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 ExprRange, ExprTuple, Variable, t
from proveit.core_expr_types import Len
from proveit.linear_algebra import ScalarMult, VecAdd
from proveit.numbers import Add, Exp, Mult, Neg, e, frac, i, one, pi, sqrt, two, zero
from proveit.physics.quantum import ket0, ket1
from proveit.physics.quantum.QPE import _ket_u, _phase

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
sub_expr2 = Neg(t)
sub_expr3 = frac(one, sqrt(two))
expr = ExprTuple(Len(operands = [ScalarMult(sub_expr3, VecAdd(ket0, ScalarMult(Exp(e, Mult(two, pi, i, Exp(two, Neg(Add(sub_expr2, one))), _phase)), ket1))), ExprRange(sub_expr1, ScalarMult(sub_expr3, VecAdd(ket0, ScalarMult(Exp(e, Mult(two, pi, i, Exp(two, Neg(sub_expr1)), _phase)), ket1))), Add(sub_expr2, two), zero), _ket_u]), Add(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(|\left(\frac{1}{\sqrt{2}} \cdot \left(\lvert 0 \rangle + \left(\mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot 2^{-\left(-t + 1\right)} \cdot \varphi} \cdot \lvert 1 \rangle\right)\right),\left(\frac{1}{\sqrt{2}} \cdot \left(\lvert 0 \rangle + \left(\mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot 2^{-\left(-t + 2\right)} \cdot \varphi} \cdot \lvert 1 \rangle\right)\right)\right), \left(\frac{1}{\sqrt{2}} \cdot \left(\lvert 0 \rangle + \left(\mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot 2^{-\left(-t + 3\right)} \cdot \varphi} \cdot \lvert 1 \rangle\right)\right)\right), \ldots, \left(\frac{1}{\sqrt{2}} \cdot \left(\lvert 0 \rangle + \left(\mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot 2^{-0} \cdot \varphi} \cdot \lvert 1 \rangle\right)\right)\right), \lvert u \rangle\right)|, t + 1\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: 3 operands: 4
2	Operation	operator: 61 operands: 5
3	Literal
4	ExprTuple	6, 7, 8
5	ExprTuple	69, 65
6	Operation	operator: 31 operands: 9
7	ExprRange	lambda_map: 10 start_index: 11 end_index: 35
8	Literal
9	ExprTuple	18, 12
10	Lambda	parameter: 66 body: 13
11	Operation	operator: 61 operands: 14
12	Operation	operator: 22 operands: 15
13	Operation	operator: 31 operands: 16
14	ExprTuple	64, 59
15	ExprTuple	26, 17
16	ExprTuple	18, 19
17	Operation	operator: 31 operands: 20
18	Operation	operator: 39 operands: 21
19	Operation	operator: 22 operands: 23
20	ExprTuple	24, 37
21	ExprTuple	65, 25
22	Literal
23	ExprTuple	26, 27
24	Operation	operator: 56 operands: 28
25	Operation	operator: 56 operands: 29
26	Operation	operator: 42 operand: 35
27	Operation	operator: 31 operands: 32
28	ExprTuple	45, 33
29	ExprTuple	59, 34
30	ExprTuple	35
31	Literal
32	ExprTuple	36, 37
33	Operation	operator: 48 operands: 38
34	Operation	operator: 39 operands: 40
35	Literal
36	Operation	operator: 56 operands: 41
37	Operation	operator: 42 operand: 65
38	ExprTuple	59, 51, 52, 44, 54
39	Literal
40	ExprTuple	65, 59
41	ExprTuple	45, 46
42	Literal
43	ExprTuple	65
44	Operation	operator: 56 operands: 47
45	Literal
46	Operation	operator: 48 operands: 49
47	ExprTuple	59, 50
48	Literal
49	ExprTuple	59, 51, 52, 53, 54
50	Operation	operator: 67 operand: 58
51	Literal
52	Literal
53	Operation	operator: 56 operands: 57
54	Literal
55	ExprTuple	58
56	Literal
57	ExprTuple	59, 60
58	Operation	operator: 61 operands: 62
59	Literal
60	Operation	operator: 67 operand: 66
61	Literal
62	ExprTuple	64, 65
63	ExprTuple	66
64	Operation	operator: 67 operand: 69
65	Literal
66	Variable
67	Literal
68	ExprTuple	69
69	Variable