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