49	Literal
50	Variable
51	Operation	operator: 52 operands: 53
52	Literal
53	ExprTuple	54, 55
54	Literal
55	Literal