Expression of type ExprTuple

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 ExprTuple, k, m
from proveit.linear_algebra import VecSum
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
sub_expr1 = [k]
sub_expr2 = Mult(Exp(e, Mult(two, pi, i, _phase, k)), Qmult(NumBra(m, _t), InverseFourierTransform(_t), NumKet(k, _t)))
expr = ExprTuple(VecSum(index_or_indices = sub_expr1, summand = sub_expr2, domain = _m_domain), Sum(index_or_indices = sub_expr1, summand = sub_expr2, 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())

\left(\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), \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)\right)

stored_expr.style_options()

name	description	default	current value	related methods
wrap_positions	position(s) at which wrapping is to occur; 'n' is after the nth comma.	()	()	('with_wrapping_at',)
justification	if any wrap positions are set, justify to the 'left', 'center', or 'right'	left	left	('with_justification',)

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	ExprTuple	1, 2
1	Operation	operator: 3 operand: 6
2	Operation	operator: 4 operand: 6
3	Literal
4	Literal
5	ExprTuple	6
6	Lambda	parameter: 43 body: 8
7	ExprTuple	43
8	Conditional	value: 9 condition: 10
9	Operation	operator: 29 operands: 11
10	Operation	operator: 12 operands: 13
11	ExprTuple	14, 15
12	Literal
13	ExprTuple	43, 16
14	Operation	operator: 46 operands: 17
15	Operation	operator: 18 operands: 19
16	Operation	operator: 20 operands: 21
17	ExprTuple	22, 23
18	Literal
19	ExprTuple	24, 25, 26
20	Literal
21	ExprTuple	27, 28
22	Literal
23	Operation	operator: 29 operands: 30
24	Operation	operator: 31 operands: 32
25	Operation	operator: 33 operand: 51
26	Operation	operator: 35 operands: 36
27	Literal
28	Operation	operator: 37 operands: 38
29	Literal
30	ExprTuple	50, 39, 40, 41, 43
31	Literal
32	ExprTuple	42, 51
33	Literal
34	ExprTuple	51
35	Literal
36	ExprTuple	43, 51
37	Literal
38	ExprTuple	44, 45
39	Literal
40	Literal
41	Literal
42	Variable
43	Variable
44	Operation	operator: 46 operands: 47
45	Operation	operator: 48 operand: 52
46	Literal
47	ExprTuple	50, 51
48	Literal
49	ExprTuple	52
50	Literal
51	Literal
52	Literal