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 ExprRange, ExprTuple, Variable, k, t
from proveit.core_expr_types import Len
from proveit.linear_algebra import ScalarMult, VecAdd, VecSum
from proveit.numbers import Exp, Interval, Mult, e, i, one, pi, subtract, two, zero
from proveit.physics.quantum import NumKet, ket0, ket1
from proveit.physics.quantum.QPE import _phase, two_pow_t

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
expr = ExprTuple(Len(operands = [VecAdd(ket0, ScalarMult(Exp(e, Mult(two, pi, i, _phase, two_pow_t)), ket1)), VecSum(index_or_indices = [k], summand = ScalarMult(Exp(e, Mult(two, pi, i, _phase, k)), NumKet(k, t)), domain = Interval(zero, subtract(two_pow_t, one)))]), Len(operands = [ExprRange(sub_expr1, sub_expr1, one, two)]))

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(|\left(\lvert 0 \rangle + \left(\mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot \varphi \cdot 2^{t}} \cdot \lvert 1 \rangle\right), \sum_{k=0}^{2^{t} - 1} \left(\mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot \varphi \cdot k} \cdot \lvert k \rangle_{t}\right)\right)|, |\left(1, \ldots, 2\right)|\right)

stored_expr.style_options()

name	description	default	current value	related methods
wrap_positions	position(s) at which wrapping is to occur; 'n' is after the nth comma.	()	()	('with_wrapping_at',)
justification	if any wrap positions are set, justify to the 'left', 'center', or 'right'	left	left	('with_justification',)

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	ExprTuple	1, 2
1	Operation	operator: 4 operands: 3
2	Operation	operator: 4 operands: 5
3	ExprTuple	6, 7
4	Literal
5	ExprTuple	8
6	Operation	operator: 9 operands: 10
7	Operation	operator: 11 operand: 16
8	ExprRange	lambda_map: 13 start_index: 63 end_index: 61
9	Literal
10	ExprTuple	14, 15
11	Literal
12	ExprTuple	16
13	Lambda	parameter: 22 body: 22
14	Operation	operator: 28 operand: 45
15	Operation	operator: 29 operands: 19
16	Lambda	parameter: 54 body: 21
17	ExprTuple	22
18	ExprTuple	45
19	ExprTuple	23, 24
20	ExprTuple	54
21	Conditional	value: 25 condition: 26
22	Variable
23	Operation	operator: 57 operands: 27
24	Operation	operator: 28 operand: 63
25	Operation	operator: 29 operands: 30
26	Operation	operator: 31 operands: 32
27	ExprTuple	43, 33
28	Literal
29	Literal
30	ExprTuple	34, 35
31	Literal
32	ExprTuple	54, 36
33	Operation	operator: 47 operands: 37
34	Operation	operator: 57 operands: 38
35	Operation	operator: 39 operands: 40
36	Operation	operator: 41 operands: 42
37	ExprTuple	61, 51, 52, 53, 55
38	ExprTuple	43, 44
39	Literal
40	ExprTuple	54, 62
41	Literal
42	ExprTuple	45, 46
43	Literal
44	Operation	operator: 47 operands: 48
45	Literal
46	Operation	operator: 49 operands: 50
47	Literal
48	ExprTuple	61, 51, 52, 53, 54
49	Literal
50	ExprTuple	55, 56
51	Literal
52	Literal
53	Literal
54	Variable
55	Operation	operator: 57 operands: 58
56	Operation	operator: 59 operand: 63
57	Literal
58	ExprTuple	61, 62
59	Literal
60	ExprTuple	63
61	Literal
62	Variable
63	Literal