Expression of type ExprTuple

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 ExprTuple, Function, f, i, n
from proveit.core_expr_types import a_i, v_i
from proveit.linear_algebra import ScalarMult, VecSum
from proveit.numbers import Interval, one
from proveit.physics.quantum import Bra, Ket, Qmult

# build up the expression from sub-expressions
sub_expr1 = [i]
sub_expr2 = Interval(one, n)
sub_expr3 = Qmult(Ket(v_i), Bra(v_i))
expr = ExprTuple(Function(f, [VecSum(index_or_indices = sub_expr1, summand = ScalarMult(a_i, sub_expr3), domain = sub_expr2)]), VecSum(index_or_indices = sub_expr1, summand = ScalarMult(Function(f, [a_i]), sub_expr3), domain = sub_expr2))

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(f\left(\sum_{i=1}^{n} \left(a_{i} \cdot \left(\lvert v_{i} \rangle \thinspace \langle v_{i} \rvert\right)\right)\right), \sum_{i=1}^{n} \left(f\left(a_{i}\right) \cdot \left(\lvert v_{i} \rangle \thinspace \langle v_{i} \rvert\right)\right)\right)

stored_expr.style_options()

name	description	default	current value	related methods
wrap_positions	position(s) at which wrapping is to occur; 'n' is after the nth comma.	()	()	('with_wrapping_at',)
justification	if any wrap positions are set, justify to the 'left', 'center', or 'right'	left	left	('with_justification',)

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	ExprTuple	1, 2
1	Operation	operator: 21 operand: 5
2	Operation	operator: 7 operand: 6
3	ExprTuple	5
4	ExprTuple	6
5	Operation	operator: 7 operand: 10
6	Lambda	parameter: 41 body: 9
7	Literal
8	ExprTuple	10
9	Conditional	value: 11 condition: 15
10	Lambda	parameter: 41 body: 12
11	Operation	operator: 17 operands: 13
12	Conditional	value: 14 condition: 15
13	ExprTuple	16, 23
14	Operation	operator: 17 operands: 18
15	Operation	operator: 19 operands: 20
16	Operation	operator: 21 operand: 25
17	Literal
18	ExprTuple	25, 23
19	Literal
20	ExprTuple	41, 24
21	Variable
22	ExprTuple	25
23	Operation	operator: 26 operands: 27
24	Operation	operator: 28 operands: 29
25	IndexedVar	variable: 30 index: 41
26	Literal
27	ExprTuple	31, 32
28	Literal
29	ExprTuple	33, 34
30	Variable
31	Operation	operator: 35 operand: 38
32	Operation	operator: 36 operand: 38
33	Literal
34	Variable
35	Literal
36	Literal
37	ExprTuple	38
38	IndexedVar	variable: 39 index: 41
39	Variable
40	ExprTuple	41
41	Variable