Expression of type Add

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, Neg, frac, one, two
from proveit.physics.quantum.QPE import _eps

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

1 - \frac{1}{2 + \frac{1}{\epsilon}} - \frac{1}{\left(2 \cdot \left(1 + \frac{1}{2 \cdot \epsilon}\right)\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',)

# display the expression information
stored_expr.expr_info()

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