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, 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), VecSum(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: 4 operand: 6
2	Operation	operator: 4 operand: 7
3	ExprTuple	6
4	Literal
5	ExprTuple	7
6	Lambda	parameter: 56 body: 8
7	Lambda	parameter: 56 body: 10
8	Conditional	value: 11 condition: 13
9	ExprTuple	56
10	Conditional	value: 12 condition: 13
11	Operation	operator: 23 operands: 14
12	Operation	operator: 47 operands: 15
13	Operation	operator: 16 operands: 17
14	ExprTuple	28, 29, 18
15	ExprTuple	27, 19
16	Literal
17	ExprTuple	56, 20
18	Operation	operator: 21 operands: 22
19	Operation	operator: 23 operands: 24
20	Operation	operator: 25 operands: 26
21	Literal
22	ExprTuple	27, 30
23	Literal
24	ExprTuple	28, 29, 30
25	Literal
26	ExprTuple	31, 32
27	Operation	operator: 49 operands: 33
28	Operation	operator: 34 operands: 35
29	Operation	operator: 36 operand: 58
30	Operation	operator: 38 operands: 39
31	Literal
32	Operation	operator: 40 operands: 41
33	ExprTuple	42, 43
34	Literal
35	ExprTuple	44, 58
36	Literal
37	ExprTuple	58
38	Literal
39	ExprTuple	56, 58
40	Literal
41	ExprTuple	45, 46
42	Literal
43	Operation	operator: 47 operands: 48
44	Variable
45	Operation	operator: 49 operands: 50
46	Operation	operator: 51 operand: 59
47	Literal
48	ExprTuple	57, 53, 54, 55, 56
49	Literal
50	ExprTuple	57, 58
51	Literal
52	ExprTuple	59
53	Literal
54	Literal
55	Literal
56	Variable
57	Literal
58	Literal
59	Literal