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, Function, Variable, k, t
from proveit.linear_algebra import ScalarMult, TensorProd, VecAdd, VecSum
from proveit.numbers import Add, 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
sub_expr1 = [k]
sub_expr2 = Exp(e, Mult(two, pi, i, _phase, k))
sub_expr3 = Interval(zero, subtract(two_pow_t, one))
expr = ExprTuple(VecSum(index_or_indices = sub_expr1, summand = ScalarMult(sub_expr2, NumKet(k, Add(t, one))), domain = Interval(zero, subtract(Mult(two, two_pow_t), one))), VecAdd(VecSum(index_or_indices = sub_expr1, summand = ScalarMult(sub_expr2, Function(Variable("_a", latex_format = r"{_{-}a}"), sub_expr1)), domain = sub_expr3), ScalarMult(Exp(e, Mult(two, pi, i, _phase, two_pow_t)), TensorProd(ket1, VecSum(index_or_indices = sub_expr1, summand = ScalarMult(sub_expr2, NumKet(k, t)), domain = sub_expr3)))))

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 {_{-}a}\left(k\right)\right)\right) + \left(\mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot \varphi \cdot 2^{t}} \cdot \left(\lvert 1 \rangle {\otimes} \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}\right)\right)\right)\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: 34 operand: 6
2	Operation	operator: 4 operands: 5
3	ExprTuple	6
4	Literal
5	ExprTuple	7, 8
6	Lambda	parameter: 72 body: 9
7	Operation	operator: 34 operand: 14
8	Operation	operator: 49 operands: 11
9	Conditional	value: 12 condition: 13
10	ExprTuple	14
11	ExprTuple	15, 16
12	Operation	operator: 49 operands: 17
13	Operation	operator: 51 operands: 18
14	Lambda	parameter: 72 body: 19
15	Operation	operator: 75 operands: 20
16	Operation	operator: 21 operands: 22
17	ExprTuple	53, 23
18	ExprTuple	72, 24
19	Conditional	value: 25 condition: 47
20	ExprTuple	61, 26
21	Literal
22	ExprTuple	27, 28
23	Operation	operator: 57 operands: 29
24	Operation	operator: 59 operands: 30
25	Operation	operator: 49 operands: 31
26	Operation	operator: 65 operands: 32
27	Operation	operator: 33 operand: 81
28	Operation	operator: 34 operand: 39
29	ExprTuple	72, 36
30	ExprTuple	63, 37
31	ExprTuple	53, 38
32	ExprTuple	79, 69, 70, 71, 73
33	Literal
34	Literal
35	ExprTuple	39
36	Operation	operator: 67 operands: 40
37	Operation	operator: 67 operands: 41
38	Operation	operator: 42 operand: 72
39	Lambda	parameter: 72 body: 44
40	ExprTuple	80, 81
41	ExprTuple	45, 74
42	Variable
43	ExprTuple	72
44	Conditional	value: 46 condition: 47
45	Operation	operator: 65 operands: 48
46	Operation	operator: 49 operands: 50
47	Operation	operator: 51 operands: 52
48	ExprTuple	79, 73
49	Literal
50	ExprTuple	53, 54
51	Literal
52	ExprTuple	72, 55
53	Operation	operator: 75 operands: 56
54	Operation	operator: 57 operands: 58
55	Operation	operator: 59 operands: 60
56	ExprTuple	61, 62
57	Literal
58	ExprTuple	72, 80
59	Literal
60	ExprTuple	63, 64
61	Literal
62	Operation	operator: 65 operands: 66
63	Literal
64	Operation	operator: 67 operands: 68
65	Literal
66	ExprTuple	79, 69, 70, 71, 72
67	Literal
68	ExprTuple	73, 74
69	Literal
70	Literal
71	Literal
72	Variable
73	Operation	operator: 75 operands: 76
74	Operation	operator: 77 operand: 81
75	Literal
76	ExprTuple	79, 80
77	Literal
78	ExprTuple	81
79	Literal
80	Variable
81	Literal