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, frac, i, one, 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 = ExprTuple(NumBra(m, _t), ScalarMult(frac(one, Exp(two, frac(_t, two))), Qmult(InverseFourierTransform(_t), VecSum(index_or_indices = [k], summand = ScalarMult(Exp(e, Mult(two, pi, i, _phase, k)), 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())

\left({_{t}}\langle m \rvert, \frac{1}{2^{\frac{t}{2}}} \cdot \left({\mathrm {FT}}^{\dag}_{t} \thinspace \left(\sum_{k=0}^{2^{t} - 1} \left(\mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot \varphi \cdot k} \cdot \lvert k \rangle_{t}\right)\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 operands: 4
2	Operation	operator: 28 operands: 5
3	Literal
4	ExprTuple	6, 59
5	ExprTuple	7, 8
6	Variable
7	Operation	operator: 22 operands: 9
8	Operation	operator: 10 operands: 11
9	ExprTuple	60, 12
10	Literal
11	ExprTuple	13, 14
12	Operation	operator: 54 operands: 15
13	Operation	operator: 16 operand: 59
14	Operation	operator: 18 operand: 21
15	ExprTuple	58, 20
16	Literal
17	ExprTuple	59
18	Literal
19	ExprTuple	21
20	Operation	operator: 22 operands: 23
21	Lambda	parameter: 51 body: 25
22	Literal
23	ExprTuple	59, 58
24	ExprTuple	51
25	Conditional	value: 26 condition: 27
26	Operation	operator: 28 operands: 29
27	Operation	operator: 30 operands: 31
28	Literal
29	ExprTuple	32, 33
30	Literal
31	ExprTuple	51, 34
32	Operation	operator: 54 operands: 35
33	Operation	operator: 36 operands: 37
34	Operation	operator: 38 operands: 39
35	ExprTuple	40, 41
36	Literal
37	ExprTuple	51, 59
38	Literal
39	ExprTuple	42, 43
40	Literal
41	Operation	operator: 44 operands: 45
42	Literal
43	Operation	operator: 46 operands: 47
44	Literal
45	ExprTuple	58, 48, 49, 50, 51
46	Literal
47	ExprTuple	52, 53
48	Literal
49	Literal
50	Literal
51	Variable
52	Operation	operator: 54 operands: 55
53	Operation	operator: 56 operand: 60
54	Literal
55	ExprTuple	58, 59
56	Literal
57	ExprTuple	60
58	Literal
59	Literal
60	Literal