Expression of type Lambda

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, Lambda, N, Variable
from proveit.core_expr_types import A_1_to_m
from proveit.linear_algebra import TensorProd
from proveit.numbers import Add, Interval, one, subtract
from proveit.physics.quantum.circuits import Input, MultiQubitElem, N_m

# build up the expression from sub-expressions
sub_expr1 = Variable("_c", latex_format = r"{_{-}c}")
sub_expr2 = Variable("_b", latex_format = r"{_{-}b}")
expr = Lambda(sub_expr1, ExprRange(sub_expr2, MultiQubitElem(element = Input(state = TensorProd(A_1_to_m), part = sub_expr2), targets = Interval(one, N_m)), Add(IndexedVar(N, subtract(sub_expr1, one)), one), IndexedVar(N, sub_expr1)).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())

{_{-}c} \mapsto \begin{array}{l} \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& \qin{A_{1} {\otimes}  A_{2} {\otimes}  \ldots {\otimes}  A_{m}~\mbox{part}~N_{{_{-}c} - 1} + 1~\mbox{on}~\{1~\ldotp \ldotp~N_{m}\}} & \qw 
} \end{array},  \\ \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& \qin{A_{1} {\otimes}  A_{2} {\otimes}  \ldots {\otimes}  A_{m}~\mbox{part}~N_{{_{-}c} - 1} + 2~\mbox{on}~\{1~\ldotp \ldotp~N_{m}\}} & \qw 
} \end{array}, \ldots,  \\ \begin{array}{c} \Qcircuit@C=1em @R=.7em{
& \qin{A_{1} {\otimes}  A_{2} {\otimes}  \ldots {\otimes}  A_{m}~\mbox{part}~N_{{_{-}c}}~\mbox{on}~\{1~\ldotp \ldotp~N_{m}\}} & \qw 
} \end{array} \end{array}

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Lambda	parameter: 29 body: 1
1	ExprRange	lambda_map: 2 start_index: 3 end_index: 4
2	Lambda	parameter: 21 body: 6
3	Operation	operator: 23 operands: 7
4	IndexedVar	variable: 27 index: 29
5	ExprTuple	21
6	Operation	operator: 9 operands: 10
7	ExprTuple	11, 36
8	ExprTuple	29
9	Literal
10	NamedExprs	element: 12 targets: 13
11	IndexedVar	variable: 27 index: 19
12	Operation	operator: 15 operands: 16
13	Operation	operator: 17 operands: 18
14	ExprTuple	19
15	Literal
16	NamedExprs	state: 20 part: 21
17	Literal
18	ExprTuple	36, 22
19	Operation	operator: 23 operands: 24
20	Operation	operator: 25 operands: 26
21	Variable
22	IndexedVar	variable: 27 index: 35
23	Literal
24	ExprTuple	29, 30
25	Literal
26	ExprTuple	31
27	Variable
28	ExprTuple	35
29	Variable
30	Operation	operator: 32 operand: 36
31	ExprRange	lambda_map: 34 start_index: 36 end_index: 35
32	Literal
33	ExprTuple	36
34	Lambda	parameter: 40 body: 37
35	Variable
36	Literal
37	IndexedVar	variable: 38 index: 40
38	Variable
39	ExprTuple	40
40	Variable