Expression of type InClass

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 k, m
from proveit.linear_algebra import ScalarMult, VecSum
from proveit.logic import InClass
from proveit.numbers import Exp, Mult, e, frac, i, one, pi, two
from proveit.physics.quantum import NumBra, NumKet, Qmult, QmultCodomain
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 = InClass(Qmult(NumBra(m, _t), frac(one, Exp(two, frac(_t, two))), InverseFourierTransform(_t), VecSum(index_or_indices = [k], summand = ScalarMult(Exp(e, Mult(two, pi, i, _phase, k)), NumKet(k, _t)), domain = _m_domain)), QmultCodomain)

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 \thinspace \frac{1}{2^{\frac{t}{2}}} \thinspace {\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) \underset{{\scriptscriptstyle c}}{\in} \mathcal{Q^*}

stored_expr.style_options()

name	description	default	current value	related methods
operation	'infix' or 'function' style formatting	infix	infix
wrap_positions	position(s) at which wrapping is to occur; '2 n - 1' is after the nth operand, '2 n' is after the nth operation.	()	()	('with_wrapping_at', 'with_wrap_before_operator', 'with_wrap_after_operator', 'without_wrapping', 'wrap_positions')
justification	if any wrap positions are set, justify to the 'left', 'center', or 'right'	center	center	('with_justification',)
direction	Direction of the relation (normal or reversed)	normal	normal	('with_direction_reversed', 'is_reversed')

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Operation	operator: 1 operands: 2
1	Literal
2	ExprTuple	3, 4
3	Operation	operator: 5 operands: 6
4	Literal
5	Literal
6	ExprTuple	7, 8, 9, 10
7	Operation	operator: 11 operands: 12
8	Operation	operator: 27 operands: 13
9	Operation	operator: 14 operand: 60
10	Operation	operator: 16 operand: 20
11	Literal
12	ExprTuple	18, 60
13	ExprTuple	61, 19
14	Literal
15	ExprTuple	60
16	Literal
17	ExprTuple	20
18	Variable
19	Operation	operator: 55 operands: 21
20	Lambda	parameter: 52 body: 23
21	ExprTuple	59, 24
22	ExprTuple	52
23	Conditional	value: 25 condition: 26
24	Operation	operator: 27 operands: 28
25	Operation	operator: 29 operands: 30
26	Operation	operator: 31 operands: 32
27	Literal
28	ExprTuple	60, 59
29	Literal
30	ExprTuple	33, 34
31	Literal
32	ExprTuple	52, 35
33	Operation	operator: 55 operands: 36
34	Operation	operator: 37 operands: 38
35	Operation	operator: 39 operands: 40
36	ExprTuple	41, 42
37	Literal
38	ExprTuple	52, 60
39	Literal
40	ExprTuple	43, 44
41	Literal
42	Operation	operator: 45 operands: 46
43	Literal
44	Operation	operator: 47 operands: 48
45	Literal
46	ExprTuple	59, 49, 50, 51, 52
47	Literal
48	ExprTuple	53, 54
49	Literal
50	Literal
51	Literal
52	Variable
53	Operation	operator: 55 operands: 56
54	Operation	operator: 57 operand: 61
55	Literal
56	ExprTuple	59, 60
57	Literal
58	ExprTuple	61
59	Literal
60	Literal
61	Literal