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.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 = Lambda(k, 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())

k \mapsto \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()

no style options

# display the expression information
stored_expr.expr_info()

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