Expression of type Sum

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 k
from proveit.numbers import Exp, Mult, Neg, Sum, e, frac, i, pi, two
from proveit.physics.quantum.QPE import _m_domain, _phase, _two_pow_t

# build up the expression from sub-expressions
expr = Sum(index_or_indices = [k], summand = Mult(Exp(e, Neg(frac(Mult(two, pi, i, k, Mult(_two_pow_t, _phase)), _two_pow_t))), Exp(e, Mult(two, pi, i, _phase, k))), domain = _m_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())

\sum_{k = 0}^{2^{t} - 1} \left(\mathsf{e}^{-\frac{2 \cdot \pi \cdot \mathsf{i} \cdot k \cdot \left(2^{t} \cdot \varphi\right)}{2^{t}}} \cdot \mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot \varphi \cdot k}\right)

stored_expr.style_options()

name	description	default	current value	related methods
with_wrapping	If 'True', wrap the Expression after the parameters	None	None/False	('with_wrapping',)
condition_wrapping	Wrap 'before' or 'after' the condition (or None).	None	None/False	('with_wrap_after_condition', 'with_wrap_before_condition')
wrap_params	If 'True', wraps every two parameters AND wraps the Expression after the parameters	None	None/False	('with_params',)
justification	justify to the 'left', 'center', or 'right' in the array cells	center	center	('with_justification',)

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Operation	operator: 1 operand: 3
1	Literal
2	ExprTuple	3
3	Lambda	parameter: 38 body: 5
4	ExprTuple	38
5	Conditional	value: 6 condition: 7
6	Operation	operator: 40 operands: 8
7	Operation	operator: 9 operands: 10
8	ExprTuple	11, 12
9	Literal
10	ExprTuple	38, 13
11	Operation	operator: 44 operands: 14
12	Operation	operator: 44 operands: 15
13	Operation	operator: 16 operands: 17
14	ExprTuple	19, 18
15	ExprTuple	19, 20
16	Literal
17	ExprTuple	21, 22
18	Operation	operator: 31 operand: 27
19	Literal
20	Operation	operator: 40 operands: 24
21	Literal
22	Operation	operator: 25 operands: 26
23	ExprTuple	27
24	ExprTuple	46, 36, 37, 43, 38
25	Literal
26	ExprTuple	42, 28
27	Operation	operator: 29 operands: 30
28	Operation	operator: 31 operand: 34
29	Literal
30	ExprTuple	33, 42
31	Literal
32	ExprTuple	34
33	Operation	operator: 40 operands: 35
34	Literal
35	ExprTuple	46, 36, 37, 38, 39
36	Literal
37	Literal
38	Variable
39	Operation	operator: 40 operands: 41
40	Literal
41	ExprTuple	42, 43
42	Operation	operator: 44 operands: 45
43	Literal
44	Literal
45	ExprTuple	46, 47
46	Literal
47	Literal