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 _m_domain, _phase, _t

# build up the expression from sub-expressions
expr = ExprTuple(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(\frac{1}{2^{\frac{t}{2}}}, \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: 14 operands: 3
2	Operation	operator: 4 operand: 7
3	ExprTuple	57, 6
4	Literal
5	ExprTuple	7
6	Operation	operator: 51 operands: 8
7	Lambda	parameter: 48 body: 10
8	ExprTuple	55, 11
9	ExprTuple	48
10	Conditional	value: 12 condition: 13
11	Operation	operator: 14 operands: 15
12	Operation	operator: 34 operands: 16
13	Operation	operator: 17 operands: 18
14	Literal
15	ExprTuple	56, 55
16	ExprTuple	19, 20
17	Literal
18	ExprTuple	48, 21
19	Operation	operator: 51 operands: 22
20	Operation	operator: 23 operands: 24
21	Operation	operator: 25 operands: 26
22	ExprTuple	27, 28
23	Literal
24	ExprTuple	29, 30, 31
25	Literal
26	ExprTuple	32, 33
27	Literal
28	Operation	operator: 34 operands: 35
29	Operation	operator: 36 operands: 37
30	Operation	operator: 38 operand: 56
31	Operation	operator: 40 operands: 41
32	Literal
33	Operation	operator: 42 operands: 43
34	Literal
35	ExprTuple	55, 44, 45, 46, 48
36	Literal
37	ExprTuple	47, 56
38	Literal
39	ExprTuple	56
40	Literal
41	ExprTuple	48, 56
42	Literal
43	ExprTuple	49, 50
44	Literal
45	Literal
46	Literal
47	Variable
48	Variable
49	Operation	operator: 51 operands: 52
50	Operation	operator: 53 operand: 57
51	Literal
52	ExprTuple	55, 56
53	Literal
54	ExprTuple	57
55	Literal
56	Literal
57	Literal