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 ExprTuple, k, t
from proveit.linear_algebra import ScalarMult, VecSum
from proveit.numbers import Add, Exp, Interval, Mult, e, i, one, pi, subtract, two, zero
from proveit.physics.quantum import NumKet
from proveit.physics.quantum.QPE import _phase, two_pow_t

# build up the expression from sub-expressions
sub_expr1 = [k]
sub_expr2 = Add(t, one)
sub_expr3 = Add(k, two_pow_t)
sub_expr4 = Interval(zero, subtract(two_pow_t, one))
expr = ExprTuple(VecSum(index_or_indices = sub_expr1, summand = ScalarMult(Exp(e, Mult(two, pi, i, _phase, k)), NumKet(k, sub_expr2)), domain = sub_expr4), VecSum(index_or_indices = sub_expr1, summand = ScalarMult(Exp(e, Mult(two, pi, i, _phase, sub_expr3)), NumKet(sub_expr3, sub_expr2)), domain = sub_expr4))

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(\sum_{k=0}^{2^{t} - 1} \left(\mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot \varphi \cdot k} \cdot \lvert k \rangle_{t + 1}\right), \sum_{k=0}^{2^{t} - 1} \left(\mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot \varphi \cdot \left(k + 2^{t}\right)} \cdot \lvert k + 2^{t} \rangle_{t + 1}\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 operand: 6
2	Operation	operator: 4 operand: 7
3	ExprTuple	6
4	Literal
5	ExprTuple	7
6	Lambda	parameter: 51 body: 8
7	Lambda	parameter: 51 body: 10
8	Conditional	value: 11 condition: 13
9	ExprTuple	51
10	Conditional	value: 12 condition: 13
11	Operation	operator: 15 operands: 14
12	Operation	operator: 15 operands: 16
13	Operation	operator: 17 operands: 18
14	ExprTuple	19, 20
15	Literal
16	ExprTuple	21, 22
17	Literal
18	ExprTuple	51, 23
19	Operation	operator: 54 operands: 24
20	Operation	operator: 27 operands: 25
21	Operation	operator: 54 operands: 26
22	Operation	operator: 27 operands: 28
23	Operation	operator: 29 operands: 30
24	ExprTuple	32, 31
25	ExprTuple	51, 34
26	ExprTuple	32, 33
27	Literal
28	ExprTuple	45, 34
29	Literal
30	ExprTuple	35, 36
31	Operation	operator: 38 operands: 37
32	Literal
33	Operation	operator: 38 operands: 39
34	Operation	operator: 47 operands: 40
35	Literal
36	Operation	operator: 47 operands: 41
37	ExprTuple	56, 42, 43, 44, 51
38	Literal
39	ExprTuple	56, 42, 43, 44, 45
40	ExprTuple	57, 53
41	ExprTuple	52, 46
42	Literal
43	Literal
44	Literal
45	Operation	operator: 47 operands: 48
46	Operation	operator: 49 operand: 53
47	Literal
48	ExprTuple	51, 52
49	Literal
50	ExprTuple	53
51	Variable
52	Operation	operator: 54 operands: 55
53	Literal
54	Literal
55	ExprTuple	56, 57
56	Literal
57	Variable