Expression of type Lambda

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 Conditional, ExprRange, IndexedVar, Lambda, M, Variable, a, i, n
from proveit.core_expr_types import a_1_to_n, a_i, v_i
from proveit.linear_algebra import ScalarMult, VecSum
from proveit.logic import And, Equals, InSet
from proveit.numbers import Complex, Interval, one
from proveit.physics.quantum import Bra, Ket, Qmult

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
expr = Lambda([a_1_to_n], Conditional(Equals(M, VecSum(index_or_indices = [i], summand = ScalarMult(a_i, Qmult(Ket(v_i), Bra(v_i))), domain = Interval(one, n))), And(ExprRange(sub_expr1, InSet(IndexedVar(a, sub_expr1), Complex), one, 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(a_{1}, a_{2}, \ldots, a_{n}\right) \mapsto \left\{M = \left(\sum_{i=1}^{n} \left(a_{i} \cdot \left(\lvert v_{i} \rangle \thinspace \langle v_{i} \rvert\right)\right)\right) \textrm{ if } \left(a_{1} \in \mathbb{C}\right) \land  \left(a_{2} \in \mathbb{C}\right) \land  \ldots \land  \left(a_{n} \in \mathbb{C}\right)\right..

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Lambda	parameters: 1 body: 2
1	ExprTuple	3
2	Conditional	value: 4 condition: 5
3	ExprRange	lambda_map: 6 start_index: 41 end_index: 42
4	Operation	operator: 7 operands: 8
5	Operation	operator: 9 operands: 10
6	Lambda	parameter: 33 body: 23
7	Literal
8	ExprTuple	11, 12
9	Literal
10	ExprTuple	13
11	Variable
12	Operation	operator: 14 operand: 17
13	ExprRange	lambda_map: 16 start_index: 41 end_index: 42
14	Literal
15	ExprTuple	17
16	Lambda	parameter: 33 body: 18
17	Lambda	parameter: 49 body: 19
18	Operation	operator: 27 operands: 20
19	Conditional	value: 21 condition: 22
20	ExprTuple	23, 24
21	Operation	operator: 25 operands: 26
22	Operation	operator: 27 operands: 28
23	IndexedVar	variable: 34 index: 33
24	Literal
25	Literal
26	ExprTuple	30, 31
27	Literal
28	ExprTuple	49, 32
29	ExprTuple	33
30	IndexedVar	variable: 34 index: 49
31	Operation	operator: 35 operands: 36
32	Operation	operator: 37 operands: 38
33	Variable
34	Variable
35	Literal
36	ExprTuple	39, 40
37	Literal
38	ExprTuple	41, 42
39	Operation	operator: 43 operand: 46
40	Operation	operator: 44 operand: 46
41	Literal
42	Variable
43	Literal
44	Literal
45	ExprTuple	46
46	IndexedVar	variable: 47 index: 49
47	Variable
48	ExprTuple	49
49	Variable