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, two_pow_t

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

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