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 Exp, Interval, Mult, e, 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 = 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)))
sub_expr3 = TensorProd(ket0, sub_expr2)
expr = ExprTuple(VecAdd(sub_expr3, ScalarMult(sub_expr1, TensorProd(ket1, sub_expr2))), VecAdd(sub_expr3, TensorProd(ScalarMult(sub_expr1, ket1), sub_expr2)))

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