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, alpha, beta, c, delta, f, j, m
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, bra_varphi

# 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(Qmult(delta, bra_varphi, alpha, VecSum(index_or_indices = sub_expr2, summand = Function(f, sub_expr2), condition = Function(Q, sub_expr2))), beta), LinMap(CartExp(Complex, m), Complex))

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(\left(\delta \thinspace \langle \varphi \rvert \thinspace \alpha \thinspace \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]\right) \thinspace \beta\right) \in \mathcal{L}\left(\mathbb{C}^{m}, \mathbb{C}\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: 11 operands: 5
4	Operation	operator: 6 operands: 7
5	ExprTuple	8, 9
6	Literal
7	ExprTuple	10, 19
8	Operation	operator: 11 operands: 12
9	Variable
10	Operation	operator: 13 operands: 14
11	Literal
12	ExprTuple	15, 16, 17, 18
13	Literal
14	ExprTuple	19, 20
15	Variable
16	Operation	operator: 21 operand: 25
17	Variable
18	Operation	operator: 23 operand: 26
19	Literal
20	Variable
21	Literal
22	ExprTuple	25
23	Literal
24	ExprTuple	26
25	Variable
26	Lambda	parameters: 32 body: 27
27	Conditional	value: 28 condition: 29
28	Operation	operator: 30 operands: 32
29	Operation	operator: 31 operands: 32
30	Variable
31	Variable
32	ExprTuple	33
33	ExprRange	lambda_map: 34 start_index: 35 end_index: 36
34	Lambda	parameter: 40 body: 37
35	Literal
36	Variable
37	IndexedVar	variable: 38 index: 40
38	Variable
39	ExprTuple	40
40	Variable