Expression of type Lambda

from the theory of proveit.physics.quantum.algebra

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 Conditional, Lambda, U, i, j, n
from proveit.core_expr_types import v_i, v_j
from proveit.linear_algebra import Adj
from proveit.logic import And, Equals, InSet
from proveit.numbers import Interval, KroneckerDelta, one
from proveit.physics.quantum import Bra, Ket, Qmult

# build up the expression from sub-expressions
sub_expr1 = Interval(one, n)
expr = Lambda([i, j], Conditional(Equals(Qmult(Bra(v_i), Adj(U), U, Ket(v_j)), KroneckerDelta(i, j)), And(InSet(i, sub_expr1), InSet(j, sub_expr1))))

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(i, j\right) \mapsto \left\{\left(\langle v_{i} \rvert \thinspace U^{\dagger} \thinspace U \thinspace \lvert v_{j} \rangle\right) = \delta_{i, j} \textrm{ if } i \in \{1~\ldotp \ldotp~n\} ,  j \in \{1~\ldotp \ldotp~n\}\right..

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

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