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

# build up the expression from sub-expressions
expr = Sum(index_or_indices = [k], summand = Mult(frac(one, Exp(two, frac(_t, two))), Mult(Exp(e, Mult(two, pi, i, _phase, k)), Exp(e, Neg(frac(Mult(two, pi, i, k, m), _two_pow_t))))), 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(\frac{1}{2^{\frac{t}{2}}} \cdot \left(\mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot \varphi \cdot k} \cdot \mathsf{e}^{-\frac{2 \cdot \pi \cdot \mathsf{i} \cdot k \cdot m}{2^{t}}}\right)\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: 51 body: 5
4	ExprTuple	51
5	Conditional	value: 6 condition: 7
6	Operation	operator: 45 operands: 8
7	Operation	operator: 9 operands: 10
8	ExprTuple	11, 12
9	Literal
10	ExprTuple	51, 13
11	Operation	operator: 41 operands: 14
12	Operation	operator: 45 operands: 15
13	Operation	operator: 16 operands: 17
14	ExprTuple	40, 18
15	ExprTuple	19, 20
16	Literal
17	ExprTuple	21, 22
18	Operation	operator: 47 operands: 23
19	Operation	operator: 47 operands: 24
20	Operation	operator: 47 operands: 25
21	Literal
22	Operation	operator: 26 operands: 27
23	ExprTuple	53, 28
24	ExprTuple	30, 29
25	ExprTuple	30, 31
26	Literal
27	ExprTuple	44, 32
28	Operation	operator: 41 operands: 33
29	Operation	operator: 45 operands: 34
30	Literal
31	Operation	operator: 36 operand: 39
32	Operation	operator: 36 operand: 40
33	ExprTuple	54, 53
34	ExprTuple	53, 49, 50, 38, 51
35	ExprTuple	39
36	Literal
37	ExprTuple	40
38	Literal
39	Operation	operator: 41 operands: 42
40	Literal
41	Literal
42	ExprTuple	43, 44
43	Operation	operator: 45 operands: 46
44	Operation	operator: 47 operands: 48
45	Literal
46	ExprTuple	53, 49, 50, 51, 52
47	Literal
48	ExprTuple	53, 54
49	Literal
50	Literal
51	Variable
52	Variable
53	Literal
54	Literal