Expression of type ScalarMult

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 ScalarMult, VecSum
from proveit.numbers import Mult, 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 = ScalarMult(Mult(alpha, beta, gamma, delta), Qmult(bra_varphi, VecSum(index_or_indices = sub_expr2, summand = Function(f, sub_expr2), condition = Function(Q, sub_expr2)), ket_psi, 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(\alpha \cdot \beta \cdot \gamma \cdot \delta\right) \cdot \left(\langle \varphi \rvert \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 \lvert \psi \rangle \thinspace \langle \varphi \rvert\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',)

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