Expression of type InSet

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 InSet
from proveit.numbers import Complex, Exp, Mult, e, i, 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 = InSet(Qmult(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)), Complex)

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(\left({_{t}}\langle m \rvert \thinspace {\mathrm {FT}}^{\dag}_{t}\right) \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) \in \mathbb{C}

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