Expression of type Equals

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 U, i, j
from proveit.core_expr_types import v_i, v_j
from proveit.linear_algebra import Adj
from proveit.logic import Equals
from proveit.numbers import KroneckerDelta
from proveit.physics.quantum import Bra, Ket, Qmult

# build up the expression from sub-expressions
expr = Equals(Qmult(Bra(v_i), Adj(U), U, Ket(v_j)), KroneckerDelta(i, j))

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(\langle v_{i} \rvert \thinspace U^{\dagger} \thinspace U \thinspace \lvert v_{j} \rangle\right) = \delta_{i, j}

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',)
direction	Direction of the relation (normal or reversed)	normal	normal	('with_direction_reversed', 'is_reversed')

# 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	Operation	operator: 5 operands: 6
4	Operation	operator: 7 operands: 8
5	Literal
6	ExprTuple	9, 10, 19, 11
7	Literal
8	ExprTuple	24, 25
9	Operation	operator: 12 operand: 18
10	Operation	operator: 14 operand: 19
11	Operation	operator: 16 operand: 20
12	Literal
13	ExprTuple	18
14	Literal
15	ExprTuple	19
16	Literal
17	ExprTuple	20
18	IndexedVar	variable: 22 index: 24
19	Variable
20	IndexedVar	variable: 22 index: 25
21	ExprTuple	24
22	Variable
23	ExprTuple	25
24	Variable
25	Variable