Expression of type Lambda

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, Lambda, k, m
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 = Lambda(k, Conditional(Mult(Exp(e, Mult(two, pi, i, _phase, k)), Qmult(NumBra(m, _t), InverseFourierTransform(_t), 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())

k \mapsto \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) \textrm{ if } k \in \{0~\ldotp \ldotp~2^{t} - 1\}\right..

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

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