Expression of type Div

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.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 = subtract(_delta_b_floor, frac(l, _two_pow_t))
expr = frac(subtract(one, Exp(e, Mult(two, pi, i, sub_expr1, _two_pow_t))), subtract(one, Exp(e, Mult(two, pi, i, sub_expr1))))

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 \left(\delta_{b_{\textit{f}}} - \frac{l}{2^{t}}\right) \cdot 2^{t}}}{1 - \mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot \left(\delta_{b_{\textit{f}}} - \frac{l}{2^{t}}\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',)
division	'inline': uses '/'; 'fraction': numerator over the denominator (also see 'frac' function)	fraction	fraction	('with_inline_style', 'with_fraction_style')

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Operation	operator: 34 operands: 1
1	ExprTuple	2, 3
2	Operation	operator: 24 operands: 4
3	Operation	operator: 24 operands: 5
4	ExprTuple	7, 6
5	ExprTuple	7, 8
6	Operation	operator: 30 operand: 11
7	Literal
8	Operation	operator: 30 operand: 12
9	ExprTuple	11
10	ExprTuple	12
11	Operation	operator: 38 operands: 13
12	Operation	operator: 38 operands: 14
13	ExprTuple	16, 15
14	ExprTuple	16, 17
15	Operation	operator: 19 operands: 18
16	Literal
17	Operation	operator: 19 operands: 20
18	ExprTuple	40, 21, 22, 23, 37
19	Literal
20	ExprTuple	40, 21, 22, 23
21	Literal
22	Literal
23	Operation	operator: 24 operands: 25
24	Literal
25	ExprTuple	26, 27
26	Operation	operator: 28 operand: 32
27	Operation	operator: 30 operand: 33
28	Literal
29	ExprTuple	32
30	Literal
31	ExprTuple	33
32	Literal
33	Operation	operator: 34 operands: 35
34	Literal
35	ExprTuple	36, 37
36	Variable
37	Operation	operator: 38 operands: 39
38	Literal
39	ExprTuple	40, 41
40	Literal
41	Literal