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 = Exp(e, Mult(two, pi, i, _phase, two_pow_t))
sub_expr2 = frac(one, Exp(two, frac(Add(t, one), two)))
sub_expr3 = 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(sub_expr2, VecAdd(TensorProd(ket0, sub_expr3), ScalarMult(sub_expr1, TensorProd(ket1, sub_expr3)))), ScalarMult(sub_expr2, TensorProd(VecAdd(ket0, ScalarMult(sub_expr1, ket1)), 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(\frac{1}{2^{\frac{t + 1}{2}}} \cdot \left(\left(\lvert 0 \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) + \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), \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: 46 operands: 3
2	Operation	operator: 46 operands: 4
3	ExprTuple	6, 5
4	ExprTuple	6, 7
5	Operation	operator: 18 operands: 8
6	Operation	operator: 26 operands: 9
7	Operation	operator: 24 operands: 10
8	ExprTuple	11, 12
9	ExprTuple	78, 13
10	ExprTuple	14, 30
11	Operation	operator: 24 operands: 15
12	Operation	operator: 46 operands: 16
13	Operation	operator: 72 operands: 17
14	Operation	operator: 18 operands: 19
15	ExprTuple	22, 30
16	ExprTuple	32, 20
17	ExprTuple	76, 21
18	Literal
19	ExprTuple	22, 23
20	Operation	operator: 24 operands: 25
21	Operation	operator: 26 operands: 27
22	Operation	operator: 38 operand: 60
23	Operation	operator: 46 operands: 29
24	Literal
25	ExprTuple	33, 30
26	Literal
27	ExprTuple	31, 76
28	ExprTuple	60
29	ExprTuple	32, 33
30	Operation	operator: 34 operand: 39
31	Operation	operator: 64 operands: 36
32	Operation	operator: 72 operands: 37
33	Operation	operator: 38 operand: 78
34	Literal
35	ExprTuple	39
36	ExprTuple	77, 78
37	ExprTuple	58, 40
38	Literal
39	Lambda	parameter: 69 body: 42
40	Operation	operator: 62 operands: 43
41	ExprTuple	69
42	Conditional	value: 44 condition: 45
43	ExprTuple	76, 66, 67, 68, 70
44	Operation	operator: 46 operands: 47
45	Operation	operator: 48 operands: 49
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