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 ExprRange, IndexedVar, Variable, a, c, l
from proveit.numbers import Exp, Mult, Sum, frac, one, two, zero
from proveit.physics.quantum.QPE import _diff_l_scaled_delta_floor, _pos_domain

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
expr = Mult(IndexedVar(a, one), Sum(index_or_indices = [l], summand = frac(one, Exp(_diff_l_scaled_delta_floor, two)), domain = _pos_domain), ExprRange(sub_expr1, IndexedVar(c, sub_expr1), one, zero))

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())

a_{1} \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)\cdot c_{1} \cdot  c_{2} \cdot  \ldots \cdot  c_{0}

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: 43 operands: 1
1	ExprTuple	2, 3, 4
2	IndexedVar	variable: 5 index: 49
3	Operation	operator: 6 operand: 10
4	ExprRange	lambda_map: 8 start_index: 49 end_index: 9
5	Variable
6	Literal
7	ExprTuple	10
8	Lambda	parameter: 18 body: 11
9	Literal
10	Lambda	parameter: 34 body: 13
11	IndexedVar	variable: 14 index: 18
12	ExprTuple	34
13	Conditional	value: 16 condition: 17
14	Variable
15	ExprTuple	18
16	Operation	operator: 19 operands: 20
17	Operation	operator: 21 operands: 22
18	Variable
19	Literal
20	ExprTuple	49, 23
21	Literal
22	ExprTuple	34, 24
23	Operation	operator: 50 operands: 25
24	Operation	operator: 26 operands: 27
25	ExprTuple	28, 54
26	Literal
27	ExprTuple	29, 30
28	Operation	operator: 39 operands: 31
29	Operation	operator: 39 operands: 32
30	Operation	operator: 50 operands: 33
31	ExprTuple	34, 35
32	ExprTuple	36, 49
33	ExprTuple	54, 37
34	Variable
35	Operation	operator: 45 operand: 41
36	Variable
37	Operation	operator: 39 operands: 40
38	ExprTuple	41
39	Literal
40	ExprTuple	55, 42
41	Operation	operator: 43 operands: 44
42	Operation	operator: 45 operand: 49
43	Literal
44	ExprTuple	47, 48
45	Literal
46	ExprTuple	49
47	Operation	operator: 50 operands: 51
48	Operation	operator: 52 operand: 56
49	Literal
50	Literal
51	ExprTuple	54, 55
52	Literal
53	ExprTuple	56
54	Literal
55	Literal
56	Literal