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 import e, l
from proveit.numbers import Add, Exp, Interval, Sum, frac, one, subtract, two
from proveit.physics.quantum.QPE import _two_pow__t_minus_one

# build up the expression from sub-expressions
sub_expr1 = Sum(index_or_indices = [l], summand = frac(one, Exp(l, two)), domain = Interval(Add(e, one), subtract(_two_pow__t_minus_one, one)))
expr = Add(sub_expr1, Add(frac(one, Exp(e, two)), 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())

\left(\sum_{l = e + 1}^{2^{t - 1} - 1} \frac{1}{l^{2}}\right) + \left(\frac{1}{e^{2}} + \left(\sum_{l = e + 1}^{2^{t - 1} - 1} \frac{1}{l^{2}}\right)\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',)

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Operation	operator: 36 operands: 1
1	ExprTuple	5, 2
2	Operation	operator: 36 operands: 3
3	ExprTuple	4, 5
4	Operation	operator: 16 operands: 6
5	Operation	operator: 7 operand: 10
6	ExprTuple	42, 9
7	Literal
8	ExprTuple	10
9	Operation	operator: 32 operands: 11
10	Lambda	parameter: 25 body: 13
11	ExprTuple	30, 34
12	ExprTuple	25
13	Conditional	value: 14 condition: 15
14	Operation	operator: 16 operands: 17
15	Operation	operator: 18 operands: 19
16	Literal
17	ExprTuple	42, 20
18	Literal
19	ExprTuple	25, 21
20	Operation	operator: 32 operands: 22
21	Operation	operator: 23 operands: 24
22	ExprTuple	25, 34
23	Literal
24	ExprTuple	26, 27
25	Variable
26	Operation	operator: 36 operands: 28
27	Operation	operator: 36 operands: 29
28	ExprTuple	30, 42
29	ExprTuple	31, 39
30	Variable
31	Operation	operator: 32 operands: 33
32	Literal
33	ExprTuple	34, 35
34	Literal
35	Operation	operator: 36 operands: 37
36	Literal
37	ExprTuple	38, 39
38	Literal
39	Operation	operator: 40 operand: 42
40	Literal
41	ExprTuple	42
42	Literal