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)
sub_expr2 = frac(Add(t, one), two)
sub_expr3 = TensorProd(VecAdd(ket0, ScalarMult(Exp(e, Mult(two, pi, i, _phase, two_pow_t)), ket1)), 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 = ExprTuple(ScalarMult(Mult(frac(one, Exp(two, subtract(sub_expr2, sub_expr1))), frac(one, Exp(two, sub_expr1))), sub_expr3), ScalarMult(frac(one, Exp(two, sub_expr2)), 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(\left(\frac{1}{2^{\frac{t + 1}{2} - \frac{t}{2}}} \cdot \frac{1}{2^{\frac{t}{2}}}\right) \cdot \left(\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(\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), \frac{1}{2^{\frac{t + 1}{2}}} \cdot \left(\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(\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: 43 operands: 3
2	Operation	operator: 43 operands: 4
3	ExprTuple	5, 7
4	ExprTuple	6, 7
5	Operation	operator: 70 operands: 8
6	Operation	operator: 68 operands: 9
7	Operation	operator: 10 operands: 11
8	ExprTuple	12, 13
9	ExprTuple	86, 14
10	Literal
11	ExprTuple	15, 16
12	Operation	operator: 68 operands: 17
13	Operation	operator: 68 operands: 18
14	Operation	operator: 80 operands: 19
15	Operation	operator: 20 operands: 21
16	Operation	operator: 22 operand: 28
17	ExprTuple	86, 24
18	ExprTuple	86, 25
19	ExprTuple	84, 47
20	Literal
21	ExprTuple	26, 27
22	Literal
23	ExprTuple	28
24	Operation	operator: 80 operands: 29
25	Operation	operator: 80 operands: 30
26	Operation	operator: 42 operand: 65
27	Operation	operator: 43 operands: 32
28	Lambda	parameter: 77 body: 34
29	ExprTuple	84, 35
30	ExprTuple	84, 62
31	ExprTuple	65
32	ExprTuple	36, 37
33	ExprTuple	77
34	Conditional	value: 38 condition: 39
35	Operation	operator: 72 operands: 40
36	Operation	operator: 80 operands: 41
37	Operation	operator: 42 operand: 86
38	Operation	operator: 43 operands: 44
39	Operation	operator: 45 operands: 46
40	ExprTuple	47, 48
41	ExprTuple	63, 49
42	Literal
43	Literal
44	ExprTuple	50, 51
45	Literal
46	ExprTuple	77, 52
47	Operation	operator: 68 operands: 53
48	Operation	operator: 82 operand: 62
49	Operation	operator: 70 operands: 55
50	Operation	operator: 80 operands: 56
51	Operation	operator: 57 operands: 58
52	Operation	operator: 59 operands: 60
53	ExprTuple	61, 84
54	ExprTuple	62
55	ExprTuple	84, 74, 75, 76, 78
56	ExprTuple	63, 64
57	Literal
58	ExprTuple	77, 85
59	Literal
60	ExprTuple	65, 66
61	Operation	operator: 72 operands: 67
62	Operation	operator: 68 operands: 69
63	Literal
64	Operation	operator: 70 operands: 71
65	Literal
66	Operation	operator: 72 operands: 73
67	ExprTuple	85, 86
68	Literal
69	ExprTuple	85, 84
70	Literal
71	ExprTuple	84, 74, 75, 76, 77
72	Literal
73	ExprTuple	78, 79
74	Literal
75	Literal
76	Literal
77	Variable
78	Operation	operator: 80 operands: 81
79	Operation	operator: 82 operand: 86
80	Literal
81	ExprTuple	84, 85
82	Literal
83	ExprTuple	86
84	Literal
85	Variable
86	Literal