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 Conditional, ConditionalSet, ExprRange, ExprTuple, U, Variable, s, t
from proveit.linear_algebra import MatrixExp
from proveit.logic import Equals, NotEquals, Set
from proveit.numbers import Add, Exp, Interval, Neg, one, two
from proveit.physics.quantum import CONTROL, I
from proveit.physics.quantum.circuits import Gate, MultiQubitElem

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
sub_expr2 = Variable("_b", latex_format = r"{_{-}b}")
sub_expr3 = Add(t, one)
sub_expr4 = Add(sub_expr2, t)
expr = ExprTuple(ExprRange(sub_expr1, ConditionalSet(Conditional(MultiQubitElem(element = CONTROL, targets = Set(sub_expr3)), Equals(sub_expr4, sub_expr1)), Conditional(Gate(operation = I).with_implicit_representation(), NotEquals(sub_expr4, sub_expr1))), one, t).with_case_simplification(), ExprRange(sub_expr1, MultiQubitElem(element = Gate(operation = MatrixExp(U, Exp(two, Neg(sub_expr2))), part = sub_expr1), targets = Interval(sub_expr3, Add(t, s))), one, s))

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\{\begin{array}{ccc}\begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \gate{CONTROL~\mbox{on}~\left\{t + 1\right\}} & \qw 
} \end{array} \textrm{ if } \left({_{-}b} + t\right) = 1 \\ \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \qw & \qw 
} \end{array} \textrm{ if } \left({_{-}b} + t\right) \neq 1\end{array}\right.., \left\{\begin{array}{ccc}\begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \gate{CONTROL~\mbox{on}~\left\{t + 1\right\}} & \qw 
} \end{array} \textrm{ if } \left({_{-}b} + t\right) = 2 \\ \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \qw & \qw 
} \end{array} \textrm{ if } \left({_{-}b} + t\right) \neq 2\end{array}\right.., \ldots, \left\{\begin{array}{ccc}\begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \gate{CONTROL~\mbox{on}~\left\{t + 1\right\}} & \qw 
} \end{array} \textrm{ if } \left({_{-}b} + t\right) = t \\ \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \qw & \qw 
} \end{array} \textrm{ if } \left({_{-}b} + t\right) \neq t\end{array}\right..,\begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \gate{U^{2^{-{_{-}b}}}~\mbox{part}~1~\mbox{on}~\{t + 1~\ldotp \ldotp~t + s\}} & \qw 
} \end{array}, \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \gate{U^{2^{-{_{-}b}}}~\mbox{part}~2~\mbox{on}~\{t + 1~\ldotp \ldotp~t + s\}} & \qw 
} \end{array}, \ldots, \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \gate{U^{2^{-{_{-}b}}}~\mbox{part}~s~\mbox{on}~\{t + 1~\ldotp \ldotp~t + s\}} & \qw 
} \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	ExprRange	lambda_map: 3 start_index: 53 end_index: 52
2	ExprRange	lambda_map: 4 start_index: 53 end_index: 44
3	Lambda	parameter: 35 body: 5
4	Lambda	parameter: 35 body: 7
5	Operation	operator: 8 operands: 9
6	ExprTuple	35
7	Operation	operator: 22 operands: 10
8	Literal
9	ExprTuple	11, 12
10	NamedExprs	element: 13 targets: 14
11	Conditional	value: 15 condition: 16
12	Conditional	value: 17 condition: 18
13	Operation	operator: 25 operands: 19
14	Operation	operator: 20 operands: 21
15	Operation	operator: 22 operands: 23
16	Operation	operator: 24 operands: 28
17	Operation	operator: 25 operands: 26
18	Operation	operator: 27 operands: 28
19	NamedExprs	operation: 29 part: 35
20	Literal
21	ExprTuple	45, 30
22	Literal
23	NamedExprs	element: 31 targets: 32
24	Literal
25	Literal
26	NamedExprs	operation: 33
27	Literal
28	ExprTuple	34, 35
29	Operation	operator: 36 operands: 37
30	Operation	operator: 48 operands: 38
31	Literal
32	Operation	operator: 39 operand: 45
33	Literal
34	Operation	operator: 48 operands: 41
35	Variable
36	Literal
37	ExprTuple	42, 43
38	ExprTuple	52, 44
39	Literal
40	ExprTuple	45
41	ExprTuple	56, 52
42	Variable
43	Operation	operator: 46 operands: 47
44	Variable
45	Operation	operator: 48 operands: 49
46	Literal
47	ExprTuple	50, 51
48	Literal
49	ExprTuple	52, 53
50	Literal
51	Operation	operator: 54 operand: 56
52	Variable
53	Literal
54	Literal
55	ExprTuple	56
56	Variable