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, four, frac, one, subtract, two
from proveit.physics.quantum.QPE import _eps, _n, _t

# build up the expression from sub-expressions
expr = Add(one, Neg(frac(one, Mult(two, Add(one, frac(one, Mult(two, _eps)))))), Neg(frac(one, Mult(four, Exp(subtract(Exp(two, subtract(_t, _n)), one), 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 \cdot \left(1 + \frac{1}{2 \cdot \epsilon}\right)} - \frac{1}{4 \cdot \left(2^{t - n} - 1\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: 36 operands: 1
1	ExprTuple	35, 2, 3
2	Operation	operator: 40 operand: 6
3	Operation	operator: 40 operand: 7
4	ExprTuple	6
5	ExprTuple	7
6	Operation	operator: 21 operands: 8
7	Operation	operator: 21 operands: 9
8	ExprTuple	35, 10
9	ExprTuple	35, 11
10	Operation	operator: 27 operands: 12
11	Operation	operator: 27 operands: 13
12	ExprTuple	33, 14
13	ExprTuple	15, 16
14	Operation	operator: 36 operands: 17
15	Literal
16	Operation	operator: 29 operands: 18
17	ExprTuple	35, 19
18	ExprTuple	20, 33
19	Operation	operator: 21 operands: 22
20	Operation	operator: 36 operands: 23
21	Literal
22	ExprTuple	35, 24
23	ExprTuple	25, 26
24	Operation	operator: 27 operands: 28
25	Operation	operator: 29 operands: 30
26	Operation	operator: 40 operand: 35
27	Literal
28	ExprTuple	33, 32
29	Literal
30	ExprTuple	33, 34
31	ExprTuple	35
32	Literal
33	Literal
34	Operation	operator: 36 operands: 37
35	Literal
36	Literal
37	ExprTuple	38, 39
38	Literal
39	Operation	operator: 40 operand: 42
40	Literal
41	ExprTuple	42
42	Literal