Expression of type Conditional

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 Conditional, k, m
from proveit.linear_algebra import ScalarMult
from proveit.logic import InSet
from proveit.numbers import 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 = Conditional(Qmult(NumBra(m, _t), InverseFourierTransform(_t), ScalarMult(Exp(e, Mult(two, pi, i, _phase, k)), NumKet(k, _t))), InSet(k, _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\{{_{t}}\langle m \rvert \thinspace {\mathrm {FT}}^{\dag}_{t} \thinspace \left(\mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot \varphi \cdot k} \cdot \lvert k \rangle_{t}\right) \textrm{ if } k \in \{0~\ldotp \ldotp~2^{t} - 1\}\right..

stored_expr.style_options()

name	description	default	current value	related methods
condition_delimiter	'comma' or 'and'	comma	comma	('with_comma_delimiter', 'with_conjunction_delimiter')

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Conditional	value: 1 condition: 2
1	Operation	operator: 3 operands: 4
2	Operation	operator: 5 operands: 6
3	Literal
4	ExprTuple	7, 8, 9
5	Literal
6	ExprTuple	42, 10
7	Operation	operator: 11 operands: 12
8	Operation	operator: 13 operand: 44
9	Operation	operator: 15 operands: 16
10	Operation	operator: 17 operands: 18
11	Literal
12	ExprTuple	19, 44
13	Literal
14	ExprTuple	44
15	Literal
16	ExprTuple	20, 21
17	Literal
18	ExprTuple	22, 23
19	Variable
20	Operation	operator: 35 operands: 24
21	Operation	operator: 25 operands: 26
22	Literal
23	Operation	operator: 27 operands: 28
24	ExprTuple	29, 30
25	Literal
26	ExprTuple	42, 44
27	Literal
28	ExprTuple	31, 32
29	Literal
30	Operation	operator: 33 operands: 34
31	Operation	operator: 35 operands: 36
32	Operation	operator: 37 operand: 45
33	Literal
34	ExprTuple	43, 39, 40, 41, 42
35	Literal
36	ExprTuple	43, 44
37	Literal
38	ExprTuple	45
39	Literal
40	Literal
41	Literal
42	Variable
43	Literal
44	Literal
45	Literal