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 ExprRange, IndexedVar, U, Variable, VertExprArray, i, m
from proveit.numbers import Interval, one
from proveit.physics.quantum import var_ket_psi
from proveit.physics.quantum.circuits import MultiQubitElem, Output

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
expr = VertExprArray(ExprRange(sub_expr1, IndexedVar(U, sub_expr1), one, i).with_front_expansion(1), [ExprRange(sub_expr1, MultiQubitElem(element = Output(state = var_ket_psi, part = sub_expr1), targets = Interval(one, m)), one, m)])

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} 
 \multirow{4}{*}{$\begin{array}{c} \uparrow \\ U_{1} \\ \downarrow \end{array}$} & \multirow{4}{*}{$\begin{array}{c} \uparrow \\ \cdots \\ \downarrow \end{array}$} & \multirow{4}{*}{$\begin{array}{c} \uparrow \\ U_{i} \\ \downarrow \end{array}$} & \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \qout{\lvert \psi \rangle~\mbox{part}~1~\mbox{on}~\{1~\ldotp \ldotp~m\}} 
} \end{array} \\
 &  &  & \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \qout{\lvert \psi \rangle~\mbox{part}~2~\mbox{on}~\{1~\ldotp \ldotp~m\}} 
} \end{array} \\
 &  &  & \vdots \\
 &  &  & \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \qout{\lvert \psi \rangle~\mbox{part}~m~\mbox{on}~\{1~\ldotp \ldotp~m\}} 
} \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, 2
1	ExprRange	lambda_map: 3 start_index: 21 end_index: 4
2	ExprTuple	5
3	Lambda	parameter: 20 body: 6
4	Variable
5	ExprRange	lambda_map: 7 start_index: 21 end_index: 22
6	IndexedVar	variable: 8 index: 20
7	Lambda	parameter: 20 body: 10
8	Variable
9	ExprTuple	20
10	Operation	operator: 11 operands: 12
11	Literal
12	NamedExprs	element: 13 targets: 14
13	Operation	operator: 15 operands: 16
14	Operation	operator: 17 operands: 18
15	Literal
16	NamedExprs	state: 19 part: 20
17	Literal
18	ExprTuple	21, 22
19	Variable
20	Variable
21	Literal
22	Variable