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
from proveit.linear_algebra import ScalarMult
from proveit.logic import InSet
from proveit.numbers import Add, Exp, Interval, Mult, e, i, one, pi, two, zero
from proveit.physics.quantum import Ket
from proveit.physics.quantum.QPE import _phase

# build up the expression from sub-expressions
expr = Lambda(k, Conditional(ScalarMult(Exp(e, Mult(two, pi, i, _phase, k)), Ket(k)), InSet(k, Interval(Add(zero, one), one))))

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 \lvert k \rangle \textrm{ if } k \in \{0 + 1~\ldotp \ldotp~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: 28 body: 1
1	Conditional	value: 2 condition: 3
2	Operation	operator: 4 operands: 5
3	Operation	operator: 6 operands: 7
4	Literal
5	ExprTuple	8, 9
6	Literal
7	ExprTuple	28, 10
8	Operation	operator: 11 operands: 12
9	Operation	operator: 13 operand: 28
10	Operation	operator: 15 operands: 16
11	Literal
12	ExprTuple	17, 18
13	Literal
14	ExprTuple	28
15	Literal
16	ExprTuple	19, 30
17	Literal
18	Operation	operator: 20 operands: 21
19	Operation	operator: 22 operands: 23
20	Literal
21	ExprTuple	24, 25, 26, 27, 28
22	Literal
23	ExprTuple	29, 30
24	Literal
25	Literal
26	Literal
27	Literal
28	Variable
29	Literal
30	Literal