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.numbers import Exp, Mult, Sum, 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 _alpha_m, _m_domain, _phase, _t

# build up the expression from sub-expressions
expr = ExprTuple(_alpha_m, Mult(frac(one, Exp(two, frac(_t, two))), 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())

\left(\alpha_{m}, \frac{1}{2^{\frac{t}{2}}} \cdot \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)\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: 52
2	Operation	operator: 39 operands: 5
3	Literal
4	ExprTuple	52
5	ExprTuple	6, 7
6	Operation	operator: 19 operands: 8
7	Operation	operator: 9 operand: 12
8	ExprTuple	62, 11
9	Literal
10	ExprTuple	12
11	Operation	operator: 56 operands: 13
12	Lambda	parameter: 53 body: 15
13	ExprTuple	60, 16
14	ExprTuple	53
15	Conditional	value: 17 condition: 18
16	Operation	operator: 19 operands: 20
17	Operation	operator: 39 operands: 21
18	Operation	operator: 22 operands: 23
19	Literal
20	ExprTuple	61, 60
21	ExprTuple	24, 25
22	Literal
23	ExprTuple	53, 26
24	Operation	operator: 56 operands: 27
25	Operation	operator: 28 operands: 29
26	Operation	operator: 30 operands: 31
27	ExprTuple	32, 33
28	Literal
29	ExprTuple	34, 35, 36
30	Literal
31	ExprTuple	37, 38
32	Literal
33	Operation	operator: 39 operands: 40
34	Operation	operator: 41 operands: 42
35	Operation	operator: 43 operand: 61
36	Operation	operator: 45 operands: 46
37	Literal
38	Operation	operator: 47 operands: 48
39	Literal
40	ExprTuple	60, 49, 50, 51, 53
41	Literal
42	ExprTuple	52, 61
43	Literal
44	ExprTuple	61
45	Literal
46	ExprTuple	53, 61
47	Literal
48	ExprTuple	54, 55
49	Literal
50	Literal
51	Literal
52	Variable
53	Variable
54	Operation	operator: 56 operands: 57
55	Operation	operator: 58 operand: 62
56	Literal
57	ExprTuple	60, 61
58	Literal
59	ExprTuple	62
60	Literal
61	Literal
62	Literal