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 = 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(frac(one, Exp(two, frac(Add(t, one), two))), VecAdd(TensorProd(ket0, sub_expr1), ScalarMult(Exp(e, Mult(two, pi, i, _phase, two_pow_t)), TensorProd(ket1, sub_expr1))))

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}}}, \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)

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: 16 operands: 3
2	Operation	operator: 4 operands: 5
3	ExprTuple	68, 6
4	Literal
5	ExprTuple	7, 8
6	Operation	operator: 62 operands: 9
7	Operation	operator: 20 operands: 10
8	Operation	operator: 36 operands: 11
9	ExprTuple	66, 12
10	ExprTuple	13, 25
11	ExprTuple	14, 15
12	Operation	operator: 16 operands: 17
13	Operation	operator: 28 operand: 50
14	Operation	operator: 62 operands: 19
15	Operation	operator: 20 operands: 21
16	Literal
17	ExprTuple	22, 66
18	ExprTuple	50
19	ExprTuple	48, 23
20	Literal
21	ExprTuple	24, 25
22	Operation	operator: 54 operands: 26
23	Operation	operator: 52 operands: 27
24	Operation	operator: 28 operand: 68
25	Operation	operator: 29 operand: 31
26	ExprTuple	67, 68
27	ExprTuple	66, 56, 57, 58, 60
28	Literal
29	Literal
30	ExprTuple	31
31	Lambda	parameter: 59 body: 33
32	ExprTuple	59
33	Conditional	value: 34 condition: 35
34	Operation	operator: 36 operands: 37
35	Operation	operator: 38 operands: 39
36	Literal
37	ExprTuple	40, 41
38	Literal
39	ExprTuple	59, 42
40	Operation	operator: 62 operands: 43
41	Operation	operator: 44 operands: 45
42	Operation	operator: 46 operands: 47
43	ExprTuple	48, 49
44	Literal
45	ExprTuple	59, 67
46	Literal
47	ExprTuple	50, 51
48	Literal
49	Operation	operator: 52 operands: 53
50	Literal
51	Operation	operator: 54 operands: 55
52	Literal
53	ExprTuple	66, 56, 57, 58, 59
54	Literal
55	ExprTuple	60, 61
56	Literal
57	Literal
58	Literal
59	Variable
60	Operation	operator: 62 operands: 63
61	Operation	operator: 64 operand: 68
62	Literal
63	ExprTuple	66, 67
64	Literal
65	ExprTuple	68
66	Literal
67	Variable
68	Literal