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, Mult, Sum, frac, one, subtract, two
from proveit.physics.quantum.QPE import _two_pow__t_minus_one

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

\left(2 \cdot \left(\sum_{l = e + 1}^{2^{t - 1} - 1} \frac{1}{l^{2}}\right)\right) + \frac{1}{e^{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: 37 operands: 1
1	ExprTuple	2, 3
2	Operation	operator: 4 operands: 5
3	Operation	operator: 17 operands: 6
4	Literal
5	ExprTuple	35, 7
6	ExprTuple	43, 8
7	Operation	operator: 9 operand: 12
8	Operation	operator: 33 operands: 11
9	Literal
10	ExprTuple	12
11	ExprTuple	31, 35
12	Lambda	parameter: 26 body: 14
13	ExprTuple	26
14	Conditional	value: 15 condition: 16
15	Operation	operator: 17 operands: 18
16	Operation	operator: 19 operands: 20
17	Literal
18	ExprTuple	43, 21
19	Literal
20	ExprTuple	26, 22
21	Operation	operator: 33 operands: 23
22	Operation	operator: 24 operands: 25
23	ExprTuple	26, 35
24	Literal
25	ExprTuple	27, 28
26	Variable
27	Operation	operator: 37 operands: 29
28	Operation	operator: 37 operands: 30
29	ExprTuple	31, 43
30	ExprTuple	32, 40
31	Variable
32	Operation	operator: 33 operands: 34
33	Literal
34	ExprTuple	35, 36
35	Literal
36	Operation	operator: 37 operands: 38
37	Literal
38	ExprTuple	39, 40
39	Literal
40	Operation	operator: 41 operand: 43
41	Literal
42	ExprTuple	43
43	Literal