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 ExprRange, ExprTuple, Function, IndexedVar, Q, Variable, alpha, beta, c, delta, f, gamma, j
from proveit.linear_algebra import VecSum
from proveit.logic import Equals, InClass
from proveit.numbers import one
from proveit.physics.quantum import Qmult, QmultCodomain, bra_varphi, ket_psi

# 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)]
sub_expr3 = Function(f, sub_expr2)
sub_expr4 = Function(Q, sub_expr2)
sub_expr5 = Qmult(bra_varphi, alpha, VecSum(index_or_indices = sub_expr2, summand = sub_expr3, condition = sub_expr4), beta, ket_psi, gamma, bra_varphi, delta)
expr = ExprTuple(InClass(sub_expr5, QmultCodomain), Equals(sub_expr5, VecSum(index_or_indices = sub_expr2, summand = Qmult(bra_varphi, alpha, sub_expr3, beta, ket_psi, gamma, bra_varphi, delta), condition = sub_expr4)).with_wrapping_at(1))

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(\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] \thinspace \beta \thinspace \lvert \psi \rangle \thinspace \gamma \thinspace \langle \varphi \rvert \thinspace \delta\right) \underset{{\scriptscriptstyle c}}{\in} \mathcal{Q^*}, \begin{array}{c} \begin{array}{l} \left(\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] \thinspace \beta \thinspace \lvert \psi \rangle \thinspace \gamma \thinspace \langle \varphi \rvert \thinspace \delta\right) \\  = \left[\sum_{c_{1}, c_{2}, \ldots, c_{j}~|~Q\left(c_{1}, c_{2}, \ldots, c_{j}\right)}~\left(\langle \varphi \rvert \thinspace \alpha \thinspace f\left(c_{1}, c_{2}, \ldots, c_{j}\right) \thinspace \beta \thinspace \lvert \psi \rangle \thinspace \gamma \thinspace \langle \varphi \rvert \thinspace \delta\right)\right] \end{array} \end{array}\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: 3 operands: 4
2	Operation	operator: 5 operands: 6
3	Literal
4	ExprTuple	8, 7
5	Literal
6	ExprTuple	8, 9
7	Literal
8	Operation	operator: 20 operands: 10
9	Operation	operator: 14 operand: 13
10	ExprTuple	28, 23, 12, 25, 26, 27, 28, 29
11	ExprTuple	13
12	Operation	operator: 14 operand: 17
13	Lambda	parameters: 32 body: 16
14	Literal
15	ExprTuple	17
16	Conditional	value: 18 condition: 22
17	Lambda	parameters: 32 body: 19
18	Operation	operator: 20 operands: 21
19	Conditional	value: 24 condition: 22
20	Literal
21	ExprTuple	28, 23, 24, 25, 26, 27, 28, 29
22	Operation	operator: 30 operands: 32
23	Variable
24	Operation	operator: 31 operands: 32
25	Variable
26	Operation	operator: 33 operand: 38
27	Variable
28	Operation	operator: 35 operand: 39
29	Variable
30	Variable
31	Variable
32	ExprTuple	37
33	Literal
34	ExprTuple	38
35	Literal
36	ExprTuple	39
37	ExprRange	lambda_map: 40 start_index: 41 end_index: 42
38	Variable
39	Variable
40	Lambda	parameter: 46 body: 43
41	Literal
42	Variable
43	IndexedVar	variable: 44 index: 46
44	Variable
45	ExprTuple	46
46	Variable