Expression of type VertExprArray

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, Variable, VertExprArray, t
from proveit.linear_algebra import TensorProd
from proveit.numbers import Add, Interval, Neg, one, zero
from proveit.physics.quantum.QPE import _ket_u, _psi_t_ket, _s
from proveit.physics.quantum.circuits import MultiQubitElem, Output

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
sub_expr2 = Add(t, _s)
sub_expr3 = TensorProd(_psi_t_ket, _ket_u)
sub_expr4 = Interval(one, sub_expr2)
expr = VertExprArray([ExprRange(sub_expr1, MultiQubitElem(element = Output(state = sub_expr3, part = Add(sub_expr1, t)), targets = sub_expr4), Add(Neg(t), one), zero), ExprRange(sub_expr1, MultiQubitElem(element = Output(state = sub_expr3, part = sub_expr1), targets = sub_expr4), Add(t, one), sub_expr2).with_wrapping_at(2,6)])

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}{c} 
 \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \qout{\lvert \psi_{t} \rangle {\otimes} \lvert u \rangle~\mbox{part}~\left(-t + 1\right) + t~\mbox{on}~\{1~\ldotp \ldotp~t + s\}} 
} \end{array} \\
\begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \qout{\lvert \psi_{t} \rangle {\otimes} \lvert u \rangle~\mbox{part}~\left(-t + 2\right) + t~\mbox{on}~\{1~\ldotp \ldotp~t + s\}} 
} \end{array} \\
\vdots \\
\begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \qout{\lvert \psi_{t} \rangle {\otimes} \lvert u \rangle~\mbox{part}~0 + t~\mbox{on}~\{1~\ldotp \ldotp~t + s\}} 
} \end{array} \\
\begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \qout{\lvert \psi_{t} \rangle {\otimes} \lvert u \rangle~\mbox{part}~t + 1~\mbox{on}~\{1~\ldotp \ldotp~t + s\}} 
} \end{array} \\
\begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \qout{\lvert \psi_{t} \rangle {\otimes} \lvert u \rangle~\mbox{part}~t + 2~\mbox{on}~\{1~\ldotp \ldotp~t + s\}} 
} \end{array} \\
\vdots \\
\begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \qout{\lvert \psi_{t} \rangle {\otimes} \lvert u \rangle~\mbox{part}~t + s~\mbox{on}~\{1~\ldotp \ldotp~t + s\}} 
} \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	ExprTuple	2, 3
2	ExprRange	lambda_map: 4 start_index: 5 end_index: 6
3	ExprRange	lambda_map: 7 start_index: 8 end_index: 30
4	Lambda	parameter: 36 body: 9
5	Operation	operator: 34 operands: 10
6	Literal
7	Lambda	parameter: 36 body: 12
8	Operation	operator: 34 operands: 13
9	Operation	operator: 16 operands: 14
10	ExprTuple	15, 29
11	ExprTuple	36
12	Operation	operator: 16 operands: 17
13	ExprTuple	42, 29
14	NamedExprs	element: 18 targets: 21
15	Operation	operator: 19 operand: 42
16	Literal
17	NamedExprs	element: 20 targets: 21
18	Operation	operator: 23 operands: 22
19	Literal
20	Operation	operator: 23 operands: 24
21	Operation	operator: 25 operands: 26
22	NamedExprs	state: 28 part: 27
23	Literal
24	NamedExprs	state: 28 part: 36
25	Literal
26	ExprTuple	29, 30
27	Operation	operator: 34 operands: 31
28	Operation	operator: 32 operands: 33
29	Literal
30	Operation	operator: 34 operands: 35
31	ExprTuple	36, 42
32	Literal
33	ExprTuple	37, 38
34	Literal
35	ExprTuple	42, 39
36	Variable
37	Operation	operator: 40 operand: 42
38	Literal
39	Literal
40	Literal
41	ExprTuple	42
42	Variable