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, t
from proveit.linear_algebra import ScalarMult, TensorProd
from proveit.logic import InSet
from proveit.numbers import Exp, Interval, Mult, e, i, one, pi, subtract, two, zero
from proveit.physics.quantum import NumKet, ket1
from proveit.physics.quantum.QPE import _phase, two_pow_t

# build up the expression from sub-expressions
expr = Lambda(k, Conditional(ScalarMult(Mult(Exp(e, Mult(two, pi, i, _phase, k)), Exp(e, Mult(two, pi, i, _phase, two_pow_t))), TensorProd(ket1, NumKet(k, t))), InSet(k, Interval(zero, subtract(two_pow_t, 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\{\left(\mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot \varphi \cdot k} \cdot \mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot \varphi \cdot 2^{t}}\right) \cdot \left(\lvert 1 \rangle {\otimes} \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: 39 body: 2
1	ExprTuple	39
2	Conditional	value: 3 condition: 4
3	Operation	operator: 5 operands: 6
4	Operation	operator: 7 operands: 8
5	Literal
6	ExprTuple	9, 10
7	Literal
8	ExprTuple	39, 11
9	Operation	operator: 35 operands: 12
10	Operation	operator: 13 operands: 14
11	Operation	operator: 15 operands: 16
12	ExprTuple	17, 18
13	Literal
14	ExprTuple	19, 20
15	Literal
16	ExprTuple	21, 22
17	Operation	operator: 45 operands: 23
18	Operation	operator: 45 operands: 24
19	Operation	operator: 25 operand: 44
20	Operation	operator: 26 operands: 27
21	Literal
22	Operation	operator: 28 operands: 29
23	ExprTuple	31, 30
24	ExprTuple	31, 32
25	Literal
26	Literal
27	ExprTuple	39, 48
28	Literal
29	ExprTuple	43, 33
30	Operation	operator: 35 operands: 34
31	Literal
32	Operation	operator: 35 operands: 36
33	Operation	operator: 37 operand: 44
34	ExprTuple	47, 40, 41, 42, 39
35	Literal
36	ExprTuple	47, 40, 41, 42, 43
37	Literal
38	ExprTuple	44
39	Variable
40	Literal
41	Literal
42	Literal
43	Operation	operator: 45 operands: 46
44	Literal
45	Literal
46	ExprTuple	47, 48
47	Literal
48	Variable