Expression of type InSet

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 i, n
from proveit.core_expr_types import v_i, w_i
from proveit.linear_algebra import Unitary, VecSum
from proveit.logic import InSet
from proveit.numbers import Interval, one
from proveit.physics.quantum import Bra, Ket, Qmult

# build up the expression from sub-expressions
expr = InSet(VecSum(index_or_indices = [i], summand = Qmult(Ket(v_i), Bra(w_i)), domain = Interval(one, n)), Unitary(n))

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(\sum_{i=1}^{n} \left(\lvert v_{i} \rangle \thinspace \langle w_{i} \rvert\right)\right) \in \textrm{U}\left(n\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',)
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: 14 operands: 1
1	ExprTuple	2, 3
2	Operation	operator: 4 operand: 8
3	Operation	operator: 6 operand: 28
4	Literal
5	ExprTuple	8
6	Literal
7	ExprTuple	28
8	Lambda	parameter: 32 body: 9
9	Conditional	value: 10 condition: 11
10	Operation	operator: 12 operands: 13
11	Operation	operator: 14 operands: 15
12	Literal
13	ExprTuple	16, 17
14	Literal
15	ExprTuple	32, 18
16	Operation	operator: 19 operand: 25
17	Operation	operator: 21 operand: 26
18	Operation	operator: 23 operands: 24
19	Literal
20	ExprTuple	25
21	Literal
22	ExprTuple	26
23	Literal
24	ExprTuple	27, 28
25	IndexedVar	variable: 29 index: 32
26	IndexedVar	variable: 30 index: 32
27	Literal
28	Variable
29	Variable
30	Variable
31	ExprTuple	32
32	Variable