Expression of type Qmult

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, f, gamma, j
from proveit.linear_algebra import VecSum
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)]
expr = Qmult(Qmult(bra_varphi, alpha, VecSum(index_or_indices = sub_expr2, summand = Function(f, sub_expr2), condition = Function(Q, sub_expr2)), beta, ket_psi, gamma), bra_varphi)

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\right) \thinspace \langle \varphi \rvert

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',)

# display the expression information
stored_expr.expr_info()

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