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, Lambda, Variable, t
from proveit.linear_algebra import ScalarMult, VecAdd
from proveit.numbers import Add, Exp, Mult, Neg, e, frac, i, one, pi, sqrt, two
from proveit.physics.quantum import ket0, ket1
from proveit.physics.quantum.QPE import _phase
from proveit.physics.quantum.circuits import Output

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
sub_expr2 = frac(one, sqrt(two))
expr = ExprTuple(Lambda(Variable("_b", latex_format = r"{_{-}b}"), Output(state = ScalarMult(sub_expr2, VecAdd(ket0, ScalarMult(Exp(e, Mult(two, pi, i, Exp(two, Neg(Add(Neg(t), one))), _phase)), ket1))))), Lambda(sub_expr1, Output(state = ScalarMult(sub_expr2, VecAdd(ket0, ScalarMult(Exp(e, Mult(two, pi, i, Exp(two, Neg(sub_expr1)), _phase)), ket1))))))

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({_{-}b} \mapsto \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \qout{\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)} 
} \end{array}, {_{-}a} \mapsto \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \qout{\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)} 
} \end{array}\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	Lambda	parameter: 6 body: 4
2	Lambda	parameter: 61 body: 5
3	ExprTuple	6
4	Operation	operator: 8 operands: 7
5	Operation	operator: 8 operands: 9
6	Variable
7	NamedExprs	state: 10
8	Literal
9	NamedExprs	state: 11
10	Operation	operator: 28 operands: 12
11	Operation	operator: 28 operands: 13
12	ExprTuple	15, 14
13	ExprTuple	15, 16
14	Operation	operator: 19 operands: 17
15	Operation	operator: 36 operands: 18
16	Operation	operator: 19 operands: 20
17	ExprTuple	23, 21
18	ExprTuple	65, 22
19	Literal
20	ExprTuple	23, 24
21	Operation	operator: 28 operands: 25
22	Operation	operator: 53 operands: 26
23	Operation	operator: 39 operand: 32
24	Operation	operator: 28 operands: 29
25	ExprTuple	30, 34
26	ExprTuple	56, 31
27	ExprTuple	32
28	Literal
29	ExprTuple	33, 34
30	Operation	operator: 53 operands: 35
31	Operation	operator: 36 operands: 37
32	Literal
33	Operation	operator: 53 operands: 38
34	Operation	operator: 39 operand: 65
35	ExprTuple	42, 41
36	Literal
37	ExprTuple	65, 56
38	ExprTuple	42, 43
39	Literal
40	ExprTuple	65
41	Operation	operator: 45 operands: 44
42	Literal
43	Operation	operator: 45 operands: 46
44	ExprTuple	56, 48, 49, 47, 51
45	Literal
46	ExprTuple	56, 48, 49, 50, 51
47	Operation	operator: 53 operands: 52
48	Literal
49	Literal
50	Operation	operator: 53 operands: 54
51	Literal
52	ExprTuple	56, 55
53	Literal
54	ExprTuple	56, 57
55	Operation	operator: 66 operand: 60
56	Literal
57	Operation	operator: 66 operand: 61
58	ExprTuple	60
59	ExprTuple	61
60	Operation	operator: 62 operands: 63
61	Variable
62	Literal
63	ExprTuple	64, 65
64	Operation	operator: 66 operand: 68
65	Literal
66	Literal
67	ExprTuple	68
68	Variable