Expression of type Len

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
from proveit.core_expr_types import Len
from proveit.linear_algebra import TensorProd
from proveit.numbers import Add, Interval, one
from proveit.physics.quantum.QPE import _ket_u, _psi__t_ket, _s, _t
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 = MultiQubitElem(element = Output(state = TensorProd(_psi__t_ket, _ket_u), part = sub_expr1), targets = Interval(one, sub_expr2))
expr = Len(operands = [ExprRange(sub_expr1, sub_expr3, one, _t).with_wrapping_at(2,6), ExprRange(sub_expr1, sub_expr3, 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())

|\left(\begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \qout{\lvert \psi_{t} \rangle {\otimes} \lvert u \rangle~\mbox{part}~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}~2~\mbox{on}~\{1~\ldotp \ldotp~t + s\}} 
} \end{array}, \ldots, \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& & \qout{\lvert \psi_{t} \rangle {\otimes} \lvert u \rangle~\mbox{part}~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}, \ldots, \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}\right)|

stored_expr.style_options()

name	description	default	current value	related methods
operation	'infix' or 'function' style formatting	infix	infix
wrap_positions	position(s) at which wrapping is to occur; '2 n - 1' is after the nth operand, '2 n' is after the nth operation.	()	()	('with_wrapping_at', 'with_wrap_before_operator', 'with_wrap_after_operator', 'without_wrapping', 'wrap_positions')
justification	if any wrap positions are set, justify to the 'left', 'center', or 'right'	center	center	('with_justification',)

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Operation	operator: 1 operands: 2
1	Literal
2	ExprTuple	3, 4
3	ExprRange	lambda_map: 5 start_index: 20 end_index: 31
4	ExprRange	lambda_map: 5 start_index: 6 end_index: 21
5	Lambda	parameter: 19 body: 8
6	Operation	operator: 24 operands: 9
7	ExprTuple	19
8	Operation	operator: 10 operands: 11
9	ExprTuple	31, 20
10	Literal
11	NamedExprs	element: 12 targets: 13
12	Operation	operator: 14 operands: 15
13	Operation	operator: 16 operands: 17
14	Literal
15	NamedExprs	state: 18 part: 19
16	Literal
17	ExprTuple	20, 21
18	Operation	operator: 22 operands: 23
19	Variable
20	Literal
21	Operation	operator: 24 operands: 25
22	Literal
23	ExprTuple	26, 27
24	Literal
25	ExprTuple	31, 28
26	Operation	operator: 29 operand: 31
27	Literal
28	Literal
29	Literal
30	ExprTuple	31
31	Literal