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