Expression of type VertExprArray

from the theory of proveit.physics.quantum.circuits

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 B, ExprRange, Function, IndexedVar, S, Variable, VertExprArray, k, n, p
from proveit.logic import InvImage
from proveit.numbers import one
from proveit.physics.quantum.circuits import MultiQubitElem

# 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 = [Function(p, [sub_expr1]), sub_expr2]
expr = VertExprArray(ExprRange(sub_expr1, [ExprRange(sub_expr2, MultiQubitElem(element = IndexedVar(B, sub_expr3), targets = Function(InvImage(p), [IndexedVar(S, sub_expr3)])), one, k)], one, n))

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())

\begin{array}{cccc} 
 \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \gate{B_{p\left(1\right), 1}~\mbox{on}~p^{\leftarrow}\left(S_{p\left(1\right), 1}\right)} & \qw 
} \end{array} & \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \gate{B_{p\left(2\right), 1}~\mbox{on}~p^{\leftarrow}\left(S_{p\left(2\right), 1}\right)} & \qw 
} \end{array} & \cdots & \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \gate{B_{p\left(n\right), 1}~\mbox{on}~p^{\leftarrow}\left(S_{p\left(n\right), 1}\right)} & \qw 
} \end{array} \\
\begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \gate{B_{p\left(1\right), 2}~\mbox{on}~p^{\leftarrow}\left(S_{p\left(1\right), 2}\right)} & \qw 
} \end{array} & \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \gate{B_{p\left(2\right), 2}~\mbox{on}~p^{\leftarrow}\left(S_{p\left(2\right), 2}\right)} & \qw 
} \end{array} & \cdots & \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \gate{B_{p\left(n\right), 2}~\mbox{on}~p^{\leftarrow}\left(S_{p\left(n\right), 2}\right)} & \qw 
} \end{array} \\
\vdots & \vdots & \ddots & \vdots \\
\begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \gate{B_{p\left(1\right), k}~\mbox{on}~p^{\leftarrow}\left(S_{p\left(1\right), k}\right)} & \qw 
} \end{array} & \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \gate{B_{p\left(2\right), k}~\mbox{on}~p^{\leftarrow}\left(S_{p\left(2\right), k}\right)} & \qw 
} \end{array} & \cdots & \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \gate{B_{p\left(n\right), k}~\mbox{on}~p^{\leftarrow}\left(S_{p\left(n\right), k}\right)} & \qw 
} \end{array} \\
\end{array}

stored_expr.style_options()

name	description	default	current value	related methods
justification	justify to the 'left', 'center', or 'right' in the array cells	center	center	with_justification

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	ExprTuple	1
1	ExprRange	lambda_map: 2 start_index: 7 end_index: 3
2	Lambda	parameter: 27 body: 4
3	Variable
4	ExprTuple	5
5	ExprRange	lambda_map: 6 start_index: 7 end_index: 8
6	Lambda	parameter: 24 body: 10
7	Literal
8	Variable
9	ExprTuple	24
10	Operation	operator: 11 operands: 12
11	Literal
12	NamedExprs	element: 13 targets: 14
13	IndexedVar	variable: 15 indices: 22
14	Operation	operator: 16 operand: 20
15	Variable
16	Operation	operator: 18 operand: 25
17	ExprTuple	20
18	Literal
19	ExprTuple	25
20	IndexedVar	variable: 21 indices: 22
21	Variable
22	ExprTuple	23, 24
23	Operation	operator: 25 operand: 27
24	Variable
25	Variable
26	ExprTuple	27
27	Variable