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, VecAdd, VecSum
from proveit.numbers import Add, Exp, Interval, Mult, e, frac, i, one, pi, subtract, two, zero
from proveit.physics.quantum import NumKet, ket0, ket1
from proveit.physics.quantum.QPE import _phase, _psi_t_ket, two_pow_t

# build up the expression from sub-expressions
sub_expr1 = Add(t, one)
sub_expr2 = frac(sub_expr1, two)
expr = ExprTuple(ScalarMult(frac(one, Exp(two, sub_expr2)), VecSum(index_or_indices = [k], summand = ScalarMult(Exp(e, Mult(two, pi, i, _phase, k)), NumKet(k, sub_expr1)), domain = Interval(zero, subtract(Mult(two, two_pow_t), one)))), TensorProd(ScalarMult(frac(one, Exp(two, subtract(sub_expr2, frac(t, two)))), VecAdd(ket0, ScalarMult(Exp(e, Mult(two, pi, i, _phase, two_pow_t)), ket1))), _psi_t_ket))

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(\frac{1}{2^{\frac{t + 1}{2}}} \cdot \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)\right), \left(\frac{1}{2^{\frac{t + 1}{2} - \frac{t}{2}}} \cdot \left(\lvert 0 \rangle + \left(\mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot \varphi \cdot 2^{t}} \cdot \lvert 1 \rangle\right)\right)\right) {\otimes} \lvert \psi_{t} \rangle\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: 36 operands: 3
2	Operation	operator: 4 operands: 5
3	ExprTuple	6, 7
4	Literal
5	ExprTuple	8, 9
6	Operation	operator: 78 operands: 10
7	Operation	operator: 11 operand: 17
8	Operation	operator: 36 operands: 13
9	Operation	operator: 14 operand: 85
10	ExprTuple	81, 16
11	Literal
12	ExprTuple	17
13	ExprTuple	18, 19
14	Literal
15	ExprTuple	85
16	Operation	operator: 82 operands: 20
17	Lambda	parameter: 64 body: 22
18	Operation	operator: 78 operands: 23
19	Operation	operator: 24 operands: 25
20	ExprTuple	84, 55
21	ExprTuple	64
22	Conditional	value: 26 condition: 27
23	ExprTuple	81, 28
24	Literal
25	ExprTuple	29, 30
26	Operation	operator: 36 operands: 31
27	Operation	operator: 32 operands: 33
28	Operation	operator: 82 operands: 34
29	Operation	operator: 51 operand: 53
30	Operation	operator: 36 operands: 37
31	ExprTuple	38, 39
32	Literal
33	ExprTuple	64, 40
34	ExprTuple	84, 41
35	ExprTuple	53
36	Literal
37	ExprTuple	42, 43
38	Operation	operator: 82 operands: 44
39	Operation	operator: 45 operands: 46
40	Operation	operator: 47 operands: 48
41	Operation	operator: 76 operands: 49
42	Operation	operator: 82 operands: 50
43	Operation	operator: 51 operand: 81
44	ExprTuple	57, 52
45	Literal
46	ExprTuple	64, 67
47	Literal
48	ExprTuple	53, 54
49	ExprTuple	55, 56
50	ExprTuple	57, 58
51	Literal
52	Operation	operator: 72 operands: 59
53	Literal
54	Operation	operator: 76 operands: 60
55	Operation	operator: 78 operands: 61
56	Operation	operator: 74 operand: 68
57	Literal
58	Operation	operator: 72 operands: 63
59	ExprTuple	84, 69, 70, 71, 64
60	ExprTuple	65, 66
61	ExprTuple	67, 84
62	ExprTuple	68
63	ExprTuple	84, 69, 70, 71, 80
64	Variable
65	Operation	operator: 72 operands: 73
66	Operation	operator: 74 operand: 81
67	Operation	operator: 76 operands: 77
68	Operation	operator: 78 operands: 79
69	Literal
70	Literal
71	Literal
72	Literal
73	ExprTuple	84, 80
74	Literal
75	ExprTuple	81
76	Literal
77	ExprTuple	85, 81
78	Literal
79	ExprTuple	85, 84
80	Operation	operator: 82 operands: 83
81	Literal
82	Literal
83	ExprTuple	84, 85
84	Literal
85	Variable