Expression of type ExprTuple

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, ExprTuple, 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, ket0
from proveit.physics.quantum.QPE import _phase, two_pow_t

# build up the expression from sub-expressions
expr = ExprTuple(Lambda(k, Conditional(ScalarMult(Exp(e, Mult(two, pi, i, _phase, k)), TensorProd(ket0, 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())

\left(k \mapsto \left\{\mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot \varphi \cdot k} \cdot \left(\lvert 0 \rangle {\otimes} \lvert k \rangle_{t}\right) \textrm{ if } k \in \{0~\ldotp \ldotp~2^{t} - 1\}\right..\right)

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

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