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.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_round, _two_pow_t

# build up the expression from sub-expressions
expr = InSet(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)))), 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())

\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}}}}} \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: 5 operands: 6
4	Literal
5	Literal
6	ExprTuple	7, 8
7	Operation	operator: 10 operands: 9
8	Operation	operator: 10 operands: 11
9	ExprTuple	13, 12
10	Literal
11	ExprTuple	13, 14
12	Operation	operator: 16 operand: 18
13	Literal
14	Operation	operator: 16 operand: 19
15	ExprTuple	18
16	Literal
17	ExprTuple	19
18	Operation	operator: 32 operands: 20
19	Operation	operator: 32 operands: 21
20	ExprTuple	23, 22
21	ExprTuple	23, 24
22	Operation	operator: 26 operands: 25
23	Literal
24	Operation	operator: 26 operands: 27
25	ExprTuple	36, 29, 30, 31, 28
26	Literal
27	ExprTuple	36, 29, 30, 31
28	Operation	operator: 32 operands: 33
29	Literal
30	Literal
31	Operation	operator: 34 operand: 38
32	Literal
33	ExprTuple	36, 37
34	Literal
35	ExprTuple	38
36	Literal
37	Literal
38	Literal