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.numbers import Add, Exp, Mult, frac, one, subtract, three, two
from proveit.physics.quantum.QPE import _eps

# build up the expression from sub-expressions
sub_expr1 = frac(one, _eps)
expr = frac(Mult(_eps, Mult(Exp(_eps, subtract(two, one)), Add(three, sub_expr1))), Mult(Exp(_eps, two), Exp(Add(two, sub_expr1), 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())

\frac{\epsilon \cdot \left(\epsilon^{2 - 1} \cdot \left(3 + \frac{1}{\epsilon}\right)\right)}{\epsilon^{2} \cdot \left(2 + \frac{1}{\epsilon}\right)^{2}}

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: 25 operands: 1
1	ExprTuple	2, 3
2	Operation	operator: 9 operands: 4
3	Operation	operator: 9 operands: 5
4	ExprTuple	29, 6
5	ExprTuple	7, 8
6	Operation	operator: 9 operands: 10
7	Operation	operator: 16 operands: 11
8	Operation	operator: 16 operands: 12
9	Literal
10	ExprTuple	13, 14
11	ExprTuple	29, 27
12	ExprTuple	15, 27
13	Operation	operator: 16 operands: 17
14	Operation	operator: 23 operands: 18
15	Operation	operator: 23 operands: 19
16	Literal
17	ExprTuple	29, 20
18	ExprTuple	21, 22
19	ExprTuple	27, 22
20	Operation	operator: 23 operands: 24
21	Literal
22	Operation	operator: 25 operands: 26
23	Literal
24	ExprTuple	27, 28
25	Literal
26	ExprTuple	32, 29
27	Literal
28	Operation	operator: 30 operand: 32
29	Literal
30	Literal
31	ExprTuple	32
32	Literal