Expression of type Mult

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 l
from proveit.numbers import Exp, Mult, Sum, four, frac, one, two
from proveit.physics.quantum.QPE import _diff_l_scaled_delta_floor, _pos_domain

# build up the expression from sub-expressions
expr = Mult(frac(one, four), Sum(index_or_indices = [l], summand = frac(one, Exp(_diff_l_scaled_delta_floor, two)), domain = _pos_domain))

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{1}{4} \cdot \left(\sum_{l = e + 1}^{2^{t - 1}} \frac{1}{\left(l - \left(2^{t} \cdot \delta_{b_{\textit{f}}}\right)\right)^{2}}\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: 37 operands: 1
1	ExprTuple	2, 3
2	Operation	operator: 13 operands: 4
3	Operation	operator: 5 operand: 8
4	ExprTuple	43, 7
5	Literal
6	ExprTuple	8
7	Literal
8	Lambda	parameter: 28 body: 10
9	ExprTuple	28
10	Conditional	value: 11 condition: 12
11	Operation	operator: 13 operands: 14
12	Operation	operator: 15 operands: 16
13	Literal
14	ExprTuple	43, 17
15	Literal
16	ExprTuple	28, 18
17	Operation	operator: 44 operands: 19
18	Operation	operator: 20 operands: 21
19	ExprTuple	22, 48
20	Literal
21	ExprTuple	23, 24
22	Operation	operator: 33 operands: 25
23	Operation	operator: 33 operands: 26
24	Operation	operator: 44 operands: 27
25	ExprTuple	28, 29
26	ExprTuple	30, 43
27	ExprTuple	48, 31
28	Variable
29	Operation	operator: 39 operand: 35
30	Variable
31	Operation	operator: 33 operands: 34
32	ExprTuple	35
33	Literal
34	ExprTuple	49, 36
35	Operation	operator: 37 operands: 38
36	Operation	operator: 39 operand: 43
37	Literal
38	ExprTuple	41, 42
39	Literal
40	ExprTuple	43
41	Operation	operator: 44 operands: 45
42	Operation	operator: 46 operand: 50
43	Literal
44	Literal
45	ExprTuple	48, 49
46	Literal
47	ExprTuple	50
48	Literal
49	Literal
50	Literal