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, Sum, e, i, pi, two
from proveit.physics.quantum import NumBra, NumKet, Qmult
from proveit.physics.quantum.QFT import InverseFourierTransform
from proveit.physics.quantum.QPE import _m_domain, _phase, _t

# build up the expression from sub-expressions
expr = Sum(index_or_indices = [k], summand = Mult(Exp(e, Mult(two, pi, i, _phase, k)), Qmult(NumBra(m, _t), InverseFourierTransform(_t), NumKet(k, _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 \left({_{t}}\langle m \rvert \thinspace {\mathrm {FT}}^{\dag}_{t} \thinspace \lvert k \rangle_{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: 40 body: 5
4	ExprTuple	40
5	Conditional	value: 6 condition: 7
6	Operation	operator: 26 operands: 8
7	Operation	operator: 9 operands: 10
8	ExprTuple	11, 12
9	Literal
10	ExprTuple	40, 13
11	Operation	operator: 43 operands: 14
12	Operation	operator: 15 operands: 16
13	Operation	operator: 17 operands: 18
14	ExprTuple	19, 20
15	Literal
16	ExprTuple	21, 22, 23
17	Literal
18	ExprTuple	24, 25
19	Literal
20	Operation	operator: 26 operands: 27
21	Operation	operator: 28 operands: 29
22	Operation	operator: 30 operand: 48
23	Operation	operator: 32 operands: 33
24	Literal
25	Operation	operator: 34 operands: 35
26	Literal
27	ExprTuple	47, 36, 37, 38, 40
28	Literal
29	ExprTuple	39, 48
30	Literal
31	ExprTuple	48
32	Literal
33	ExprTuple	40, 48
34	Literal
35	ExprTuple	41, 42
36	Literal
37	Literal
38	Literal
39	Variable
40	Variable
41	Operation	operator: 43 operands: 44
42	Operation	operator: 45 operand: 49
43	Literal
44	ExprTuple	47, 48
45	Literal
46	ExprTuple	49
47	Literal
48	Literal
49	Literal