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, Variable, k, t
from proveit.linear_algebra import ScalarMult, VecAdd, 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 = ScalarMult(Exp(e, Mult(two, pi, i, _phase, k)), NumKet(k, Add(t, one)))
expr = ExprTuple(VecSum(index_or_indices = sub_expr1, summand = sub_expr2, domain = Interval(zero, subtract(Mult(two, two_pow_t), one))), VecAdd(VecSum(index_or_indices = sub_expr1, summand = sub_expr2, domain = Interval(zero, subtract(two_pow_t, one))), Variable("_a", latex_format = r"{_{-}a}")))

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}^{\left(2 \cdot 2^{t}\right) - 1} \left(\mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot \varphi \cdot k} \cdot \lvert k \rangle_{t + 1}\right), \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)\right) + {_{-}a}\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: 10 operand: 6
2	Operation	operator: 4 operands: 5
3	ExprTuple	6
4	Literal
5	ExprTuple	7, 8
6	Lambda	parameter: 50 body: 9
7	Operation	operator: 10 operand: 13
8	Variable
9	Conditional	value: 18 condition: 12
10	Literal
11	ExprTuple	13
12	Operation	operator: 23 operands: 14
13	Lambda	parameter: 50 body: 16
14	ExprTuple	50, 17
15	ExprTuple	50
16	Conditional	value: 18 condition: 19
17	Operation	operator: 33 operands: 20
18	Operation	operator: 21 operands: 22
19	Operation	operator: 23 operands: 24
20	ExprTuple	39, 25
21	Literal
22	ExprTuple	26, 27
23	Literal
24	ExprTuple	50, 28
25	Operation	operator: 45 operands: 29
26	Operation	operator: 53 operands: 30
27	Operation	operator: 31 operands: 32
28	Operation	operator: 33 operands: 34
29	ExprTuple	35, 52
30	ExprTuple	36, 37
31	Literal
32	ExprTuple	50, 38
33	Literal
34	ExprTuple	39, 40
35	Operation	operator: 42 operands: 41
36	Literal
37	Operation	operator: 42 operands: 43
38	Operation	operator: 45 operands: 44
39	Literal
40	Operation	operator: 45 operands: 46
41	ExprTuple	57, 51
42	Literal
43	ExprTuple	57, 47, 48, 49, 50
44	ExprTuple	58, 59
45	Literal
46	ExprTuple	51, 52
47	Literal
48	Literal
49	Literal
50	Variable
51	Operation	operator: 53 operands: 54
52	Operation	operator: 55 operand: 59
53	Literal
54	ExprTuple	57, 58
55	Literal
56	ExprTuple	59
57	Literal
58	Variable
59	Literal