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

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