Expression of type Equals

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, gamma, j
from proveit.linear_algebra import VecSum
from proveit.logic import Equals
from proveit.numbers import one
from proveit.physics.quantum import Qmult, 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)
expr = Equals(Qmult(bra_varphi, alpha, VecSum(index_or_indices = sub_expr2, summand = sub_expr3, condition = sub_expr4), beta, ket_psi, gamma, bra_varphi, delta), VecSum(index_or_indices = sub_expr2, summand = Qmult(bra_varphi, alpha, sub_expr3, beta, ket_psi, gamma, bra_varphi, delta), condition = sub_expr4))

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(\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]

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: 15 operands: 5
4	Operation	operator: 9 operand: 8
5	ExprTuple	23, 18, 7, 20, 21, 22, 23, 24
6	ExprTuple	8
7	Operation	operator: 9 operand: 12
8	Lambda	parameters: 27 body: 11
9	Literal
10	ExprTuple	12
11	Conditional	value: 13 condition: 17
12	Lambda	parameters: 27 body: 14
13	Operation	operator: 15 operands: 16
14	Conditional	value: 19 condition: 17
15	Literal
16	ExprTuple	23, 18, 19, 20, 21, 22, 23, 24
17	Operation	operator: 25 operands: 27
18	Variable
19	Operation	operator: 26 operands: 27
20	Variable
21	Operation	operator: 28 operand: 33
22	Variable
23	Operation	operator: 30 operand: 34
24	Variable
25	Variable
26	Variable
27	ExprTuple	32
28	Literal
29	ExprTuple	33
30	Literal
31	ExprTuple	34
32	ExprRange	lambda_map: 35 start_index: 36 end_index: 37
33	Variable
34	Variable
35	Lambda	parameter: 41 body: 38
36	Literal
37	Variable
38	IndexedVar	variable: 39 index: 41
39	Variable
40	ExprTuple	41
41	Variable