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 ScalarMult, 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 = NumBra(m, _t)
sub_expr3 = InverseFourierTransform(_t)
sub_expr4 = NumKet(k, _t)
sub_expr5 = Exp(e, Mult(two, pi, i, _phase, k))
expr = ExprTuple(VecSum(index_or_indices = sub_expr1, summand = Qmult(sub_expr2, sub_expr3, ScalarMult(sub_expr5, sub_expr4)), domain = _m_domain), Sum(index_or_indices = sub_expr1, summand = Mult(sub_expr5, Qmult(sub_expr2, sub_expr3, sub_expr4)), 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({_{t}}\langle m \rvert \thinspace {\mathrm {FT}}^{\dag}_{t} \thinspace \left(\mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot \varphi \cdot k} \cdot \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: 7
2	Operation	operator: 5 operand: 8
3	Literal
4	ExprTuple	7
5	Literal
6	ExprTuple	8
7	Lambda	parameter: 57 body: 9
8	Lambda	parameter: 57 body: 11
9	Conditional	value: 12 condition: 14
10	ExprTuple	57
11	Conditional	value: 13 condition: 14
12	Operation	operator: 24 operands: 15
13	Operation	operator: 48 operands: 16
14	Operation	operator: 17 operands: 18
15	ExprTuple	29, 30, 19
16	ExprTuple	28, 20
17	Literal
18	ExprTuple	57, 21
19	Operation	operator: 22 operands: 23
20	Operation	operator: 24 operands: 25
21	Operation	operator: 26 operands: 27
22	Literal
23	ExprTuple	28, 31
24	Literal
25	ExprTuple	29, 30, 31
26	Literal
27	ExprTuple	32, 33
28	Operation	operator: 50 operands: 34
29	Operation	operator: 35 operands: 36
30	Operation	operator: 37 operand: 59
31	Operation	operator: 39 operands: 40
32	Literal
33	Operation	operator: 41 operands: 42
34	ExprTuple	43, 44
35	Literal
36	ExprTuple	45, 59
37	Literal
38	ExprTuple	59
39	Literal
40	ExprTuple	57, 59
41	Literal
42	ExprTuple	46, 47
43	Literal
44	Operation	operator: 48 operands: 49
45	Variable
46	Operation	operator: 50 operands: 51
47	Operation	operator: 52 operand: 60
48	Literal
49	ExprTuple	58, 54, 55, 56, 57
50	Literal
51	ExprTuple	58, 59
52	Literal
53	ExprTuple	60
54	Literal
55	Literal
56	Literal
57	Variable
58	Literal
59	Literal
60	Literal