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, Mod, Mult, Neg, e, frac, i, pi, two
from proveit.physics.quantum.QPE import _m_domain, _phase, _two_pow_t

# build up the expression from sub-expressions
expr = Lambda(k, Conditional(Mult(Exp(e, Neg(frac(Mult(two, pi, i, k, Mod(m, _two_pow_t)), _two_pow_t))), Exp(e, Mult(two, pi, i, _phase, k))), 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}^{-\frac{2 \cdot \pi \cdot \mathsf{i} \cdot k \cdot \left(m ~\textup{mod}~ 2^{t}\right)}{2^{t}}} \cdot \mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot \varphi \cdot k} \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: 33 operands: 5
4	Operation	operator: 6 operands: 7
5	ExprTuple	8, 9
6	Literal
7	ExprTuple	37, 10
8	Operation	operator: 43 operands: 11
9	Operation	operator: 43 operands: 12
10	Operation	operator: 13 operands: 14
11	ExprTuple	16, 15
12	ExprTuple	16, 17
13	Literal
14	ExprTuple	18, 19
15	Operation	operator: 29 operand: 24
16	Literal
17	Operation	operator: 33 operands: 21
18	Literal
19	Operation	operator: 22 operands: 23
20	ExprTuple	24
21	ExprTuple	45, 35, 36, 25, 37
22	Literal
23	ExprTuple	42, 26
24	Operation	operator: 27 operands: 28
25	Literal
26	Operation	operator: 29 operand: 32
27	Literal
28	ExprTuple	31, 42
29	Literal
30	ExprTuple	32
31	Operation	operator: 33 operands: 34
32	Literal
33	Literal
34	ExprTuple	45, 35, 36, 37, 38
35	Literal
36	Literal
37	Variable
38	Operation	operator: 39 operands: 40
39	Literal
40	ExprTuple	41, 42
41	Variable
42	Operation	operator: 43 operands: 44
43	Literal
44	ExprTuple	45, 46
45	Literal
46	Literal