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 ExprRange, Function, IndexedVar, Q, Variable, c, f, j, m, n
from proveit.linear_algebra import LinMap, VecSum
from proveit.logic import CartExp, InSet
from proveit.numbers import Complex, one
from proveit.physics.quantum import Qmult

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
sub_expr2 = [ExprRange(sub_expr1, IndexedVar(c, sub_expr1), one, j)]
expr = InSet(Qmult(VecSum(index_or_indices = sub_expr2, summand = Function(f, sub_expr2), condition = Function(Q, sub_expr2))), LinMap(CartExp(Complex, m), CartExp(Complex, 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_{c_{1}, c_{2}, \ldots, c_{j}~|~Q\left(c_{1}, c_{2}, \ldots, c_{j}\right)}~f\left(c_{1}, c_{2}, \ldots, c_{j}\right)\right] \in \mathcal{L}\left(\mathbb{C}^{m}, \mathbb{C}^{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: 1 operands: 2
1	Literal
2	ExprTuple	3, 4
3	Operation	operator: 5 operand: 9
4	Operation	operator: 7 operands: 8
5	Literal
6	ExprTuple	9
7	Literal
8	ExprTuple	10, 11
9	Operation	operator: 12 operand: 17
10	Operation	operator: 15 operands: 14
11	Operation	operator: 15 operands: 16
12	Literal
13	ExprTuple	17
14	ExprTuple	19, 18
15	Literal
16	ExprTuple	19, 20
17	Lambda	parameters: 26 body: 21
18	Variable
19	Literal
20	Variable
21	Conditional	value: 22 condition: 23
22	Operation	operator: 24 operands: 26
23	Operation	operator: 25 operands: 26
24	Variable
25	Variable
26	ExprTuple	27
27	ExprRange	lambda_map: 28 start_index: 29 end_index: 30
28	Lambda	parameter: 34 body: 31
29	Literal
30	Variable
31	IndexedVar	variable: 32 index: 34
32	Variable
33	ExprTuple	34
34	Variable