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, Lambda, 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, three, two
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("_b", latex_format = r"{_{-}b}")
sub_expr2 = Variable("_a", latex_format = r"{_{-}a}")
sub_expr3 = frac(one, sqrt(two))
expr = ExprTuple(Len(operands = [Lambda(sub_expr1, ScalarMult(sub_expr3, VecAdd(ket0, ScalarMult(Exp(e, Mult(two, pi, i, Exp(two, Neg(Add(Neg(t), one))), _phase)), ket1)))), Lambda(sub_expr2, ScalarMult(sub_expr3, VecAdd(ket0, ScalarMult(Exp(e, Mult(two, pi, i, Exp(two, Neg(sub_expr2)), _phase)), ket1)))), Lambda(sub_expr1, _ket_u)]), Len(operands = [ExprRange(sub_expr2, sub_expr2, one, three)]))

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({_{-}b} \mapsto \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)\right), {_{-}a} \mapsto \left(\frac{1}{\sqrt{2}} \cdot \left(\lvert 0 \rangle + \left(\mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot 2^{-{_{-}a}} \cdot \varphi} \cdot \lvert 1 \rangle\right)\right)\right), {_{-}b} \mapsto \lvert u \rangle\right)|, |\left(1, 2, \ldots, 3\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	6, 7, 8
4	Literal
5	ExprTuple	9
6	Lambda	parameter: 18 body: 10
7	Lambda	parameter: 66 body: 11
8	Lambda	parameter: 18 body: 13
9	ExprRange	lambda_map: 14 start_index: 70 end_index: 15
10	Operation	operator: 33 operands: 16
11	Operation	operator: 33 operands: 17
12	ExprTuple	18
13	Literal
14	Lambda	parameter: 66 body: 66
15	Literal
16	ExprTuple	20, 19
17	ExprTuple	20, 21
18	Variable
19	Operation	operator: 24 operands: 22
20	Operation	operator: 41 operands: 23
21	Operation	operator: 24 operands: 25
22	ExprTuple	28, 26
23	ExprTuple	70, 27
24	Literal
25	ExprTuple	28, 29
26	Operation	operator: 33 operands: 30
27	Operation	operator: 58 operands: 31
28	Operation	operator: 44 operand: 37
29	Operation	operator: 33 operands: 34
30	ExprTuple	35, 39
31	ExprTuple	61, 36
32	ExprTuple	37
33	Literal
34	ExprTuple	38, 39
35	Operation	operator: 58 operands: 40
36	Operation	operator: 41 operands: 42
37	Literal
38	Operation	operator: 58 operands: 43
39	Operation	operator: 44 operand: 70
40	ExprTuple	47, 46
41	Literal
42	ExprTuple	70, 61
43	ExprTuple	47, 48
44	Literal
45	ExprTuple	70
46	Operation	operator: 50 operands: 49
47	Literal
48	Operation	operator: 50 operands: 51
49	ExprTuple	61, 53, 54, 52, 56
50	Literal
51	ExprTuple	61, 53, 54, 55, 56
52	Operation	operator: 58 operands: 57
53	Literal
54	Literal
55	Operation	operator: 58 operands: 59
56	Literal
57	ExprTuple	61, 60
58	Literal
59	ExprTuple	61, 62
60	Operation	operator: 71 operand: 65
61	Literal
62	Operation	operator: 71 operand: 66
63	ExprTuple	65
64	ExprTuple	66
65	Operation	operator: 67 operands: 68
66	Variable
67	Literal
68	ExprTuple	69, 70
69	Operation	operator: 71 operand: 73
70	Literal
71	Literal
72	ExprTuple	73
73	Variable